Universilibros
Mi Carro ( libros)
Total: 0

Hay en tu carro

Carro Vacío

Geometría

    Libros del Tema

    Introducción a la geometría | Autor: Carlos Javier Rojas Álvarez

    Isbn: 978-958-741-683-1 | Año: 2016 | Páginas: 222
    TableProducts Object
    (
        [virtuemart_product_id] => 3702
        [virtuemart_vendor_id] => 1
        [product_parent_id] => 0
        [product_sku] => 3736
        [product_gtin] => 978-958-741-683-1
        [product_mpn] => 9789587415919
        [product_name] => Introducción a la geometría
        [slug] => introduccion-a-la-geometria
        [product_s_desc] => 
        [product_desc] => 

    Este texto está dirigido a estudiantes de arquitectura y diseño industrial o alumnos de secundaria que deseen complementar sus conocimientos sobre geometría elemental. Su propósito es aplicar la geometría a las dimensiones de objetos de la vida cotidiana, mediante la revisión de conceptos como semejanza, perímetro, área y volumen y funciones. Además, contiene una unidad para iniciar al alumno en el estudio de la suma de vectores con el método del triángulo, y con el principio de equilibrio de una partícula.

    [product_weight] => 0.3500 [product_weight_uom] => KG [product_length] => 24.0000 [product_width] => 16.0000 [product_height] => 0.0000 [product_lwh_uom] => CM [product_url] => [product_in_stock] => 7 [product_ordered] => 0 [product_stockhandle] => 0 [low_stock_notification] => 0 [product_available_date] => 2019-02-13 15:10:29 [product_availability] => [product_special] => 0 [product_discontinued] => 0 [pordering] => 0 [product_sales] => 0 [product_unit] => KG [product_packaging] => 0 [product_params] => [intnotes] => [customtitle] => Libro: Introducción a la geometría | Autor: Carlos Javier Rojas Álvarez | Isbn: 9789587416831 [metadesc] =>

    Este texto está dirigido a estudiantes de arquitectura y diseño industrial o alumnos de secundaria que deseen complementar sus conocimientos sobre geometría elemental. Su propósito es aplicar la geometría a las dimensiones de objetos de la vida cotidiana, mediante la revisión de conceptos como semejanza, perímetro, área y volumen y funciones. Además, contiene una unidad para...

    [metakey] => Editorial Universidad del Norte, Geometría, Carlos Javier Rojas Álvarez, 978-958-741-683-1, 9789587415919 [metarobot] => [metaauthor] => Universilibros - Una institución al servicio de la cultura nacional [layout] => 0 [published] => 1 [product_canon_category_id] => [_lhash:VmTable:private] => aed38cd390be9b7647ac2d608365e6ab [_tbl:protected] => #__virtuemart_products [_tbl_lang:protected] => #__virtuemart_products_es_es [_tbl_key:protected] => virtuemart_product_id [_tbl_keys:protected] => Array ( [0] => virtuemart_product_id ) [_pkey:protected] => virtuemart_product_id [_pkeyForm:protected] => cid [_obkeys:protected] => Array ( [product_name] => 1 [slug] => 1 ) [_unique:protected] => 1 [_unique_name:protected] => Array ( [slug] => 1 ) [_orderingKey:protected] => ordering [_slugAutoName:protected] => product_name [_slugName:protected] => slug [_db:protected] => JDatabaseDriverMysqli Object ( [name] => mysqli [serverType] => mysql [connection:protected] => mysqli Object ( [affected_rows] => 1 [client_info] => mysqlnd 5.0.12-dev - 20150407 - $Id: 38fea24f2847fa7519001be390c98ae0acafe387 $ [client_version] => 50012 [connect_errno] => 0 [connect_error] => [errno] => 0 [error] => [error_list] => Array ( ) [field_count] => 1 [host_info] => Localhost via UNIX socket [info] => [insert_id] => 0 [server_info] => 5.7.28 [server_version] => 50728 [stat] => Uptime: 19101 Threads: 1 Questions: 1233547 Slow queries: 0 Opens: 43325 Flush tables: 1 Open tables: 2000 Queries per second avg: 64.580 [sqlstate] => 00000 [protocol_version] => 10 [thread_id] => 10603 [warning_count] => 0 ) [nameQuote:protected] => ` [nullDate:protected] => 0000-00-00 00:00:00 [_database:JDatabaseDriver:private] => universi_backup [count:protected] => 91 [cursor:protected] => [debug:protected] => [limit:protected] => 0 [log:protected] => Array ( ) [timings:protected] => Array ( ) [callStacks:protected] => Array ( ) [offset:protected] => 0 [options:protected] => Array ( [driver] => mysqli [host] => localhost [user] => universi_backup [password] => L2d604E=M7P~ [database] => universi_backup [prefix] => univer_ [select] => 1 [port] => 3306 [socket] => ) [sql:protected] => JDatabaseQueryMysqli Object ( [offset:protected] => 0 [limit:protected] => 0 [db:protected] => JDatabaseDriverMysqli Object *RECURSION* [sql:protected] => [type:protected] => select [element:protected] => [select:protected] => JDatabaseQueryElement Object ( [name:protected] => SELECT [elements:protected] => Array ( [0] => a.category_parent_id ) [glue:protected] => , ) [delete:protected] => [update:protected] => [insert:protected] => [from:protected] => JDatabaseQueryElement Object ( [name:protected] => FROM [elements:protected] => Array ( [0] => `#__virtuemart_category_categories` AS `a` ) [glue:protected] => , ) [join:protected] => [set:protected] => [where:protected] => JDatabaseQueryElement Object ( [name:protected] => WHERE [elements:protected] => Array ( [0] => `category_child_id` = "33" ) [glue:protected] => AND ) [group:protected] => [having:protected] => [columns:protected] => [values:protected] => [order:protected] => [autoIncrementField:protected] => [call:protected] => [exec:protected] => [union:protected] => [unionAll:protected] => [selectRowNumber:protected] => ) [tablePrefix:protected] => univer_ [utf:protected] => 1 [utf8mb4:protected] => 1 [errorNum:protected] => 0 [errorMsg:protected] => [transactionDepth:protected] => 0 [disconnectHandlers:protected] => Array ( ) ) [_rules:protected] => [_trackAssets:protected] => [_locked:protected] => [_loggable:protected] => 1 [_xParams] => product_params [_varsToPushParam] => Array ( [min_order_level] => Array ( [0] => [1] => float ) [max_order_level] => Array ( [0] => [1] => float ) [step_order_level] => Array ( [0] => [1] => float ) [product_box] => Array ( [0] => [1] => float ) ) [_translatable] => 1 [_translatableFields:protected] => Array ( [0] => product_name [1] => product_s_desc [2] => product_desc [3] => metadesc [4] => metakey [5] => customtitle [slug] => slug ) [_hashName:protected] => [_omittedHashFields:protected] => Array ( ) [_cryptedFields] => [_langTag:protected] => es_es [_ltmp] => [_loadedWithLangFallback] => 0 [_loaded] => 1 [_updateNulls:protected] => 1 [_toConvertDec:protected] => [_tablePreFix] => p. [_autoincrement] => 1 [_observers] => JObserverUpdater Object ( [aliases:protected] => Array ( ) [observers:protected] => Array ( ) [doCallObservers:protected] => 1 ) [created_on] => 2019-02-13 15:10:29 [created_by] => 1230 [modified_on] => 2019-02-13 15:14:11 [modified_by] => 1230 [min_order_level] => [max_order_level] => [step_order_level] => [product_box] => [allIds] => Array ( [0] => 3702 ) [virtuemart_media_id] => Array ( [0] => 4835 ) [shoppergroups] => [allPrices] => Array ( [0] => Array ( [virtuemart_product_price_id] => 3691 [virtuemart_product_id] => 3702 [virtuemart_shoppergroup_id] => 0 [product_price] => 36000 [override] => 0 [product_override_price] => 0 [product_tax_id] => 0 [product_discount_id] => 0 [product_currency] => 31 [product_price_publish_up] => 0000-00-00 00:00:00 [product_price_publish_down] => 0000-00-00 00:00:00 [price_quantity_start] => 0 [price_quantity_end] => 0 [created_on] => 2019-02-13 15:10:29 [created_by] => 1230 [modified_on] => 2019-02-13 15:14:11 [modified_by] => 1230 [locked_on] => 0000-00-00 00:00:00 [locked_by] => 0 [costPrice] => 36000 [basePrice] => 36000 [basePriceVariant] => 36000 [basePriceWithTax] => 0 [discountedPriceWithoutTax] => 32400 [priceBeforeTax] => 32400 [salesPrice] => 32400 [taxAmount] => 0 [salesPriceWithDiscount] => 0 [salesPriceTemp] => 32400 [unitPrice] => 0 [discountAmount] => -3600 [priceWithoutTax] => 32400 [variantModification] => 0 [DBTax] => Array ( [2] => Array ( [0] => Descuento 10% [1] => 10.0000 [2] => -% [3] => 0 [4] => 31 [5] => [6] => 1 [7] => 2 ) ) [Tax] => Array ( ) [VatTax] => Array ( ) [DATax] => Array ( ) [Marge] => Array ( ) [salesPriceTt] => 32400 [discountedPriceWithoutTaxTt] => 32400 [priceWithoutTaxTt] => 32400 [discountAmountTt] => -3600 [taxAmountTt] => 0 ) ) [selectedPrice] => 0 [virtuemart_manufacturer_id] => Array ( ) [mf_name] => [mf_desc] => [mf_url] => [categoryItem] => Array ( [0] => Array ( [virtuemart_category_id] => 33 [virtuemart_vendor_id] => 1 [category_name] => Geometría [slug] => geometria [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros sobre Geometría | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 0000-00-00 00:00:00 [created_by] => 0 [modified_on] => 2017-03-22 14:08:14 [modified_by] => 634 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 17898 ) [1] => Array ( [virtuemart_category_id] => 106 [virtuemart_vendor_id] => 1 [category_name] => Libro [slug] => libro [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2016-08-05 15:55:35 [created_by] => 634 [modified_on] => 2016-08-21 02:46:29 [modified_by] => 634 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 17900 ) [2] => Array ( [virtuemart_category_id] => 4526 [virtuemart_vendor_id] => 1 [category_name] => Editorial Universidad del Norte [slug] => editorial-universidad-del-norte [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros de Editorial Universidad del Norte | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2019-01-21 22:45:24 [created_by] => 1230 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 17897 ) [3] => Array ( [virtuemart_category_id] => 4616 [virtuemart_vendor_id] => 1 [category_name] => Carlos Javier Rojas Álvarez [slug] => carlos-javier-rojas-lvarez [category_description] =>

    Profesor investigador del Departamento de Matemáticas y Estadística de la Universidad del Norte (Colombia).

    Licenciado en Matemáticas y Física de la Universidad del Atlántico (Colombia).

    Magíster en Educación de la Universidad del Norte (Colombia).

    Es coautor de los libros de estadística descriptiva y distribuciones de probabilidad y Matemáticas básicas, 4a. ed.; además, es autor de los libros Introducción a la geometría, 2a. ed. y Razonamiento cuantitativo. Ha sido ganador del Premio Innovación Pedagógica Uninorte en los años 2004, 2007, 2011 y 2013.

    [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros de Carlos Javier Rojas Álvarez | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2019-02-04 21:01:02 [created_by] => 1230 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 17899 ) ) [canonCatId] => 33 [canonCatIdname] => [categories] => Array ( [0] => 33 [1] => 106 [2] => 4526 [3] => 4616 ) [virtuemart_category_id] => 33 [ordering] => 0 [id] => 17898 [category_name] => Geometría [orderable] => 1 [modificatorSum] => 0 [product_tax_id] => 0 [amount] => 1 [quantity] => 1 [prices] => Array ( [virtuemart_product_price_id] => 3691 [virtuemart_product_id] => 3702 [virtuemart_shoppergroup_id] => 0 [product_price] => 36000 [override] => 0 [product_override_price] => 0 [product_tax_id] => 0 [product_discount_id] => 0 [product_currency] => 31 [product_price_publish_up] => 0000-00-00 00:00:00 [product_price_publish_down] => 0000-00-00 00:00:00 [price_quantity_start] => 0 [price_quantity_end] => 0 [created_on] => 2019-02-13 15:10:29 [created_by] => 1230 [modified_on] => 2019-02-13 15:14:11 [modified_by] => 1230 [locked_on] => 0000-00-00 00:00:00 [locked_by] => 0 [costPrice] => 36000 [basePrice] => 36000 [basePriceVariant] => 36000 [basePriceWithTax] => 0 [discountedPriceWithoutTax] => 32400 [priceBeforeTax] => 32400 [salesPrice] => 32400 [taxAmount] => 0 [salesPriceWithDiscount] => 0 [salesPriceTemp] => 32400 [unitPrice] => 0 [discountAmount] => -3600 [priceWithoutTax] => 32400 [variantModification] => 0 [DBTax] => Array ( [2] => Array ( [0] => Descuento 10% [1] => 10.0000 [2] => -% [3] => 0 [4] => 31 [5] => [6] => 1 [7] => 2 ) ) [Tax] => Array ( ) [VatTax] => Array ( ) [DATax] => Array ( ) [Marge] => Array ( ) [salesPriceTt] => 32400 [discountedPriceWithoutTaxTt] => 32400 [priceWithoutTaxTt] => 32400 [discountAmountTt] => -3600 [taxAmountTt] => 0 ) [canonical] => index.php?option=com_virtuemart&view=productdetails&virtuemart_product_id=3702&virtuemart_category_id=33 [link] => index.php?option=com_virtuemart&view=productdetails&virtuemart_product_id=3702&virtuemart_category_id=33 [addToCartButton] => [images] => Array ( [0] => VmImage Object ( [media_attributes] => 0 [setRole] => [file_name] => 3736_1 [file_extension] => jpg [virtuemart_media_id] => 4835 [_foldersToTest:VmMediaHandler:private] => Array ( [0] => /home/universilibros/public_html/images/stories/virtuemart/product/ [1] => /home/universilibros/public_html/images/stories/virtuemart/product/resized/ ) [_actions:VmMediaHandler:private] => Array ( ) [_mLocation:VmMediaHandler:private] => Array ( ) [_hidden:VmMediaHandler:private] => Array ( ) [theme_url] => components/com_virtuemart/ [virtuemart_vendor_id] => 1 [file_title] => Introducción a la geometría [file_description] => [file_meta] => Libro: Introducción a la geometría | Autor: Carlos Javier Rojas Álvarez | Isbn: 9789587416831 [file_class] => [file_mimetype] => image/jpeg [file_type] => product [file_url] => images/stories/virtuemart/product/3736_1.jpg [file_url_thumb] => [published] => 1 [file_is_downloadable] => 0 [file_is_forSale] => 0 [file_is_product_image] => 0 [shared] => 0 [file_params] => [file_lang] => [created_on] => 2019-02-13 15:10:29 [created_by] => 1230 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [file_url_folder] => images/stories/virtuemart/product/ [file_path_folder] => images/stories/virtuemart/product/ [file_url_folder_thumb] => images/stories/virtuemart/product/resized/ [media_role] => file_is_displayable [file_name_thumb] => 3736_1_0x90 ) ) [file_url_thumb] => [file_url] => images/stories/virtuemart/product/3736_1.jpg [stock] => stdClass Object ( [stock_tip] => Hay gran cantidad de existencias de este producto [stock_level] => normalstock ) [customfieldsSorted] => Array ( [normal] => Array ( [0] => stdClass Object ( [virtuemart_custom_id] => 4 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Año [show_title] => 0 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 19409 [virtuemart_product_id] => 3702 [customfield_value] => 2016 [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => 2016 ) [1] => stdClass Object ( [virtuemart_custom_id] => 5 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Terminado [show_title] => 0 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 19410 [virtuemart_product_id] => 3702 [customfield_value] => Tapa Blanda [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => Tapa Blanda ) [2] => stdClass Object ( [virtuemart_custom_id] => 7 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Paginas [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 19411 [virtuemart_product_id] => 3702 [customfield_value] => 222 [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => 222 ) [3] => stdClass Object ( [virtuemart_custom_id] => 11 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Edicion [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty="0"|selectType="0"| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 19412 [virtuemart_product_id] => 3702 [customfield_value] => Segunda [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => Segunda ) [4] => stdClass Object ( [virtuemart_custom_id] => 15 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Reimpresion [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 19413 [virtuemart_product_id] => 3702 [customfield_value] => Primera 2018 [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => Primera 2018 ) [5] => stdClass Object ( [virtuemart_custom_id] => 14 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Subtitulo [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 19414 [virtuemart_product_id] => 3702 [customfield_value] => 2da. Edición revisada y aumentada [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => 2da. Edición revisada y aumentada ) [6] => stdClass Object ( [virtuemart_custom_id] => 3 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Indice [show_title] => 0 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => X [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => 0 [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 19408 [virtuemart_product_id] => 3702 [customfield_value] =>

    CONTENIDO

     

    INTRODUCCIÓN

     

    CONCEPTOS PRELIMINARES

    1. Términos primitivos
    2. Posición relativa de puntos
    3. Segmento
    4. Rayos
    5. Ángulos
    6. Triángulos
    7. Cuadriláteros
    8. Polígonos
    9. La circunferencia
    10. Sólidos

    Bibliografía

     

    Unidad 1

    SEMEJANZA

     

    Problema

    1.1 Proporción

    1.2 Polígonos semejantes

    1.3 El criterio de semejanza AA

    1.4 La pendiente de la recta

    Bibliografía

     

    Unidad 2

    PERÍMETRO Y ÁREA

     

    Problema

    2.1. Unidades arbitrarias

    2.2. Estimación

    2.3. Área de polígonos

    2.4. Partes de un círculo

    Bibliografía

     

    Unidad 3

    ÁREA Y VOLUMEN

     

    Problema

    3.1 Unidades de volumen

    3.2 Prismas y pirámides

    3.3 Cilindros y conos

    3.4 Tronco de pirámide y de cono

    Bibliografía

     

    Unidad 4

    FUNCIONES

     

    Problema

    4.1 Conceptos básicos

    4.2 Funciones como modelos matemáticos

    Bibliografía

     

    Unidad 5

    VECTORES

     

    Problema

    5.1 Escalares y vectores

    5.2 Componentes de un vector

    5.3 Vectores unitarios

    5.4 Suma de vectores

    Bibliografía

    [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => 0 [display] =>

    CONTENIDO

     

    INTRODUCCIÓN

     

    CONCEPTOS PRELIMINARES

    1. Términos primitivos
    2. Posición relativa de puntos
    3. Segmento
    4. Rayos
    5. Ángulos
    6. Triángulos
    7. Cuadriláteros
    8. Polígonos
    9. La circunferencia
    10. Sólidos

    Bibliografía

     

    Unidad 1

    SEMEJANZA

     

    Problema

    1.1 Proporción

    1.2 Polígonos semejantes

    1.3 El criterio de semejanza AA

    1.4 La pendiente de la recta

    Bibliografía

     

    Unidad 2

    PERÍMETRO Y ÁREA

     

    Problema

    2.1. Unidades arbitrarias

    2.2. Estimación

    2.3. Área de polígonos

    2.4. Partes de un círculo

    Bibliografía

     

    Unidad 3

    ÁREA Y VOLUMEN

     

    Problema

    3.1 Unidades de volumen

    3.2 Prismas y pirámides

    3.3 Cilindros y conos

    3.4 Tronco de pirámide y de cono

    Bibliografía

     

    Unidad 4

    FUNCIONES

     

    Problema

    4.1 Conceptos básicos

    4.2 Funciones como modelos matemáticos

    Bibliografía

     

    Unidad 5

    VECTORES

     

    Problema

    5.1 Escalares y vectores

    5.2 Componentes de un vector

    5.3 Vectores unitarios

    5.4 Suma de vectores

    Bibliografía

    ) ) ) )
    Precio de venta con descuento:
    Descuentos Universilibros10%
    Precio
    Antes:
    COP
    $ 36.000
    Ahora:
    COP
    $ 32.400
    Descuento: COP $ -3.600
    Precio / kg:

    Geometría para diseño gráfico | Autor: Carlos Javier Rojas Álvarez

    Isbn: 978-958-741-858-3 | Año: 2017 | Páginas: 133
    TableProducts Object
    (
        [virtuemart_product_id] => 3637
        [virtuemart_vendor_id] => 1
        [product_parent_id] => 0
        [product_sku] => 3671
        [product_gtin] => 978-958-741-858-3
        [product_mpn] => 9789587418583
        [product_name] => Geometría para diseño gráfico
        [slug] => geometria-para-diseno-grafico
        [product_s_desc] => 
        [product_desc] => 

    Este texto está dirigido a estudiantes de Diseño Gráfico, Arquitectura, Artes y básica secundaria. Su propósito es aplicar la geometría a algunas situaciones relacionadas con el diseño, tales como las vistas de un sólido, la proporción y el número áureo, sin perder la rigurosidad de los conceptos y propiedades de la geometría elemental.

    [product_weight] => 0.1400 [product_weight_uom] => KG [product_length] => 24.0000 [product_width] => 16.0000 [product_height] => 0.0000 [product_lwh_uom] => CM [product_url] => [product_in_stock] => 2 [product_ordered] => 0 [product_stockhandle] => 0 [low_stock_notification] => 0 [product_available_date] => 2019-02-04 21:52:53 [product_availability] => [product_special] => 0 [product_discontinued] => 0 [pordering] => 0 [product_sales] => 0 [product_unit] => KG [product_packaging] => 0 [product_params] => [intnotes] => [customtitle] => Libro: Geometría para diseño gráfico | Autor: Carlos Javier Rojas Álvarez | Isbn: 9789587418583 [metadesc] =>

    Este texto está dirigido a estudiantes de Diseño Gráfico, Arquitectura, Artes y básica secundaria. Su propósito es aplicar la geometría a algunas situaciones relacionadas con el diseño, tales como las vistas de un sólido, la proporción y el número áureo, sin perder la rigurosidad de los conceptos y propiedades de la geometría elemental.

    [metakey] => Editorial Universidad del Norte, Geometría, Carlos Javier Rojas Álvarez, 978-958-741-858-3, 9789587418583 [metarobot] => [metaauthor] => Universilibros - Una institución al servicio de la cultura nacional [layout] => 0 [published] => 1 [product_canon_category_id] => [_lhash:VmTable:private] => 3d2065a27faa0a326b7f4e83ae681f66 [_tbl:protected] => #__virtuemart_products [_tbl_lang:protected] => #__virtuemart_products_es_es [_tbl_key:protected] => virtuemart_product_id [_tbl_keys:protected] => Array ( [0] => virtuemart_product_id ) [_pkey:protected] => virtuemart_product_id [_pkeyForm:protected] => cid [_obkeys:protected] => Array ( [product_name] => 1 [slug] => 1 ) [_unique:protected] => 1 [_unique_name:protected] => Array ( [slug] => 1 ) [_orderingKey:protected] => ordering [_slugAutoName:protected] => product_name [_slugName:protected] => slug [_db:protected] => JDatabaseDriverMysqli Object ( [name] => mysqli [serverType] => mysql [connection:protected] => mysqli Object ( [affected_rows] => -1 [client_info] => mysqlnd 5.0.12-dev - 20150407 - $Id: 38fea24f2847fa7519001be390c98ae0acafe387 $ [client_version] => 50012 [connect_errno] => 0 [connect_error] => [errno] => 0 [error] => [error_list] => Array ( ) [field_count] => 1 [host_info] => Localhost via UNIX socket [info] => [insert_id] => 0 [server_info] => 5.7.28 [server_version] => 50728 [stat] => Uptime: 19101 Threads: 1 Questions: 1233548 Slow queries: 0 Opens: 43325 Flush tables: 1 Open tables: 2000 Queries per second avg: 64.580 [sqlstate] => 00000 [protocol_version] => 10 [thread_id] => 10603 [warning_count] => 0 ) [nameQuote:protected] => ` [nullDate:protected] => 0000-00-00 00:00:00 [_database:JDatabaseDriver:private] => universi_backup [count:protected] => 91 [cursor:protected] => [debug:protected] => [limit:protected] => 0 [log:protected] => Array ( ) [timings:protected] => Array ( ) [callStacks:protected] => Array ( ) [offset:protected] => 0 [options:protected] => Array ( [driver] => mysqli [host] => localhost [user] => universi_backup [password] => L2d604E=M7P~ [database] => universi_backup [prefix] => univer_ [select] => 1 [port] => 3306 [socket] => ) [sql:protected] => JDatabaseQueryMysqli Object ( [offset:protected] => 0 [limit:protected] => 0 [db:protected] => JDatabaseDriverMysqli Object *RECURSION* [sql:protected] => [type:protected] => select [element:protected] => [select:protected] => JDatabaseQueryElement Object ( [name:protected] => SELECT [elements:protected] => Array ( [0] => a.category_parent_id ) [glue:protected] => , ) [delete:protected] => [update:protected] => [insert:protected] => [from:protected] => JDatabaseQueryElement Object ( [name:protected] => FROM [elements:protected] => Array ( [0] => `#__virtuemart_category_categories` AS `a` ) [glue:protected] => , ) [join:protected] => [set:protected] => [where:protected] => JDatabaseQueryElement Object ( [name:protected] => WHERE [elements:protected] => Array ( [0] => `category_child_id` = "33" ) [glue:protected] => AND ) [group:protected] => [having:protected] => [columns:protected] => [values:protected] => [order:protected] => [autoIncrementField:protected] => [call:protected] => [exec:protected] => [union:protected] => [unionAll:protected] => [selectRowNumber:protected] => ) [tablePrefix:protected] => univer_ [utf:protected] => 1 [utf8mb4:protected] => 1 [errorNum:protected] => 0 [errorMsg:protected] => [transactionDepth:protected] => 0 [disconnectHandlers:protected] => Array ( ) ) [_rules:protected] => [_trackAssets:protected] => [_locked:protected] => [_loggable:protected] => 1 [_xParams] => product_params [_varsToPushParam] => Array ( [min_order_level] => Array ( [0] => [1] => float ) [max_order_level] => Array ( [0] => [1] => float ) [step_order_level] => Array ( [0] => [1] => float ) [product_box] => Array ( [0] => [1] => float ) ) [_translatable] => 1 [_translatableFields:protected] => Array ( [0] => product_name [1] => product_s_desc [2] => product_desc [3] => metadesc [4] => metakey [5] => customtitle [slug] => slug ) [_hashName:protected] => [_omittedHashFields:protected] => Array ( ) [_cryptedFields] => [_langTag:protected] => es_es [_ltmp] => [_loadedWithLangFallback] => 0 [_loaded] => 1 [_updateNulls:protected] => 1 [_toConvertDec:protected] => [_tablePreFix] => p. [_autoincrement] => 1 [_observers] => JObserverUpdater Object ( [aliases:protected] => Array ( ) [observers:protected] => Array ( ) [doCallObservers:protected] => 1 ) [created_on] => 2019-02-04 21:52:53 [created_by] => 1230 [modified_on] => 2019-02-13 20:02:39 [modified_by] => 1230 [min_order_level] => [max_order_level] => [step_order_level] => [product_box] => [allIds] => Array ( [0] => 3637 ) [virtuemart_media_id] => Array ( [0] => 4714 ) [shoppergroups] => [allPrices] => Array ( [0] => Array ( [virtuemart_product_price_id] => 3627 [virtuemart_product_id] => 3637 [virtuemart_shoppergroup_id] => 0 [product_price] => 35000 [override] => 0 [product_override_price] => 0 [product_tax_id] => 0 [product_discount_id] => 0 [product_currency] => 31 [product_price_publish_up] => 0000-00-00 00:00:00 [product_price_publish_down] => 0000-00-00 00:00:00 [price_quantity_start] => 0 [price_quantity_end] => 0 [created_on] => 2019-02-04 21:52:53 [created_by] => 1230 [modified_on] => 2019-02-13 20:02:39 [modified_by] => 1230 [locked_on] => 0000-00-00 00:00:00 [locked_by] => 0 [costPrice] => 35000 [basePrice] => 35000 [basePriceVariant] => 35000 [basePriceWithTax] => 0 [discountedPriceWithoutTax] => 31500 [priceBeforeTax] => 31500 [salesPrice] => 31500 [taxAmount] => 0 [salesPriceWithDiscount] => 0 [salesPriceTemp] => 31500 [unitPrice] => 0 [discountAmount] => -3500 [priceWithoutTax] => 31500 [variantModification] => 0 [DBTax] => Array ( [2] => Array ( [0] => Descuento 10% [1] => 10.0000 [2] => -% [3] => 0 [4] => 31 [5] => [6] => 1 [7] => 2 ) ) [Tax] => Array ( ) [VatTax] => Array ( ) [DATax] => Array ( ) [Marge] => Array ( ) [salesPriceTt] => 31500 [discountedPriceWithoutTaxTt] => 31500 [priceWithoutTaxTt] => 31500 [discountAmountTt] => -3500 [taxAmountTt] => 0 ) ) [selectedPrice] => 0 [virtuemart_manufacturer_id] => Array ( ) [mf_name] => [mf_desc] => [mf_url] => [categoryItem] => Array ( [0] => Array ( [virtuemart_category_id] => 33 [virtuemart_vendor_id] => 1 [category_name] => Geometría [slug] => geometria [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros sobre Geometría | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 0000-00-00 00:00:00 [created_by] => 0 [modified_on] => 2017-03-22 14:08:14 [modified_by] => 634 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 17573 ) [1] => Array ( [virtuemart_category_id] => 106 [virtuemart_vendor_id] => 1 [category_name] => Libro [slug] => libro [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2016-08-05 15:55:35 [created_by] => 634 [modified_on] => 2016-08-21 02:46:29 [modified_by] => 634 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 17575 ) [2] => Array ( [virtuemart_category_id] => 4526 [virtuemart_vendor_id] => 1 [category_name] => Editorial Universidad del Norte [slug] => editorial-universidad-del-norte [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros de Editorial Universidad del Norte | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2019-01-21 22:45:24 [created_by] => 1230 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 17572 ) [3] => Array ( [virtuemart_category_id] => 4616 [virtuemart_vendor_id] => 1 [category_name] => Carlos Javier Rojas Álvarez [slug] => carlos-javier-rojas-lvarez [category_description] =>

    Profesor investigador del Departamento de Matemáticas y Estadística de la Universidad del Norte (Colombia).

    Licenciado en Matemáticas y Física de la Universidad del Atlántico (Colombia).

    Magíster en Educación de la Universidad del Norte (Colombia).

    Es coautor de los libros de estadística descriptiva y distribuciones de probabilidad y Matemáticas básicas, 4a. ed.; además, es autor de los libros Introducción a la geometría, 2a. ed. y Razonamiento cuantitativo. Ha sido ganador del Premio Innovación Pedagógica Uninorte en los años 2004, 2007, 2011 y 2013.

    [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros de Carlos Javier Rojas Álvarez | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2019-02-04 21:01:02 [created_by] => 1230 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 17574 ) ) [canonCatId] => 33 [canonCatIdname] => [categories] => Array ( [0] => 33 [1] => 106 [2] => 4526 [3] => 4616 ) [virtuemart_category_id] => 33 [ordering] => 0 [id] => 17573 [category_name] => Geometría [orderable] => 1 [modificatorSum] => 0 [product_tax_id] => 0 [amount] => 1 [quantity] => 1 [prices] => Array ( [virtuemart_product_price_id] => 3627 [virtuemart_product_id] => 3637 [virtuemart_shoppergroup_id] => 0 [product_price] => 35000 [override] => 0 [product_override_price] => 0 [product_tax_id] => 0 [product_discount_id] => 0 [product_currency] => 31 [product_price_publish_up] => 0000-00-00 00:00:00 [product_price_publish_down] => 0000-00-00 00:00:00 [price_quantity_start] => 0 [price_quantity_end] => 0 [created_on] => 2019-02-04 21:52:53 [created_by] => 1230 [modified_on] => 2019-02-13 20:02:39 [modified_by] => 1230 [locked_on] => 0000-00-00 00:00:00 [locked_by] => 0 [costPrice] => 35000 [basePrice] => 35000 [basePriceVariant] => 35000 [basePriceWithTax] => 0 [discountedPriceWithoutTax] => 31500 [priceBeforeTax] => 31500 [salesPrice] => 31500 [taxAmount] => 0 [salesPriceWithDiscount] => 0 [salesPriceTemp] => 31500 [unitPrice] => 0 [discountAmount] => -3500 [priceWithoutTax] => 31500 [variantModification] => 0 [DBTax] => Array ( [2] => Array ( [0] => Descuento 10% [1] => 10.0000 [2] => -% [3] => 0 [4] => 31 [5] => [6] => 1 [7] => 2 ) ) [Tax] => Array ( ) [VatTax] => Array ( ) [DATax] => Array ( ) [Marge] => Array ( ) [salesPriceTt] => 31500 [discountedPriceWithoutTaxTt] => 31500 [priceWithoutTaxTt] => 31500 [discountAmountTt] => -3500 [taxAmountTt] => 0 ) [canonical] => index.php?option=com_virtuemart&view=productdetails&virtuemart_product_id=3637&virtuemart_category_id=33 [link] => index.php?option=com_virtuemart&view=productdetails&virtuemart_product_id=3637&virtuemart_category_id=33 [addToCartButton] => [images] => Array ( [0] => VmImage Object ( [media_attributes] => 0 [setRole] => [file_name] => 3671_1 [file_extension] => jpg [virtuemart_media_id] => 4714 [_foldersToTest:VmMediaHandler:private] => Array ( [0] => /home/universilibros/public_html/images/stories/virtuemart/product/ [1] => /home/universilibros/public_html/images/stories/virtuemart/product/resized/ ) [_actions:VmMediaHandler:private] => Array ( ) [_mLocation:VmMediaHandler:private] => Array ( ) [_hidden:VmMediaHandler:private] => Array ( ) [theme_url] => components/com_virtuemart/ [virtuemart_vendor_id] => 1 [file_title] => Geometría para diseño gráfico [file_description] => [file_meta] => Libro: Geometría para diseño gráfico | Autor: Carlos Javier Rojas Álvarez | Isbn: 9789587418583 [file_class] => [file_mimetype] => image/jpeg [file_type] => product [file_url] => images/stories/virtuemart/product/3671_1.jpg [file_url_thumb] => [published] => 1 [file_is_downloadable] => 0 [file_is_forSale] => 0 [file_is_product_image] => 0 [shared] => 0 [file_params] => [file_lang] => [created_on] => 2019-02-04 21:52:53 [created_by] => 1230 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [file_url_folder] => images/stories/virtuemart/product/ [file_path_folder] => images/stories/virtuemart/product/ [file_url_folder_thumb] => images/stories/virtuemart/product/resized/ [media_role] => file_is_displayable [file_name_thumb] => 3671_1_0x90 ) ) [file_url_thumb] => [file_url] => images/stories/virtuemart/product/3671_1.jpg [stock] => stdClass Object ( [stock_tip] => Hay gran cantidad de existencias de este producto [stock_level] => normalstock ) [customfieldsSorted] => Array ( [normal] => Array ( [0] => stdClass Object ( [virtuemart_custom_id] => 3 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Indice [show_title] => 0 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => X [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => 0 [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 19036 [virtuemart_product_id] => 3637 [customfield_value] =>

    CONTENIDO

     

    INTRODUCCIÓN

     

    CONCEPTOS PRELIMINARES

    1. Términos primitivos
    2. Posición relativa de puntos
    3. Segmento
    4. Rayos y ángulos
    5. Polígonos
    6. La circunferencia
    7. Sólidos

    Referencias

     

    Unidad 1

    PROYECCIONES

    1.  1.1. Conceptos básicos
    2.  1.2. Proyección de vista múltiple
    3.  1.3. Proyección isométrica

    Referencias

     

    Unidad 2

    PROPORCIONES

    2.1. Proporción

    2.2. La proporción áurea

    Referencias

     

    ANEXOS

    [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => 0 [display] =>

    CONTENIDO

     

    INTRODUCCIÓN

     

    CONCEPTOS PRELIMINARES

    1. Términos primitivos
    2. Posición relativa de puntos
    3. Segmento
    4. Rayos y ángulos
    5. Polígonos
    6. La circunferencia
    7. Sólidos

    Referencias

     

    Unidad 1

    PROYECCIONES

    1.  1.1. Conceptos básicos
    2.  1.2. Proyección de vista múltiple
    3.  1.3. Proyección isométrica

    Referencias

     

    Unidad 2

    PROPORCIONES

    2.1. Proporción

    2.2. La proporción áurea

    Referencias

     

    ANEXOS

    ) [1] => stdClass Object ( [virtuemart_custom_id] => 4 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Año [show_title] => 0 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 19037 [virtuemart_product_id] => 3637 [customfield_value] => 2017 [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => 2017 ) [2] => stdClass Object ( [virtuemart_custom_id] => 5 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Terminado [show_title] => 0 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 19038 [virtuemart_product_id] => 3637 [customfield_value] => Tapa Blanda [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => Tapa Blanda ) [3] => stdClass Object ( [virtuemart_custom_id] => 7 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Paginas [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 19039 [virtuemart_product_id] => 3637 [customfield_value] => 133 [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => 133 ) [4] => stdClass Object ( [virtuemart_custom_id] => 11 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Edicion [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty="0"|selectType="0"| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 19040 [virtuemart_product_id] => 3637 [customfield_value] => Primera [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => Primera ) ) ) )
    Precio de venta con descuento:
    Descuentos Universilibros10%
    Precio
    Antes:
    COP
    $ 35.000
    Ahora:
    COP
    $ 31.500
    Descuento: COP $ -3.500
    Precio / kg:
    TableProducts Object
    (
        [virtuemart_product_id] => 3286
        [virtuemart_vendor_id] => 1
        [product_parent_id] => 0
        [product_sku] => 3316
        [product_gtin] => 6666
        [product_mpn] => 6666
        [product_name] => Solucionario un recorrido por la geometria
        [slug] => solucionario-un-recorrido-por-la-geometria
        [product_s_desc] => 
        [product_desc] => 
        [product_weight] => 0.1300
        [product_weight_uom] => KG
        [product_length] => 23.0000
        [product_width] => 16.0000
        [product_height] => 0.0000
        [product_lwh_uom] => CM
        [product_url] => 
        [product_in_stock] => 1
        [product_ordered] => 0
        [product_stockhandle] => 0
        [low_stock_notification] => 0
        [product_available_date] => 2018-11-21 11:57:49
        [product_availability] => 
        [product_special] => 0
        [product_discontinued] => 0
        [pordering] => 0
        [product_sales] => 0
        [product_unit] => KG
        [product_packaging] => 0
        [product_params] => min_order_level=""|max_order_level=""|step_order_level=""|product_box=""|
        [intnotes] => 
        [customtitle] => Libro: Solucionario un recorrido por la geometria | Autor: Germán Rincón Abella | Isbn: 6666
        [metadesc] => Solucionario un recorrido por la geometria
        [metakey] => Universidad Antonio Nariño, Geometría, Germán Rincón Abella, 6666, 6666
        [metarobot] => 
        [metaauthor] => Universilibros - Una institución al servicio de la cultura nacional
        [layout] => default
        [published] => 1
        [product_canon_category_id] => 
        [_lhash:VmTable:private] => 9eaad52d603ff315e0d81631c2f0eb71
        [_tbl:protected] => #__virtuemart_products
        [_tbl_lang:protected] => #__virtuemart_products_es_es
        [_tbl_key:protected] => virtuemart_product_id
        [_tbl_keys:protected] => Array
            (
                [0] => virtuemart_product_id
            )
    
        [_pkey:protected] => virtuemart_product_id
        [_pkeyForm:protected] => cid
        [_obkeys:protected] => Array
            (
                [product_name] => 1
                [slug] => 1
            )
    
        [_unique:protected] => 1
        [_unique_name:protected] => Array
            (
                [slug] => 1
            )
    
        [_orderingKey:protected] => ordering
        [_slugAutoName:protected] => product_name
        [_slugName:protected] => slug
        [_db:protected] => JDatabaseDriverMysqli Object
            (
                [name] => mysqli
                [serverType] => mysql
                [connection:protected] => mysqli Object
                    (
                        [affected_rows] => -1
                        [client_info] => mysqlnd 5.0.12-dev - 20150407 - $Id: 38fea24f2847fa7519001be390c98ae0acafe387 $
                        [client_version] => 50012
                        [connect_errno] => 0
                        [connect_error] => 
                        [errno] => 0
                        [error] => 
                        [error_list] => Array
                            (
                            )
    
                        [field_count] => 1
                        [host_info] => Localhost via UNIX socket
                        [info] => 
                        [insert_id] => 0
                        [server_info] => 5.7.28
                        [server_version] => 50728
                        [stat] => Uptime: 19101  Threads: 1  Questions: 1233549  Slow queries: 0  Opens: 43325  Flush tables: 1  Open tables: 2000  Queries per second avg: 64.580
                        [sqlstate] => 00000
                        [protocol_version] => 10
                        [thread_id] => 10603
                        [warning_count] => 0
                    )
    
                [nameQuote:protected] => `
                [nullDate:protected] => 0000-00-00 00:00:00
                [_database:JDatabaseDriver:private] => universi_backup
                [count:protected] => 91
                [cursor:protected] => 
                [debug:protected] => 
                [limit:protected] => 0
                [log:protected] => Array
                    (
                    )
    
                [timings:protected] => Array
                    (
                    )
    
                [callStacks:protected] => Array
                    (
                    )
    
                [offset:protected] => 0
                [options:protected] => Array
                    (
                        [driver] => mysqli
                        [host] => localhost
                        [user] => universi_backup
                        [password] => L2d604E=M7P~
                        [database] => universi_backup
                        [prefix] => univer_
                        [select] => 1
                        [port] => 3306
                        [socket] => 
                    )
    
                [sql:protected] => JDatabaseQueryMysqli Object
                    (
                        [offset:protected] => 0
                        [limit:protected] => 0
                        [db:protected] => JDatabaseDriverMysqli Object
     *RECURSION*
                        [sql:protected] => 
                        [type:protected] => select
                        [element:protected] => 
                        [select:protected] => JDatabaseQueryElement Object
                            (
                                [name:protected] => SELECT
                                [elements:protected] => Array
                                    (
                                        [0] => a.category_parent_id
                                    )
    
                                [glue:protected] => ,
                            )
    
                        [delete:protected] => 
                        [update:protected] => 
                        [insert:protected] => 
                        [from:protected] => JDatabaseQueryElement Object
                            (
                                [name:protected] => FROM
                                [elements:protected] => Array
                                    (
                                        [0] => `#__virtuemart_category_categories` AS `a`
                                    )
    
                                [glue:protected] => ,
                            )
    
                        [join:protected] => 
                        [set:protected] => 
                        [where:protected] => JDatabaseQueryElement Object
                            (
                                [name:protected] => WHERE
                                [elements:protected] => Array
                                    (
                                        [0] => `category_child_id` = "33"
                                    )
    
                                [glue:protected] =>  AND 
                            )
    
                        [group:protected] => 
                        [having:protected] => 
                        [columns:protected] => 
                        [values:protected] => 
                        [order:protected] => 
                        [autoIncrementField:protected] => 
                        [call:protected] => 
                        [exec:protected] => 
                        [union:protected] => 
                        [unionAll:protected] => 
                        [selectRowNumber:protected] => 
                    )
    
                [tablePrefix:protected] => univer_
                [utf:protected] => 1
                [utf8mb4:protected] => 1
                [errorNum:protected] => 0
                [errorMsg:protected] => 
                [transactionDepth:protected] => 0
                [disconnectHandlers:protected] => Array
                    (
                    )
    
            )
    
        [_rules:protected] => 
        [_trackAssets:protected] => 
        [_locked:protected] => 
        [_loggable:protected] => 1
        [_xParams] => product_params
        [_varsToPushParam] => Array
            (
                [min_order_level] => Array
                    (
                        [0] => 
                        [1] => float
                    )
    
                [max_order_level] => Array
                    (
                        [0] => 
                        [1] => float
                    )
    
                [step_order_level] => Array
                    (
                        [0] => 
                        [1] => float
                    )
    
                [product_box] => Array
                    (
                        [0] => 
                        [1] => float
                    )
    
            )
    
        [_translatable] => 1
        [_translatableFields:protected] => Array
            (
                [0] => product_name
                [1] => product_s_desc
                [2] => product_desc
                [3] => metadesc
                [4] => metakey
                [5] => customtitle
                [slug] => slug
            )
    
        [_hashName:protected] => 
        [_omittedHashFields:protected] => Array
            (
            )
    
        [_cryptedFields] => 
        [_langTag:protected] => es_es
        [_ltmp] => 
        [_loadedWithLangFallback] => 0
        [_loaded] => 1
        [_updateNulls:protected] => 1
        [_toConvertDec:protected] => 
        [_tablePreFix] => p.
        [_autoincrement] => 1
        [_observers] => JObserverUpdater Object
            (
                [aliases:protected] => Array
                    (
                    )
    
                [observers:protected] => Array
                    (
                    )
    
                [doCallObservers:protected] => 1
            )
    
        [created_on] => 2018-11-21 11:57:49
        [created_by] => 639
        [modified_on] => 2018-11-21 17:58:41
        [modified_by] => 639
        [min_order_level] => 
        [max_order_level] => 
        [step_order_level] => 
        [product_box] => 
        [allIds] => Array
            (
                [0] => 3286
            )
    
        [virtuemart_media_id] => Array
            (
                [0] => 4123
            )
    
        [shoppergroups] => 
        [allPrices] => Array
            (
                [0] => Array
                    (
                        [virtuemart_product_price_id] => 3276
                        [virtuemart_product_id] => 3286
                        [virtuemart_shoppergroup_id] => 0
                        [product_price] => 24000
                        [override] => 0
                        [product_override_price] => 0
                        [product_tax_id] => 0
                        [product_discount_id] => 0
                        [product_currency] => 31
                        [product_price_publish_up] => 0000-00-00 00:00:00
                        [product_price_publish_down] => 0000-00-00 00:00:00
                        [price_quantity_start] => 0
                        [price_quantity_end] => 0
                        [created_on] => 2018-11-21 11:57:49
                        [created_by] => 639
                        [modified_on] => 2018-11-21 17:58:41
                        [modified_by] => 639
                        [locked_on] => 0000-00-00 00:00:00
                        [locked_by] => 0
                        [costPrice] => 24000
                        [basePrice] => 24000
                        [basePriceVariant] => 24000
                        [basePriceWithTax] => 0
                        [discountedPriceWithoutTax] => 21600
                        [priceBeforeTax] => 21600
                        [salesPrice] => 21600
                        [taxAmount] => 0
                        [salesPriceWithDiscount] => 0
                        [salesPriceTemp] => 21600
                        [unitPrice] => 0
                        [discountAmount] => -2400
                        [priceWithoutTax] => 21600
                        [variantModification] => 0
                        [DBTax] => Array
                            (
                                [2] => Array
                                    (
                                        [0] => Descuento 10%
                                        [1] => 10.0000
                                        [2] => -%
                                        [3] => 0
                                        [4] => 31
                                        [5] => 
                                        [6] => 1
                                        [7] => 2
                                    )
    
                            )
    
                        [Tax] => Array
                            (
                            )
    
                        [VatTax] => Array
                            (
                            )
    
                        [DATax] => Array
                            (
                            )
    
                        [Marge] => Array
                            (
                            )
    
                        [salesPriceTt] => 21600
                        [discountedPriceWithoutTaxTt] => 21600
                        [priceWithoutTaxTt] => 21600
                        [discountAmountTt] => -2400
                        [taxAmountTt] => 0
                    )
    
            )
    
        [selectedPrice] => 0
        [virtuemart_manufacturer_id] => Array
            (
            )
    
        [mf_name] => 
        [mf_desc] => 
        [mf_url] => 
        [categoryItem] => Array
            (
                [0] => Array
                    (
                        [virtuemart_category_id] => 33
                        [virtuemart_vendor_id] => 1
                        [category_name] => Geometría
                        [slug] => geometria
                        [category_description] => 
                        [category_template] => 0
                        [category_layout] => 0
                        [category_product_layout] => 0
                        [products_per_row] => 0
                        [ordering] => 0
                        [shared] => 0
                        [cat_params] => 
                        [limit_list_step] => 0
                        [limit_list_initial] => 0
                        [metadesc] => 
                        [customtitle] => Libros sobre Geometría | Universilibros
                        [metakey] => 
                        [metarobot] => 
                        [metaauthor] => 
                        [published] => 1
                        [created_on] => 0000-00-00 00:00:00
                        [created_by] => 0
                        [modified_on] => 2017-03-22 14:08:14
                        [modified_by] => 634
                        [show_store_desc] => 
                        [showcategory_desc] => 
                        [showcategory] => 
                        [categories_per_row] => 
                        [showproducts] => 
                        [omitLoaded] => 
                        [showsearch] => 
                        [productsublayout] => 
                        [featured] => 
                        [featured_rows] => 
                        [omitLoaded_featured] => 
                        [discontinued] => 
                        [discontinued_rows] => 
                        [omitLoaded_discontinued] => 
                        [latest] => 
                        [latest_rows] => 
                        [omitLoaded_latest] => 
                        [topten] => 
                        [topten_rows] => 
                        [omitLoaded_topten] => 
                        [recent] => 
                        [recent_rows] => 
                        [omitLoaded_recent] => 
                        [id] => 16010
                    )
    
                [1] => Array
                    (
                        [virtuemart_category_id] => 106
                        [virtuemart_vendor_id] => 1
                        [category_name] => Libro
                        [slug] => libro
                        [category_description] => 
                        [category_template] => 0
                        [category_layout] => 0
                        [category_product_layout] => 0
                        [products_per_row] => 0
                        [ordering] => 0
                        [shared] => 0
                        [cat_params] => 
                        [limit_list_step] => 0
                        [limit_list_initial] => 0
                        [metadesc] => 
                        [customtitle] => 
                        [metakey] => 
                        [metarobot] => 
                        [metaauthor] => 
                        [published] => 1
                        [created_on] => 2016-08-05 15:55:35
                        [created_by] => 634
                        [modified_on] => 2016-08-21 02:46:29
                        [modified_by] => 634
                        [show_store_desc] => 
                        [showcategory_desc] => 
                        [showcategory] => 
                        [categories_per_row] => 
                        [showproducts] => 
                        [omitLoaded] => 
                        [showsearch] => 
                        [productsublayout] => 
                        [featured] => 
                        [featured_rows] => 
                        [omitLoaded_featured] => 
                        [discontinued] => 
                        [discontinued_rows] => 
                        [omitLoaded_discontinued] => 
                        [latest] => 
                        [latest_rows] => 
                        [omitLoaded_latest] => 
                        [topten] => 
                        [topten_rows] => 
                        [omitLoaded_topten] => 
                        [recent] => 
                        [recent_rows] => 
                        [omitLoaded_recent] => 
                        [id] => 16012
                    )
    
                [2] => Array
                    (
                        [virtuemart_category_id] => 4291
                        [virtuemart_vendor_id] => 1
                        [category_name] => Universidad Antonio Nariño
                        [slug] => universidad-antonio-narino
                        [category_description] => 
                        [category_template] => 0
                        [category_layout] => 0
                        [category_product_layout] => 0
                        [products_per_row] => 0
                        [ordering] => 0
                        [shared] => 0
                        [cat_params] => 
                        [limit_list_step] => 0
                        [limit_list_initial] => 0
                        [metadesc] => 
                        [customtitle] => Libros de Universidad Antonio Nariño | Universilibros
                        [metakey] => 
                        [metarobot] => 
                        [metaauthor] => 
                        [published] => 1
                        [created_on] => 2018-11-21 11:53:40
                        [created_by] => 639
                        [modified_on] => 0000-00-00 00:00:00
                        [modified_by] => 0
                        [show_store_desc] => 
                        [showcategory_desc] => 
                        [showcategory] => 
                        [categories_per_row] => 
                        [showproducts] => 
                        [omitLoaded] => 
                        [showsearch] => 
                        [productsublayout] => 
                        [featured] => 
                        [featured_rows] => 
                        [omitLoaded_featured] => 
                        [discontinued] => 
                        [discontinued_rows] => 
                        [omitLoaded_discontinued] => 
                        [latest] => 
                        [latest_rows] => 
                        [omitLoaded_latest] => 
                        [topten] => 
                        [topten_rows] => 
                        [omitLoaded_topten] => 
                        [recent] => 
                        [recent_rows] => 
                        [omitLoaded_recent] => 
                        [id] => 16009
                    )
    
                [3] => Array
                    (
                        [virtuemart_category_id] => 4292
                        [virtuemart_vendor_id] => 1
                        [category_name] => Germán Rincón Abella
                        [slug] => german-rincon-abella
                        [category_description] => 
                        [category_template] => 0
                        [category_layout] => 0
                        [category_product_layout] => 0
                        [products_per_row] => 0
                        [ordering] => 0
                        [shared] => 0
                        [cat_params] => 
                        [limit_list_step] => 0
                        [limit_list_initial] => 0
                        [metadesc] => 
                        [customtitle] => Libros de Germán Rincón Abella | Universilibros
                        [metakey] => 
                        [metarobot] => 
                        [metaauthor] => 
                        [published] => 1
                        [created_on] => 2018-11-21 11:54:13
                        [created_by] => 639
                        [modified_on] => 0000-00-00 00:00:00
                        [modified_by] => 0
                        [show_store_desc] => 
                        [showcategory_desc] => 
                        [showcategory] => 
                        [categories_per_row] => 
                        [showproducts] => 
                        [omitLoaded] => 
                        [showsearch] => 
                        [productsublayout] => 
                        [featured] => 
                        [featured_rows] => 
                        [omitLoaded_featured] => 
                        [discontinued] => 
                        [discontinued_rows] => 
                        [omitLoaded_discontinued] => 
                        [latest] => 
                        [latest_rows] => 
                        [omitLoaded_latest] => 
                        [topten] => 
                        [topten_rows] => 
                        [omitLoaded_topten] => 
                        [recent] => 
                        [recent_rows] => 
                        [omitLoaded_recent] => 
                        [id] => 16011
                    )
    
            )
    
        [canonCatId] => 33
        [canonCatIdname] => 
        [categories] => Array
            (
                [0] => 33
                [1] => 106
                [2] => 4291
                [3] => 4292
            )
    
        [virtuemart_category_id] => 33
        [ordering] => 0
        [id] => 16010
        [category_name] => Geometría
        [orderable] => 1
        [modificatorSum] => 0
        [product_tax_id] => 0
        [amount] => 1
        [quantity] => 1
        [prices] => Array
            (
                [virtuemart_product_price_id] => 3276
                [virtuemart_product_id] => 3286
                [virtuemart_shoppergroup_id] => 0
                [product_price] => 24000
                [override] => 0
                [product_override_price] => 0
                [product_tax_id] => 0
                [product_discount_id] => 0
                [product_currency] => 31
                [product_price_publish_up] => 0000-00-00 00:00:00
                [product_price_publish_down] => 0000-00-00 00:00:00
                [price_quantity_start] => 0
                [price_quantity_end] => 0
                [created_on] => 2018-11-21 11:57:49
                [created_by] => 639
                [modified_on] => 2018-11-21 17:58:41
                [modified_by] => 639
                [locked_on] => 0000-00-00 00:00:00
                [locked_by] => 0
                [costPrice] => 24000
                [basePrice] => 24000
                [basePriceVariant] => 24000
                [basePriceWithTax] => 0
                [discountedPriceWithoutTax] => 21600
                [priceBeforeTax] => 21600
                [salesPrice] => 21600
                [taxAmount] => 0
                [salesPriceWithDiscount] => 0
                [salesPriceTemp] => 21600
                [unitPrice] => 0
                [discountAmount] => -2400
                [priceWithoutTax] => 21600
                [variantModification] => 0
                [DBTax] => Array
                    (
                        [2] => Array
                            (
                                [0] => Descuento 10%
                                [1] => 10.0000
                                [2] => -%
                                [3] => 0
                                [4] => 31
                                [5] => 
                                [6] => 1
                                [7] => 2
                            )
    
                    )
    
                [Tax] => Array
                    (
                    )
    
                [VatTax] => Array
                    (
                    )
    
                [DATax] => Array
                    (
                    )
    
                [Marge] => Array
                    (
                    )
    
                [salesPriceTt] => 21600
                [discountedPriceWithoutTaxTt] => 21600
                [priceWithoutTaxTt] => 21600
                [discountAmountTt] => -2400
                [taxAmountTt] => 0
            )
    
        [canonical] => index.php?option=com_virtuemart&view=productdetails&virtuemart_product_id=3286&virtuemart_category_id=33
        [link] => index.php?option=com_virtuemart&view=productdetails&virtuemart_product_id=3286&virtuemart_category_id=33
        [addToCartButton] => 
        [images] => Array
            (
                [0] => VmImage Object
                    (
                        [media_attributes] => 0
                        [setRole] => 
                        [file_name] => 3316_1
                        [file_extension] => jpg
                        [virtuemart_media_id] => 4123
                        [_foldersToTest:VmMediaHandler:private] => Array
                            (
                                [0] => /home/universilibros/public_html/images/stories/virtuemart/product/
                                [1] => /home/universilibros/public_html/images/stories/virtuemart/product/resized/
                            )
    
                        [_actions:VmMediaHandler:private] => Array
                            (
                            )
    
                        [_mLocation:VmMediaHandler:private] => Array
                            (
                            )
    
                        [_hidden:VmMediaHandler:private] => Array
                            (
                            )
    
                        [theme_url] => components/com_virtuemart/
                        [virtuemart_vendor_id] => 1
                        [file_title] => Solucionario un recorrido por la geometria
                        [file_description] => 
                        [file_meta] => Libro: Solucionario un recorrido por la geometria - Autor: Germán Rincón Abella - Isbn: 6666
                        [file_class] => 
                        [file_mimetype] => image/jpeg
                        [file_type] => product
                        [file_url] => images/stories/virtuemart/product/3316_1.jpg
                        [file_url_thumb] => 
                        [published] => 1
                        [file_is_downloadable] => 0
                        [file_is_forSale] => 0
                        [file_is_product_image] => 0
                        [shared] => 0
                        [file_params] => 
                        [file_lang] => 
                        [created_on] => 2018-11-21 11:57:49
                        [created_by] => 639
                        [modified_on] => 2018-11-21 17:58:41
                        [modified_by] => 639
                        [file_url_folder] => images/stories/virtuemart/product/
                        [file_path_folder] => images/stories/virtuemart/product/
                        [file_url_folder_thumb] => images/stories/virtuemart/product/resized/
                        [media_role] => file_is_displayable
                        [file_name_thumb] => 3316_1_0x90
                    )
    
            )
    
        [file_url_thumb] => 
        [file_url] => images/stories/virtuemart/product/3316_1.jpg
        [stock] => stdClass Object
            (
                [stock_tip] => Hay gran cantidad de existencias de este producto
                [stock_level] => normalstock
            )
    
        [customfieldsSorted] => Array
            (
                [normal] => Array
                    (
                        [0] => stdClass Object
                            (
                                [virtuemart_custom_id] => 3
                                [custom_parent_id] => 0
                                [virtuemart_vendor_id] => 1
                                [custom_jplugin_id] => 0
                                [custom_element] => 0
                                [admin_only] => 0
                                [custom_title] => Indice
                                [show_title] => 0
                                [custom_tip] => 
                                [custom_value] => 
                                [custom_desc] => 
                                [field_type] => X
                                [is_list] => 0
                                [is_hidden] => 0
                                [is_cart_attribute] => 0
                                [is_input] => 0
                                [layout_pos] => 
                                [custom_params] => 0
                                [shared] => 0
                                [published] => 1
                                [ordering] => 0
                                [virtuemart_shoppergroup_id] => 
                                [virtuemart_customfield_id] => 17297
                                [virtuemart_product_id] => 3286
                                [customfield_value] => 

    CONTENIDO

    1. Geometría del triangulo
    • Medianas
    • Mediatices
    • Bisectrices
    • Alturas
    • Línea de Euler y círculo de los nueve puntos

     

    1. Círculo
    • Potencia de un punto
    • Eje radical
    • Línea de Simson

     

    1. Cuadriláteros
    • Cuadriláteros concíclicos
    • Cuadriláteros inscribibles

     

    1. Colinealidad y concurrencia
    • Teorema de Ceva
    • Teorema de Melaneo
    • Teorema de Pappus
    • Teorema de Pascal
    • Principios de dualidad

     

    1. Lugar Geométrico
    2. Transformaciones
    • Traslación
    • Reflexión
    • Rotación
    • Homotecia

     

    1. Conjugación Armónica
    • Puntos conjugados armónicos
    • Puntos y rectas polares

     

    1. Inversión
    2. Problemas olímpicos
    [customfield_price] => 0.000000 [customfield_params] => [fpublished] => 0 [override] => 0 [disabler] => 0 [_varsToPushParam] => 0 [display] =>

    CONTENIDO

    1. Geometría del triangulo
    • Medianas
    • Mediatices
    • Bisectrices
    • Alturas
    • Línea de Euler y círculo de los nueve puntos

     

    1. Círculo
    • Potencia de un punto
    • Eje radical
    • Línea de Simson

     

    1. Cuadriláteros
    • Cuadriláteros concíclicos
    • Cuadriláteros inscribibles

     

    1. Colinealidad y concurrencia
    • Teorema de Ceva
    • Teorema de Melaneo
    • Teorema de Pappus
    • Teorema de Pascal
    • Principios de dualidad

     

    1. Lugar Geométrico
    2. Transformaciones
    • Traslación
    • Reflexión
    • Rotación
    • Homotecia

     

    1. Conjugación Armónica
    • Puntos conjugados armónicos
    • Puntos y rectas polares

     

    1. Inversión
    2. Problemas olímpicos
    ) [1] => stdClass Object ( [virtuemart_custom_id] => 4 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Año [show_title] => 0 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 17298 [virtuemart_product_id] => 3286 [customfield_value] => 1996 [customfield_price] => 0.000000 [customfield_params] => [fpublished] => 0 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => 1996 ) [2] => stdClass Object ( [virtuemart_custom_id] => 5 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Terminado [show_title] => 0 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 17299 [virtuemart_product_id] => 3286 [customfield_value] => Tapa Blanda [customfield_price] => 0.000000 [customfield_params] => [fpublished] => 0 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => Tapa Blanda ) [3] => stdClass Object ( [virtuemart_custom_id] => 7 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Paginas [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 17300 [virtuemart_product_id] => 3286 [customfield_value] => 77 [customfield_price] => 0.000000 [customfield_params] => [fpublished] => 0 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => 77 ) [4] => stdClass Object ( [virtuemart_custom_id] => 11 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Edicion [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty="0"|selectType="0"| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 17301 [virtuemart_product_id] => 3286 [customfield_value] => Primera [customfield_price] => 0.000000 [customfield_params] => [fpublished] => 0 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => Primera ) ) ) )
    Precio de venta con descuento:
    Descuentos Universilibros10%
    Precio
    Antes:
    COP
    $ 24.000
    Ahora:
    COP
    $ 21.600
    Descuento: COP $ -2.400
    Precio / kg:
    TableProducts Object
    (
        [virtuemart_product_id] => 859
        [virtuemart_vendor_id] => 1
        [product_parent_id] => 0
        [product_sku] => 825
        [product_gtin] => 958-9029-81-7
        [product_mpn] => 9589029817
        [product_name] => La geometría de alberto durero. Estudio y modelación de sus construcciones
        [slug] => la-geometria-de-alberto-durero-estudio-y-modelacion-de-sus-construcciones
        [product_s_desc] => 
        [product_desc] => 

    El escenario natural para estudiar las posibles relaciones entre ciencia y arte es, sin duda alguna, el período conocido con el nombre de Renacimiento italiano. Hombres de ciencia como Benedetti, Galileo y Kepler adelantaron su trabajo científico influenciados en gran medida por sus orientaciones teóricas en relación con el arte: Benedetti y Galileo estaban especialmente interesados en las artes pictóricas, en tanto que Kepler y Galileo compartían una profunda admiración por la música. Hombres de arte como Piero della Francesca, Leonardo da Vinci y Durero sintieron la profunda necesidad de arraigar su práctica artística en principios universales provenientes de la matemática y la física. El matrimonio entre ciencia y arte produjo beneficios que se pueden sentir en cada uno de los extremos involucrados. A manera de ejemplo, los pintores adquirieron técnicas que les permitió representar en forma más convincente los espacios que exigían la presencia de la tercera dimensión, los científicos se vieron animados a discutir matemáticamente los fenómenos asociados con la percepción, y, por último, los matemáticos abrieron la posibilidad de construir y desarrollar una nueva rama adscrita a sus disciplinas, nos referimos a la geometría proyectiva.

    [product_weight] => 0.5000 [product_weight_uom] => KG [product_length] => 28.0000 [product_width] => 21.0000 [product_height] => 0.0000 [product_lwh_uom] => CM [product_url] => [product_in_stock] => 2 [product_ordered] => 0 [product_stockhandle] => 0 [low_stock_notification] => 0 [product_available_date] => 2017-04-24 12:01:32 [product_availability] => [product_special] => 0 [product_discontinued] => 0 [pordering] => 0 [product_sales] => 0 [product_unit] => KG [product_packaging] => 0 [product_params] => [intnotes] => [customtitle] => La geometría de alberto durero. Estudio y modelación de sus construcciones | Carlos Alberto Cardona Suárez | 9589029817 [metadesc] =>

    El escenario natural para estudiar las posibles relaciones entre ciencia y arte es, sin duda alguna, el período conocido con el nombre de Renacimiento italiano. Hombres de ciencia como Benedetti, Galileo y Kepler adelantaron su trabajo científico influenciados en gran medida por sus orientaciones teóricas en relación con el arte: Benedetti y Galileo...

    [metakey] => Exactas, Universidad Jorge Tadeo Lozano, Geometría, Carlos Alberto Cardona Suárez, 958-9029-81-7, 9789589029817 [metarobot] => [metaauthor] => Universilibros - Una institución al servicio de la cultura nacional [layout] => 0 [published] => 1 [product_canon_category_id] => [_lhash:VmTable:private] => 51d1357efc6d8434d826873cd563d6ac [_tbl:protected] => #__virtuemart_products [_tbl_lang:protected] => #__virtuemart_products_es_es [_tbl_key:protected] => virtuemart_product_id [_tbl_keys:protected] => Array ( [0] => virtuemart_product_id ) [_pkey:protected] => virtuemart_product_id [_pkeyForm:protected] => cid [_obkeys:protected] => Array ( [product_name] => 1 [slug] => 1 ) [_unique:protected] => 1 [_unique_name:protected] => Array ( [slug] => 1 ) [_orderingKey:protected] => ordering [_slugAutoName:protected] => product_name [_slugName:protected] => slug [_db:protected] => JDatabaseDriverMysqli Object ( [name] => mysqli [serverType] => mysql [connection:protected] => mysqli Object ( [affected_rows] => -1 [client_info] => mysqlnd 5.0.12-dev - 20150407 - $Id: 38fea24f2847fa7519001be390c98ae0acafe387 $ [client_version] => 50012 [connect_errno] => 0 [connect_error] => [errno] => 0 [error] => [error_list] => Array ( ) [field_count] => 1 [host_info] => Localhost via UNIX socket [info] => [insert_id] => 0 [server_info] => 5.7.28 [server_version] => 50728 [stat] => Uptime: 19101 Threads: 1 Questions: 1233550 Slow queries: 0 Opens: 43325 Flush tables: 1 Open tables: 2000 Queries per second avg: 64.580 [sqlstate] => 00000 [protocol_version] => 10 [thread_id] => 10603 [warning_count] => 0 ) [nameQuote:protected] => ` [nullDate:protected] => 0000-00-00 00:00:00 [_database:JDatabaseDriver:private] => universi_backup [count:protected] => 91 [cursor:protected] => [debug:protected] => [limit:protected] => 0 [log:protected] => Array ( ) [timings:protected] => Array ( ) [callStacks:protected] => Array ( ) [offset:protected] => 0 [options:protected] => Array ( [driver] => mysqli [host] => localhost [user] => universi_backup [password] => L2d604E=M7P~ [database] => universi_backup [prefix] => univer_ [select] => 1 [port] => 3306 [socket] => ) [sql:protected] => JDatabaseQueryMysqli Object ( [offset:protected] => 0 [limit:protected] => 0 [db:protected] => JDatabaseDriverMysqli Object *RECURSION* [sql:protected] => [type:protected] => select [element:protected] => [select:protected] => JDatabaseQueryElement Object ( [name:protected] => SELECT [elements:protected] => Array ( [0] => a.category_parent_id ) [glue:protected] => , ) [delete:protected] => [update:protected] => [insert:protected] => [from:protected] => JDatabaseQueryElement Object ( [name:protected] => FROM [elements:protected] => Array ( [0] => `#__virtuemart_category_categories` AS `a` ) [glue:protected] => , ) [join:protected] => [set:protected] => [where:protected] => JDatabaseQueryElement Object ( [name:protected] => WHERE [elements:protected] => Array ( [0] => `category_child_id` = "33" ) [glue:protected] => AND ) [group:protected] => [having:protected] => [columns:protected] => [values:protected] => [order:protected] => [autoIncrementField:protected] => [call:protected] => [exec:protected] => [union:protected] => [unionAll:protected] => [selectRowNumber:protected] => ) [tablePrefix:protected] => univer_ [utf:protected] => 1 [utf8mb4:protected] => 1 [errorNum:protected] => 0 [errorMsg:protected] => [transactionDepth:protected] => 0 [disconnectHandlers:protected] => Array ( ) ) [_rules:protected] => [_trackAssets:protected] => [_locked:protected] => [_loggable:protected] => 1 [_xParams] => product_params [_varsToPushParam] => Array ( [min_order_level] => Array ( [0] => [1] => float ) [max_order_level] => Array ( [0] => [1] => float ) [step_order_level] => Array ( [0] => [1] => float ) [product_box] => Array ( [0] => [1] => float ) ) [_translatable] => 1 [_translatableFields:protected] => Array ( [0] => product_name [1] => product_s_desc [2] => product_desc [3] => metadesc [4] => metakey [5] => customtitle [slug] => slug ) [_hashName:protected] => [_omittedHashFields:protected] => Array ( ) [_cryptedFields] => [_langTag:protected] => es_es [_ltmp] => [_loadedWithLangFallback] => 0 [_loaded] => 1 [_updateNulls:protected] => 1 [_toConvertDec:protected] => [_tablePreFix] => p. [_autoincrement] => 1 [_observers] => JObserverUpdater Object ( [aliases:protected] => Array ( ) [observers:protected] => Array ( ) [doCallObservers:protected] => 1 ) [created_on] => 2017-04-24 12:01:32 [created_by] => 634 [modified_on] => 2017-04-24 12:01:32 [modified_by] => 634 [min_order_level] => [max_order_level] => [step_order_level] => [product_box] => [allIds] => Array ( [0] => 859 ) [virtuemart_media_id] => Array ( [0] => 1218 ) [shoppergroups] => [allPrices] => Array ( [0] => Array ( [virtuemart_product_price_id] => 859 [virtuemart_product_id] => 859 [virtuemart_shoppergroup_id] => 0 [product_price] => 50000 [override] => 0 [product_override_price] => 0 [product_tax_id] => 0 [product_discount_id] => 0 [product_currency] => 31 [product_price_publish_up] => 0000-00-00 00:00:00 [product_price_publish_down] => 0000-00-00 00:00:00 [price_quantity_start] => 0 [price_quantity_end] => 0 [created_on] => 2017-04-24 12:01:32 [created_by] => 634 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [locked_on] => 0000-00-00 00:00:00 [locked_by] => 0 [costPrice] => 50000 [basePrice] => 50000 [basePriceVariant] => 50000 [basePriceWithTax] => 0 [discountedPriceWithoutTax] => 45000 [priceBeforeTax] => 45000 [salesPrice] => 45000 [taxAmount] => 0 [salesPriceWithDiscount] => 0 [salesPriceTemp] => 45000 [unitPrice] => 0 [discountAmount] => -5000 [priceWithoutTax] => 45000 [variantModification] => 0 [DBTax] => Array ( [2] => Array ( [0] => Descuento 10% [1] => 10.0000 [2] => -% [3] => 0 [4] => 31 [5] => [6] => 1 [7] => 2 ) ) [Tax] => Array ( ) [VatTax] => Array ( ) [DATax] => Array ( ) [Marge] => Array ( ) [salesPriceTt] => 45000 [discountedPriceWithoutTaxTt] => 45000 [priceWithoutTaxTt] => 45000 [discountAmountTt] => -5000 [taxAmountTt] => 0 ) ) [selectedPrice] => 0 [virtuemart_manufacturer_id] => Array ( ) [mf_name] => [mf_desc] => [mf_url] => [categoryItem] => Array ( [0] => Array ( [virtuemart_category_id] => 33 [virtuemart_vendor_id] => 1 [category_name] => Geometría [slug] => geometria [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros sobre Geometría | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 0000-00-00 00:00:00 [created_by] => 0 [modified_on] => 2017-03-22 14:08:14 [modified_by] => 634 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 4232 ) [1] => Array ( [virtuemart_category_id] => 106 [virtuemart_vendor_id] => 1 [category_name] => Libro [slug] => libro [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2016-08-05 15:55:35 [created_by] => 634 [modified_on] => 2016-08-21 02:46:29 [modified_by] => 634 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 4238 ) [2] => Array ( [virtuemart_category_id] => 109 [virtuemart_vendor_id] => 1 [category_name] => CD-DVD [slug] => cd-dvd [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2016-08-05 15:56:13 [created_by] => 634 [modified_on] => 2016-08-21 02:47:37 [modified_by] => 634 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 4239 ) [3] => Array ( [virtuemart_category_id] => 361 [virtuemart_vendor_id] => 1 [category_name] => Universidad Jorge Tadeo Lozano [slug] => universidad-jorge-tadeo-lozano [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros de Universidad Jorge Tadeo Lozano | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2017-02-23 19:06:07 [created_by] => 634 [modified_on] => 2017-04-24 18:02:43 [modified_by] => 634 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 4231 ) [4] => Array ( [virtuemart_category_id] => 1475 [virtuemart_vendor_id] => 1 [category_name] => Carlos Alberto Cardona Suárez [slug] => carlos-alberto-cardona-suarez [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros de Carlos Alberto Cardona Suárez | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2017-04-24 12:01:32 [created_by] => 634 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 4233 ) [5] => Array ( [virtuemart_category_id] => 1519 [virtuemart_vendor_id] => 1 [category_name] => Adelina Ocaña Gómez [slug] => adelina-ocana-gomez [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros de Adelina Ocaña Gómez | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2017-04-24 12:01:32 [created_by] => 634 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 4234 ) [6] => Array ( [virtuemart_category_id] => 1520 [virtuemart_vendor_id] => 1 [category_name] => Nathalie Josefina Dussan Robles [slug] => nathalie-josefina-dussan-robles [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros de Nathalie Josefina Dussan Robles | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2017-04-24 12:01:32 [created_by] => 634 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 4235 ) [7] => Array ( [virtuemart_category_id] => 1521 [virtuemart_vendor_id] => 1 [category_name] => Sonia Ivonne Cubillos Vanegas [slug] => sonia-ivonne-cubillos-vanegas [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros de Sonia Ivonne Cubillos Vanegas | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2017-04-24 12:01:32 [created_by] => 634 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 4236 ) [8] => Array ( [virtuemart_category_id] => 1522 [virtuemart_vendor_id] => 1 [category_name] => Julio César Ocaña Gómez [slug] => julio-cesar-ocana-gomez [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros de Julio César Ocaña Gómez | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2017-04-24 12:01:32 [created_by] => 634 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 4237 ) ) [canonCatId] => 33 [canonCatIdname] => [categories] => Array ( [0] => 33 [1] => 106 [2] => 109 [3] => 361 [4] => 1475 [5] => 1519 [6] => 1520 [7] => 1521 [8] => 1522 ) [virtuemart_category_id] => 33 [ordering] => 0 [id] => 4232 [category_name] => Geometría [orderable] => 1 [modificatorSum] => 0 [product_tax_id] => 0 [amount] => 1 [quantity] => 1 [prices] => Array ( [virtuemart_product_price_id] => 859 [virtuemart_product_id] => 859 [virtuemart_shoppergroup_id] => 0 [product_price] => 50000 [override] => 0 [product_override_price] => 0 [product_tax_id] => 0 [product_discount_id] => 0 [product_currency] => 31 [product_price_publish_up] => 0000-00-00 00:00:00 [product_price_publish_down] => 0000-00-00 00:00:00 [price_quantity_start] => 0 [price_quantity_end] => 0 [created_on] => 2017-04-24 12:01:32 [created_by] => 634 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [locked_on] => 0000-00-00 00:00:00 [locked_by] => 0 [costPrice] => 50000 [basePrice] => 50000 [basePriceVariant] => 50000 [basePriceWithTax] => 0 [discountedPriceWithoutTax] => 45000 [priceBeforeTax] => 45000 [salesPrice] => 45000 [taxAmount] => 0 [salesPriceWithDiscount] => 0 [salesPriceTemp] => 45000 [unitPrice] => 0 [discountAmount] => -5000 [priceWithoutTax] => 45000 [variantModification] => 0 [DBTax] => Array ( [2] => Array ( [0] => Descuento 10% [1] => 10.0000 [2] => -% [3] => 0 [4] => 31 [5] => [6] => 1 [7] => 2 ) ) [Tax] => Array ( ) [VatTax] => Array ( ) [DATax] => Array ( ) [Marge] => Array ( ) [salesPriceTt] => 45000 [discountedPriceWithoutTaxTt] => 45000 [priceWithoutTaxTt] => 45000 [discountAmountTt] => -5000 [taxAmountTt] => 0 ) [canonical] => index.php?option=com_virtuemart&view=productdetails&virtuemart_product_id=859&virtuemart_category_id=33 [link] => index.php?option=com_virtuemart&view=productdetails&virtuemart_product_id=859&virtuemart_category_id=33 [addToCartButton] => [images] => Array ( [0] => VmImage Object ( [media_attributes] => 0 [setRole] => [file_name] => 825_1 [file_extension] => jpg [virtuemart_media_id] => 1218 [_foldersToTest:VmMediaHandler:private] => Array ( [0] => /home/universilibros/public_html/images/stories/virtuemart/product/ [1] => /home/universilibros/public_html/images/stories/virtuemart/product/resized/ ) [_actions:VmMediaHandler:private] => Array ( ) [_mLocation:VmMediaHandler:private] => Array ( ) [_hidden:VmMediaHandler:private] => Array ( ) [theme_url] => components/com_virtuemart/ [virtuemart_vendor_id] => 1 [file_title] => La geometría de alberto durero. Estudio y modelación de sus construcciones [file_description] => [file_meta] => La geometría de alberto durero. Estudio y modelación de sus construcciones - Carlos Alberto Cardona Suárez - 9589029817 [file_class] => [file_mimetype] => image/jpeg [file_type] => product [file_url] => images/stories/virtuemart/product/825_1.jpg [file_url_thumb] => [published] => 1 [file_is_downloadable] => 0 [file_is_forSale] => 0 [file_is_product_image] => 0 [shared] => 0 [file_params] => [file_lang] => [created_on] => 2017-04-24 12:01:32 [created_by] => 634 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [file_url_folder] => images/stories/virtuemart/product/ [file_path_folder] => images/stories/virtuemart/product/ [file_url_folder_thumb] => images/stories/virtuemart/product/resized/ [media_role] => file_is_displayable [file_name_thumb] => 825_1_0x90 ) ) [file_url_thumb] => [file_url] => images/stories/virtuemart/product/825_1.jpg [stock] => stdClass Object ( [stock_tip] => Hay gran cantidad de existencias de este producto [stock_level] => normalstock ) [customfieldsSorted] => Array ( [normal] => Array ( [0] => stdClass Object ( [virtuemart_custom_id] => 16 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Indice - Url PDF [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0|multiplyPrice=""| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 4252 [virtuemart_product_id] => 859 [customfield_value] => /images/files/JTL077109-Indice.pdf [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => /images/files/JTL077109-Indice.pdf ) [1] => stdClass Object ( [virtuemart_custom_id] => 4 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Año [show_title] => 0 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 4253 [virtuemart_product_id] => 859 [customfield_value] => 2006 [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => 2006 ) [2] => stdClass Object ( [virtuemart_custom_id] => 5 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Terminado [show_title] => 0 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 4254 [virtuemart_product_id] => 859 [customfield_value] => Rustico [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => Rustico ) [3] => stdClass Object ( [virtuemart_custom_id] => 7 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Paginas [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 4255 [virtuemart_product_id] => 859 [customfield_value] => 366 [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => 366 ) [4] => stdClass Object ( [virtuemart_custom_id] => 11 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Edicion [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty="0"|selectType="0"| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 4256 [virtuemart_product_id] => 859 [customfield_value] => PRIMERA [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => PRIMERA ) [5] => stdClass Object ( [virtuemart_custom_id] => 12 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Temas Libro [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 4257 [virtuemart_product_id] => 859 [customfield_value] => Durero. Alberto 1471-1528-Crítica e interpretación.Pintores alemanes [customfield_price] => [customfield_params] => [fpublished] => 1 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => Durero. Alberto 1471-1528-Crítica e interpretación.Pintores alemanes ) ) ) )
    Precio de venta con descuento:
    Descuentos Universilibros10%
    Precio
    Antes:
    COP
    $ 50.000
    Ahora:
    COP
    $ 45.000
    Descuento: COP $ -5.000
    Precio / kg:

    Geometría vectorial | Fernando Valdes Macias

    Isbn: 978-958-722-198-5 | Año: 2014 | Páginas: 122
    TableProducts Object
    (
        [virtuemart_product_id] => 502
        [virtuemart_vendor_id] => 1
        [product_parent_id] => 0
        [product_sku] => 472
        [product_gtin] => 978-958-722-198-5
        [product_mpn] => 9789587221985
        [product_name] => Geometría vectorial
        [slug] => geometria-vectorial
        [product_s_desc] => 
        [product_desc] => 

    El camino hacia la creatividad es ver lo conocido con una referencia diferente: este libro introduce el estudio de ciertos temas de la geometría sintética o pura, utilizando las propiedades de los vectores; este estudio se denomina Geometría Vectorial, y se realiza considerando que cada figura geométrica tiene de manera intrínseca sus propiedades y que al adherir o superponer vectores que coinciden con los lados y formas de las figuras geométricas, se procede a extraer nuevas propiedades y demostraciones cuyos resultados se encuentran en los textos clásicos de geometría euclidiana. Cada figura es una síntesis de leyes que se descubren y se combinan para generar teoremas cuyas aplicaciones resultan interesantes para el entendimiento del espacio euclidiano. El análisis vectorial nos permite transformar en vectores cada segmento de las figuras geométricas y así por este camino llegar al estudio más a fondo de algunos teoremas y problemas de la geometría euclidiana.

    [product_weight] => 0.5000 [product_weight_uom] => KG [product_length] => 23.0000 [product_width] => 16.0000 [product_height] => 0.0000 [product_lwh_uom] => CM [product_url] => [product_in_stock] => 8 [product_ordered] => 0 [product_stockhandle] => 0 [low_stock_notification] => 0 [product_available_date] => 2017-03-28 17:30:27 [product_availability] => [product_special] => 0 [product_discontinued] => 0 [pordering] => 0 [product_sales] => 0 [product_unit] => KG [product_packaging] => 0 [product_params] => min_order_level=""|max_order_level=""|step_order_level=""|product_box=""| [intnotes] => [customtitle] => Geometría vectorial | Fernando Valdes Macias | 9789587221985 [metadesc] =>

    El camino hacia la creatividad es ver lo conocido con una referencia diferente: este libro introduce el estudio de ciertos temas de la geometría sintética o pura, utilizando las propiedades de los vectores; este estudio se denomina Geometría Vectorial, y se realiza considerando que cada figura geométrica tiene de manera intrínseca sus propiedades y...

    [metakey] => Exactas, Universidad Tecnológica de Pereira, Geometría, Fernando Valdes Macias, 978-958-722-198-5, 9789587221985 [metarobot] => [metaauthor] => Universilibros - Una institución al servicio de la cultura nacional [layout] => 0 [published] => 1 [product_canon_category_id] => [_lhash:VmTable:private] => fe3a5eaca043dfdc575de21160175dd1 [_tbl:protected] => #__virtuemart_products [_tbl_lang:protected] => #__virtuemart_products_es_es [_tbl_key:protected] => virtuemart_product_id [_tbl_keys:protected] => Array ( [0] => virtuemart_product_id ) [_pkey:protected] => virtuemart_product_id [_pkeyForm:protected] => cid [_obkeys:protected] => Array ( [product_name] => 1 [slug] => 1 ) [_unique:protected] => 1 [_unique_name:protected] => Array ( [slug] => 1 ) [_orderingKey:protected] => ordering [_slugAutoName:protected] => product_name [_slugName:protected] => slug [_db:protected] => JDatabaseDriverMysqli Object ( [name] => mysqli [serverType] => mysql [connection:protected] => mysqli Object ( [affected_rows] => -1 [client_info] => mysqlnd 5.0.12-dev - 20150407 - $Id: 38fea24f2847fa7519001be390c98ae0acafe387 $ [client_version] => 50012 [connect_errno] => 0 [connect_error] => [errno] => 0 [error] => [error_list] => Array ( ) [field_count] => 1 [host_info] => Localhost via UNIX socket [info] => [insert_id] => 0 [server_info] => 5.7.28 [server_version] => 50728 [stat] => Uptime: 19101 Threads: 1 Questions: 1233551 Slow queries: 0 Opens: 43325 Flush tables: 1 Open tables: 2000 Queries per second avg: 64.580 [sqlstate] => 00000 [protocol_version] => 10 [thread_id] => 10603 [warning_count] => 0 ) [nameQuote:protected] => ` [nullDate:protected] => 0000-00-00 00:00:00 [_database:JDatabaseDriver:private] => universi_backup [count:protected] => 91 [cursor:protected] => [debug:protected] => [limit:protected] => 0 [log:protected] => Array ( ) [timings:protected] => Array ( ) [callStacks:protected] => Array ( ) [offset:protected] => 0 [options:protected] => Array ( [driver] => mysqli [host] => localhost [user] => universi_backup [password] => L2d604E=M7P~ [database] => universi_backup [prefix] => univer_ [select] => 1 [port] => 3306 [socket] => ) [sql:protected] => JDatabaseQueryMysqli Object ( [offset:protected] => 0 [limit:protected] => 0 [db:protected] => JDatabaseDriverMysqli Object *RECURSION* [sql:protected] => [type:protected] => select [element:protected] => [select:protected] => JDatabaseQueryElement Object ( [name:protected] => SELECT [elements:protected] => Array ( [0] => a.category_parent_id ) [glue:protected] => , ) [delete:protected] => [update:protected] => [insert:protected] => [from:protected] => JDatabaseQueryElement Object ( [name:protected] => FROM [elements:protected] => Array ( [0] => `#__virtuemart_category_categories` AS `a` ) [glue:protected] => , ) [join:protected] => [set:protected] => [where:protected] => JDatabaseQueryElement Object ( [name:protected] => WHERE [elements:protected] => Array ( [0] => `category_child_id` = "33" ) [glue:protected] => AND ) [group:protected] => [having:protected] => [columns:protected] => [values:protected] => [order:protected] => [autoIncrementField:protected] => [call:protected] => [exec:protected] => [union:protected] => [unionAll:protected] => [selectRowNumber:protected] => ) [tablePrefix:protected] => univer_ [utf:protected] => 1 [utf8mb4:protected] => 1 [errorNum:protected] => 0 [errorMsg:protected] => [transactionDepth:protected] => 0 [disconnectHandlers:protected] => Array ( ) ) [_rules:protected] => [_trackAssets:protected] => [_locked:protected] => [_loggable:protected] => 1 [_xParams] => product_params [_varsToPushParam] => Array ( [min_order_level] => Array ( [0] => [1] => float ) [max_order_level] => Array ( [0] => [1] => float ) [step_order_level] => Array ( [0] => [1] => float ) [product_box] => Array ( [0] => [1] => float ) ) [_translatable] => 1 [_translatableFields:protected] => Array ( [0] => product_name [1] => product_s_desc [2] => product_desc [3] => metadesc [4] => metakey [5] => customtitle [slug] => slug ) [_hashName:protected] => [_omittedHashFields:protected] => Array ( ) [_cryptedFields] => [_langTag:protected] => es_es [_ltmp] => [_loadedWithLangFallback] => 0 [_loaded] => 1 [_updateNulls:protected] => 1 [_toConvertDec:protected] => [_tablePreFix] => p. [_autoincrement] => 1 [_observers] => JObserverUpdater Object ( [aliases:protected] => Array ( ) [observers:protected] => Array ( ) [doCallObservers:protected] => 1 ) [created_on] => 2017-03-28 17:30:27 [created_by] => 634 [modified_on] => 2017-03-29 16:33:40 [modified_by] => 639 [min_order_level] => [max_order_level] => [step_order_level] => [product_box] => [allIds] => Array ( [0] => 502 ) [virtuemart_media_id] => Array ( [0] => 845 ) [shoppergroups] => [allPrices] => Array ( [0] => Array ( [virtuemart_product_price_id] => 502 [virtuemart_product_id] => 502 [virtuemart_shoppergroup_id] => 0 [product_price] => 25000 [override] => 0 [product_override_price] => 0 [product_tax_id] => 0 [product_discount_id] => 0 [product_currency] => 31 [product_price_publish_up] => 0000-00-00 00:00:00 [product_price_publish_down] => 0000-00-00 00:00:00 [price_quantity_start] => 0 [price_quantity_end] => 0 [created_on] => 2017-03-28 17:30:27 [created_by] => 634 [modified_on] => 2017-03-29 16:33:40 [modified_by] => 639 [locked_on] => 0000-00-00 00:00:00 [locked_by] => 0 [costPrice] => 25000 [basePrice] => 25000 [basePriceVariant] => 25000 [basePriceWithTax] => 0 [discountedPriceWithoutTax] => 22500 [priceBeforeTax] => 22500 [salesPrice] => 22500 [taxAmount] => 0 [salesPriceWithDiscount] => 0 [salesPriceTemp] => 22500 [unitPrice] => 0 [discountAmount] => -2500 [priceWithoutTax] => 22500 [variantModification] => 0 [DBTax] => Array ( [2] => Array ( [0] => Descuento 10% [1] => 10.0000 [2] => -% [3] => 0 [4] => 31 [5] => [6] => 1 [7] => 2 ) ) [Tax] => Array ( ) [VatTax] => Array ( ) [DATax] => Array ( ) [Marge] => Array ( ) [salesPriceTt] => 22500 [discountedPriceWithoutTaxTt] => 22500 [priceWithoutTaxTt] => 22500 [discountAmountTt] => -2500 [taxAmountTt] => 0 ) ) [selectedPrice] => 0 [virtuemart_manufacturer_id] => Array ( ) [mf_name] => [mf_desc] => [mf_url] => [categoryItem] => Array ( [0] => Array ( [virtuemart_category_id] => 33 [virtuemart_vendor_id] => 1 [category_name] => Geometría [slug] => geometria [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros sobre Geometría | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 0000-00-00 00:00:00 [created_by] => 0 [modified_on] => 2017-03-22 14:08:14 [modified_by] => 634 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 2419 ) [1] => Array ( [virtuemart_category_id] => 106 [virtuemart_vendor_id] => 1 [category_name] => Libro [slug] => libro [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2016-08-05 15:55:35 [created_by] => 634 [modified_on] => 2016-08-21 02:46:29 [modified_by] => 634 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 2422 ) [2] => Array ( [virtuemart_category_id] => 370 [virtuemart_vendor_id] => 1 [category_name] => Universidad Tecnológica de Pereira [slug] => universidad-tecnologica-de-pereira [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros de Universidad Tecnológica de Pereira | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2017-02-23 19:42:27 [created_by] => 634 [modified_on] => 2017-03-28 22:36:10 [modified_by] => 634 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 2418 ) [3] => Array ( [virtuemart_category_id] => 988 [virtuemart_vendor_id] => 1 [category_name] => Fernando Valdes Macias [slug] => fernando-valdes-macias [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros de Fernando Valdes Macias | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2017-03-28 17:30:27 [created_by] => 634 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 2420 ) [4] => Array ( [virtuemart_category_id] => 989 [virtuemart_vendor_id] => 1 [category_name] => Hernando Parra Lara [slug] => hernando-parra-lara [category_description] => [category_template] => 0 [category_layout] => 0 [category_product_layout] => 0 [products_per_row] => 0 [ordering] => 0 [shared] => 0 [cat_params] => [limit_list_step] => 0 [limit_list_initial] => 0 [metadesc] => [customtitle] => Libros de Hernando Parra Lara | Universilibros [metakey] => [metarobot] => [metaauthor] => [published] => 1 [created_on] => 2017-03-28 17:30:27 [created_by] => 634 [modified_on] => 0000-00-00 00:00:00 [modified_by] => 0 [show_store_desc] => [showcategory_desc] => [showcategory] => [categories_per_row] => [showproducts] => [omitLoaded] => [showsearch] => [productsublayout] => [featured] => [featured_rows] => [omitLoaded_featured] => [discontinued] => [discontinued_rows] => [omitLoaded_discontinued] => [latest] => [latest_rows] => [omitLoaded_latest] => [topten] => [topten_rows] => [omitLoaded_topten] => [recent] => [recent_rows] => [omitLoaded_recent] => [id] => 2421 ) ) [canonCatId] => 33 [canonCatIdname] => [categories] => Array ( [0] => 33 [1] => 106 [2] => 370 [3] => 988 [4] => 989 ) [virtuemart_category_id] => 33 [ordering] => 0 [id] => 2419 [category_name] => Geometría [orderable] => 1 [modificatorSum] => 0 [product_tax_id] => 0 [amount] => 1 [quantity] => 1 [prices] => Array ( [virtuemart_product_price_id] => 502 [virtuemart_product_id] => 502 [virtuemart_shoppergroup_id] => 0 [product_price] => 25000 [override] => 0 [product_override_price] => 0 [product_tax_id] => 0 [product_discount_id] => 0 [product_currency] => 31 [product_price_publish_up] => 0000-00-00 00:00:00 [product_price_publish_down] => 0000-00-00 00:00:00 [price_quantity_start] => 0 [price_quantity_end] => 0 [created_on] => 2017-03-28 17:30:27 [created_by] => 634 [modified_on] => 2017-03-29 16:33:40 [modified_by] => 639 [locked_on] => 0000-00-00 00:00:00 [locked_by] => 0 [costPrice] => 25000 [basePrice] => 25000 [basePriceVariant] => 25000 [basePriceWithTax] => 0 [discountedPriceWithoutTax] => 22500 [priceBeforeTax] => 22500 [salesPrice] => 22500 [taxAmount] => 0 [salesPriceWithDiscount] => 0 [salesPriceTemp] => 22500 [unitPrice] => 0 [discountAmount] => -2500 [priceWithoutTax] => 22500 [variantModification] => 0 [DBTax] => Array ( [2] => Array ( [0] => Descuento 10% [1] => 10.0000 [2] => -% [3] => 0 [4] => 31 [5] => [6] => 1 [7] => 2 ) ) [Tax] => Array ( ) [VatTax] => Array ( ) [DATax] => Array ( ) [Marge] => Array ( ) [salesPriceTt] => 22500 [discountedPriceWithoutTaxTt] => 22500 [priceWithoutTaxTt] => 22500 [discountAmountTt] => -2500 [taxAmountTt] => 0 ) [canonical] => index.php?option=com_virtuemart&view=productdetails&virtuemart_product_id=502&virtuemart_category_id=33 [link] => index.php?option=com_virtuemart&view=productdetails&virtuemart_product_id=502&virtuemart_category_id=33 [addToCartButton] => [images] => Array ( [0] => VmImage Object ( [media_attributes] => 0 [setRole] => [file_name] => 472_1 [file_extension] => jpg [virtuemart_media_id] => 845 [_foldersToTest:VmMediaHandler:private] => Array ( [0] => /home/universilibros/public_html/images/stories/virtuemart/product/ [1] => /home/universilibros/public_html/images/stories/virtuemart/product/resized/ ) [_actions:VmMediaHandler:private] => Array ( ) [_mLocation:VmMediaHandler:private] => Array ( ) [_hidden:VmMediaHandler:private] => Array ( ) [theme_url] => components/com_virtuemart/ [virtuemart_vendor_id] => 1 [file_title] => Geometría vectorial [file_description] => [file_meta] => Geometría vectorial - Fernando Valdes Macias - 9789587221985 [file_class] => [file_mimetype] => image/jpeg [file_type] => product [file_url] => images/stories/virtuemart/product/472_1.jpg [file_url_thumb] => [published] => 1 [file_is_downloadable] => 0 [file_is_forSale] => 0 [file_is_product_image] => 0 [shared] => 0 [file_params] => [file_lang] => [created_on] => 2017-03-28 17:30:27 [created_by] => 634 [modified_on] => 2017-03-29 16:33:40 [modified_by] => 639 [file_url_folder] => images/stories/virtuemart/product/ [file_path_folder] => images/stories/virtuemart/product/ [file_url_folder_thumb] => images/stories/virtuemart/product/resized/ [media_role] => file_is_displayable [file_name_thumb] => 472_1_0x90 ) ) [file_url_thumb] => [file_url] => images/stories/virtuemart/product/472_1.jpg [stock] => stdClass Object ( [stock_tip] => Hay gran cantidad de existencias de este producto [stock_level] => normalstock ) [customfieldsSorted] => Array ( [normal] => Array ( [0] => stdClass Object ( [virtuemart_custom_id] => 3 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Indice [show_title] => 0 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => X [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => 0 [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 2285 [virtuemart_product_id] => 502 [customfield_value] =>
    1. Introducción a los vectores
    1.1 Magnitudes
    1.1.1 Vectores
    1.1.2 Igualdad de vectores
    1.2 Álgebra de vectores
    1.2.1 Suma geométrica de vectores
    1.2.2 Adherencia vectorial
    1.2.3 Ángulo entre vectores
    1.2.4 Magnitud de la suma de dos vectores
    1.2.5 Diferencia de vectores
    1.2.6 Referencia vectorial
    1.2.7 Multiplicación por escalares (Escalamiento)
    1.2.8 El vector unitario
    1.2.9 Problemas
    1.3 Dependencia lineal
    1.3.1 Problemas
    1.4 Formas simétricas de un vector
    1.4.1 Aplicaciones geométricas
    1.4.2 Problemas

    2. Producto escalar
    2.5 Propiedades del producto escalar
    2.5.1 Proyección vectorial y escalar
    2.5.2 Teorema de Pitágoras
    2.5.3 Problema de Stewart
    2.6 Problemas

    3. Vectores en coordenadas
    3.7 Vectores en JR2
    3.7.1 Propiedades
    3.7.2 Otra notación por componentes
    3.7.3 Distancia entre dos puntos
    3.7.4 Forma simétrica de un vector en coordenadas
    3.8 Vectores en R3
    3.8.1 Distancia entre puntos en R3
    3.9 Problemas
    3.10 Determinantes
    3.10.1 Propiedades de los determinantes
    3.10.2 Ejemplos
    3.10.3 Solución de ecuaciones
    3.11 Problemas

    4. Producto vectorial
    4.12 Producto cruz
    4.12.1 Representación geométrica del producto cruz
    4.12.2 Interpretación geométrica de la magnitud del producto cruz
    4.12.3 Propiedades del producto cruz
    4.13 Problemas
    4.14 La línea recta en el espacio
    4.14.1 Distancia de un punto a una recta
    4.15 Problemas
    4.16 El plano en el espacio
    4.17 Problemas

    5. Traslación y rotación de ejes
    5.17.1 Traslación
    5.17.2 Rotación
    5.17.3 Clasificación de las cónicas
    5.18 Problemas

    Conclusiones

    [customfield_price] => 0.000000 [customfield_params] => [fpublished] => 0 [override] => 0 [disabler] => 0 [_varsToPushParam] => 0 [display] =>
    1. Introducción a los vectores
    1.1 Magnitudes
    1.1.1 Vectores
    1.1.2 Igualdad de vectores
    1.2 Álgebra de vectores
    1.2.1 Suma geométrica de vectores
    1.2.2 Adherencia vectorial
    1.2.3 Ángulo entre vectores
    1.2.4 Magnitud de la suma de dos vectores
    1.2.5 Diferencia de vectores
    1.2.6 Referencia vectorial
    1.2.7 Multiplicación por escalares (Escalamiento)
    1.2.8 El vector unitario
    1.2.9 Problemas
    1.3 Dependencia lineal
    1.3.1 Problemas
    1.4 Formas simétricas de un vector
    1.4.1 Aplicaciones geométricas
    1.4.2 Problemas

    2. Producto escalar
    2.5 Propiedades del producto escalar
    2.5.1 Proyección vectorial y escalar
    2.5.2 Teorema de Pitágoras
    2.5.3 Problema de Stewart
    2.6 Problemas

    3. Vectores en coordenadas
    3.7 Vectores en JR2
    3.7.1 Propiedades
    3.7.2 Otra notación por componentes
    3.7.3 Distancia entre dos puntos
    3.7.4 Forma simétrica de un vector en coordenadas
    3.8 Vectores en R3
    3.8.1 Distancia entre puntos en R3
    3.9 Problemas
    3.10 Determinantes
    3.10.1 Propiedades de los determinantes
    3.10.2 Ejemplos
    3.10.3 Solución de ecuaciones
    3.11 Problemas

    4. Producto vectorial
    4.12 Producto cruz
    4.12.1 Representación geométrica del producto cruz
    4.12.2 Interpretación geométrica de la magnitud del producto cruz
    4.12.3 Propiedades del producto cruz
    4.13 Problemas
    4.14 La línea recta en el espacio
    4.14.1 Distancia de un punto a una recta
    4.15 Problemas
    4.16 El plano en el espacio
    4.17 Problemas

    5. Traslación y rotación de ejes
    5.17.1 Traslación
    5.17.2 Rotación
    5.17.3 Clasificación de las cónicas
    5.18 Problemas

    Conclusiones

    ) [1] => stdClass Object ( [virtuemart_custom_id] => 4 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Año [show_title] => 0 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 2286 [virtuemart_product_id] => 502 [customfield_value] => 2014 [customfield_price] => 0.000000 [customfield_params] => addEmpty=0|selectType=0| [fpublished] => 0 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => 2014 ) [2] => stdClass Object ( [virtuemart_custom_id] => 5 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Terminado [show_title] => 0 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 2287 [virtuemart_product_id] => 502 [customfield_value] => Rustico [customfield_price] => 0.000000 [customfield_params] => addEmpty=0|selectType=0| [fpublished] => 0 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => Rustico ) [3] => stdClass Object ( [virtuemart_custom_id] => 7 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Paginas [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 2288 [virtuemart_product_id] => 502 [customfield_value] => 122 [customfield_price] => 0.000000 [customfield_params] => addEmpty=0|selectType=0| [fpublished] => 0 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => 122 ) [4] => stdClass Object ( [virtuemart_custom_id] => 11 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Edicion [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty="0"|selectType="0"| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 2289 [virtuemart_product_id] => 502 [customfield_value] => PRIMERA [customfield_price] => 0.000000 [customfield_params] => addEmpty=0|selectType=0| [fpublished] => 0 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => PRIMERA ) [5] => stdClass Object ( [virtuemart_custom_id] => 12 [custom_parent_id] => 0 [virtuemart_vendor_id] => 1 [custom_jplugin_id] => 0 [custom_element] => 0 [admin_only] => 0 [custom_title] => Temas Libro [show_title] => 1 [custom_tip] => [custom_value] => [custom_desc] => [field_type] => S [is_list] => 0 [is_hidden] => 0 [is_cart_attribute] => 0 [is_input] => 0 [layout_pos] => [custom_params] => addEmpty=0|selectType=0| [shared] => 0 [published] => 1 [ordering] => 0 [virtuemart_shoppergroup_id] => [virtuemart_customfield_id] => 2290 [virtuemart_product_id] => 502 [customfield_value] => Geometrial vectorial.Analisis vectorial.Problemas, ejercicios.Universidad tecnologica de pereira [customfield_price] => 0.000000 [customfield_params] => addEmpty=0|selectType=0| [fpublished] => 0 [override] => 0 [disabler] => 0 [_varsToPushParam] => Array ( [addEmpty] => Array ( [0] => 0 [1] => int ) [selectType] => Array ( [0] => 0 [1] => int ) [multiplyPrice] => Array ( [0] => [1] => string ) [transform] => Array ( [0] => [1] => area ) ) [addEmpty] => 0 [selectType] => 0 [multiplyPrice] => [transform] => [_xParams] => customfield_params [display] => Geometrial vectorial.Analisis vectorial.Problemas, ejercicios.Universidad tecnologica de pereira ) ) ) )
    Precio de venta con descuento:
    Descuentos Universilibros10%
    Precio
    Antes:
    COP
    $ 25.000
    Ahora:
    COP
    $ 22.500
    Descuento: COP $ -2.500
    Precio / kg: