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本文目的:在闡述單用一圆規所能作的圖形的範圍。本文结论:凡能用直尺圆規作出的點,單用一圆規也能作出。凡能用直尺圆規作出的點都不外乎三種情况:ⅰ.直綫與圆的交點;ⅱ.直线与直线的交點;ⅲ.圆与圆的交點。情况ⅲ可單用一圆規作出其理自明,不必再證;而直线又總是聯结二點作出的。因此,要達到上述結論,只須也是必須證明以下兩點:
The purpose of this article is to explain the range of figures that can be made using a compass alone. The paper concludes that any point that can be made with a ruler can be made with a compass only. The points that can be made with a ruler are nothing more than three things: i. the intersection of a line and a circle; ii. the intersection of a straight line and a straight line; iii. the intersection of a circle and a circle. Case iii can be self-explanatory with a compass alone and no longer need to be proved; the straight line is always made in conjunction with two points. Therefore, in order to achieve the above conclusions, it is only necessary and must prove the following two points: