The Project Gutenberg eBook of 海島算經, by active 3rd century-4th century Hui Liu

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。

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