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Euclid: Elementa

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DEFINITIONS. 
DEFINITIONES. 
界說二則 
1 Any rectangular parallelogram is said to be contained by the two straight lines containing the right angle. 
OMNE parallelogrammum rectangulum contineri dicitur sub rectis duabus lineis, quæ rectum comprehendunt angulum. 
第一界
凡直角形之兩邊、函一直角者。為直角形之矩線。
如甲乙、偕乙丙。函甲乙丙直角。得此兩邊。卽知直角形大小之度。今別作戊線、己線。與甲乙、乙丙、各等。亦卽知甲乙丙丁直角形大小之度。則戊、偕己、兩線。為直角形之矩線。
此例與算法通。如上圖。一邊得三。一邊得四。相乘得十二。則三、偕四、兩邊、為十二之矩數。凡直角諸形之內四角、皆直。故不必更言四邊、及平行線。止名為直角形。省文也。
凡直角諸形。不必全舉四角。止舉對角二字。卽指全形。如甲乙丙丁直角形。止舉甲丙、或乙丁。亦省文也。 
2 And in any parallelogrammic area let any one whatever of the parallelograms about its diameter with the two complements be called a gnomon. 
IN omni parallelogrammo spatio, vnumquodlibet eorum, quæ circa diametrum illius sunt, parallelogrammorum, cum duobus complementis, Gnomon vocetur. 
第二界
諸方形、有對角線者。其兩餘方形。任偕一角線方形。為罄折形。(p. 八四)
甲乙丙丁、方形。任直、斜角。作甲丙對角線。從庚點作戊己、辛壬、兩線。與方形邊平行。而分本形為四方形。其辛己、庚乙、兩形為餘方形。辛戊、己壬、兩形為角線方形。一卷界 \\ 說三六兩餘方形。任偕一角線方形。為罄折形。如辛己、庚乙、兩餘方形。偕己壬角線方形。同在癸子丑圜界內者。是癸子丑罄折形也。用辛戊角線方形、倣此。 
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