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Title: 海島算經 Author: active 3rd century-4th century Hui Liu Release date: October 20, 2008 [eBook #26979] Most recently updated: January 4, 2021 Language: Chinese Credits: Produced by Yvonne *** START OF THE PROJECT GUTENBERG EBOOK 海島算經 *** Produced by Yvonne 今有望海島，立兩表，齊高三丈，前後相去千步，令後表與前表參相直。從前表 卻行一百二十三步，人目著地取望島峯，與表末參合。從後表卻行一百二十七步 ，人目著地取望島峯，亦與表末參合。問島高及去表各幾何？ 答曰：島高四里五十五步；去表一百二里一百五十步。 術曰：以表高乘表間為實；相多為法，除之。所得加表高，即得島高。求前表去 島遠近者：以前表卻行乘表間為實；相多為法。除之，得島去表數。 今有望松生山上，不知高下。立兩表齊，高二丈，前後相去五十步，令後表與前 表參相直。從前表卻行七步四尺，薄地遙望松末，與表端參合。又望松本，入表 二尺八寸。复從後表卻行八步五尺，薄地遙望松末，亦與表端參合。問松高及山 去表各幾何？ 答曰：松高一十二丈二尺八寸；山去表一里二十八步、七分步之四。 術曰：以入表乘表間為實。相多為法，除之。加入表，即得松高。求表去山遠近 者：置表間，以前表卻行乘之為實。相多為法，除之，得山去表。 今有南望方邑，不知大小。立兩表東、西去六丈，齊人目，以索連之。令東表與 邑東南隅及東北隅參相直。當東表之北卻行五步，遙望邑西北隅，入索東端二丈 二尺六寸半。又卻北行去表一十三步二尺，遙望邑西北隅，適與西表相參合。問 邑方及邑去表各幾何？ 答曰：邑方三里四十三步、四分步之三；邑去表四里四十五步。 術曰：以入索乘後去表，以兩表相去除之，所得為景差；以前去表減之，不盡以 為法。置後去表，以前去表減之，餘以乘入索為實。實如法而一，得邑方。求去 表遠近者：置後去表，以景差減之，餘以乘前去表為實。實如法而一，得邑去表 。 今有望深谷，偃矩岸上，令句高六尺。從句端望谷底，入下股九尺一寸。又設重 矩于上，其矩間相去三丈。更從句端望谷底，入上股八尺五寸。問谷深幾何？ 答曰：四十一丈九尺。 術曰：置矩間，以上股乘之，為實。上、下股相減，餘為法，除之。所得以句高 減之，即得谷深。 今有登山望樓，樓在平地。偃矩山上，令句高六尺。從句端斜望樓足，入下股一 丈二尺。又設重矩于上，令其間相去三丈。更從句端斜望樓足，入上股一丈一尺 四寸。又立小表于入股之會，復從句端斜望樓岑端，入小表八寸。問樓高幾何？ 答曰：八丈。 術曰：上下股相減，餘為法；置矩閒，以下股乘之，如句高而一。所得，以入小 表乘之，為實。實如法而一，即是樓高。 今有東南望波口，立兩表南、北相去九丈，以索薄地連之。當北表之西卻行去表 六丈，薄地遙望波口南岸，入索北端四丈二寸。以望北岸，入前所望表里一丈二 尺。又卻後行1去表一十三丈五尺。薄地遙望波口南岸，與南表參合。問波口廣 幾何？ 答曰：一里二百步。 術曰：以後去表乘入索，如表相去而一。所得，以前去表減之，餘以為法；復以 前去表減後去表，餘以乘入所望表里為實，實如法而一，得波口廣。 今有望清淵，淵下有白石。偃矩岸上，令句高三尺。斜望水岸，入下股四尺五寸 。望白石，入下股二尺四寸。又設重矩于上，其間相去四尺。更從句端斜望水岸， 入上股四尺。以望白石，入上股二尺二寸。問水深幾何？ 答曰：一丈二尺。 術曰：置望水上下股相減，餘以乘望石上股為上率。又以望石上下股相減，餘以 乘望水上股為下率。兩率相減，餘以乘矩間為實；以二差相乘為法。實如法而一 ，得水深。 又術：列望水上下股及望石上下股，相減，餘幷為法。以望石下股減望水下股， 餘以乘矩間為實，實如法而一，得水深。 今有登山望津，津在山南。偃矩山上，令句高一丈二尺。從句端斜望津南岸，入 下股二丈三尺一寸。又望津北岸，入前望股裏一丈八寸。更登高巖北，卻行二十 二步，上登五十一步，偃矩山上。更從句端斜望津南岸，入上股二丈二尺。問津 廣幾何？ 答曰：二里一百二步。 術曰：以句高乘下股，如上股而一。所得以句高減之，餘為法；置北行，以句高 乘之，如上股而一。所得以減上登，餘以乘入股裏為實。實如法而一，即得津廣 。 今有登山臨邑，邑在山南。偃矩山上，令句高三尺五寸。令句端與邑東南隅及東 北隅參相直。從句端遙望東北隅，入下股一丈二尺。又施橫句于入股之會，從立 句端望西北隅，入橫句五尺。望東南隅，入下股一丈八尺。又設重矩于上，令矩 間相去四丈。更從立句端望東南隅，入上股一丈七尺五寸。問邑廣長各幾何？ 答曰：南北長一里一百步；東西廣一里三十三步、少半步。 術曰：以句高乘東南隅入下股，如上股而一，所得減句高，餘為法；以東北隅下 股減東南隅下股，餘以乘矩間為實。實如法而一，得邑南北長也。求邑廣：以入 橫句乘矩間為實。實如法而一，即得邑東西廣。 *** END OF THE PROJECT GUTENBERG EBOOK 海島算經 *** Updated editions will replace the previous one—the old editions will be renamed. 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