01 / 点 是没有部分的东西。

A point is that which has no part.

02 / 线 是没有宽的长。

A line is breadthless length.

03 / 线之端是点。

The extremities of a line are points.

04 / 直线 是其上均匀放置着点的线。

A straight line is a line which lies evenly with the points on itself.

05 / 面 是只有长和宽的东西。

A surface is that which has length and breadth only.

06 / 面之端是线。

The extremities of a surface are lines.

07 / 平面 是其上均匀放置着直线的面。

A plane surface is a surface which lies evenly with the straight lines on itself.

08 / 平面角 是一个平面上两条线之间的倾斜，它们相交且不在一条直线上。

A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.

09 / 且当夹这个角的线是直线时，这个角叫作 直线角 。

And when the lines containing the angle are straight, the angle is called rectilineal .

10 / 当一条直线与另一条直线交成的邻角彼此相等时，这些等角中的每一个都是 直角 ，且称这条直线 垂直 于另一条直线。

When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right , and the straight line standing on the other is called a perpendicular to that on which it stands.

11 / 钝角 是大于直角的角。

An obtuse angle is an angle greater than a right angle.

12 / 锐角 是小于直角的角。

An acute angle is an angle less than a right angle.

13 / 边界 是某个东西的端。

A boundary is that which is an extremity of anything.

14 / 形 是由某一边界或若干边界所围成的东西。

A figure is that which is contained by any boundary or boundaries.

15 / 圆 是由一条线所围成的平面形，其内有一点与这条线上的点连成的所有线段都相等；

A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another;

16 / 且这个点叫作 圆心 。

And the point is called the centre of the circle.

17 / 圆的 直径 是任意一条过圆心作出且沿两个方向被圆周截得的直线，且该直线把圆二等分。

A diameter of the circle is any straight line drawn through the centre and terminated in both directions by the circumference of the circle, and such a straight line also bisects the circle.

18 / 半圆 是由直径和它截得的圆周 所围成的图形。且半圆的心和圆心相同。

A semicircle is the figure contained by the diameter and the circumference cut off by it. And the centre of the semicircle is the same as that of the circle.

19 / 直线形 是由直线围成的形， 三边形 是由三条直线围成的形， 四边形 是由四条直线围成的形， 多边形 是由四条以上直线围成的形。

Rectilineal figures are those which are contained by straight lines, trilateral figures being those contained by three, quadrilateral those contained by four, and multilateral those contained by more than four straight lines.

20 / 在三边形中，三边均相等的叫作 等边三角形 ，只有两边相等的叫作 等腰三角形 ，三边各不相等的叫作 不等边三角形 。

Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal.

21 / 此外，在三边形中，有一个直角的叫作 直角三角形 ，有一个钝角的叫作 钝角三角形 ，三个角均为锐角的叫作 锐角三角形 。

Further, of trilateral figures, a right-angled triangle is that which has a right angle, an obtuse-angled triangle that which has an obtuse angle, and an acute-angled triangle that which has its three angles acute.

22 / 在四边形中，等边且均为直角的叫作 正方形 ，均为直角但不等边的叫作 长方形 ，等边但非直角的叫作 菱形 ，对角对边相等但不等边且非直角的叫作 长菱形 ，其他四边形叫作 不规则四边形 。

Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia .

23 / 平行 直线 是同一平面上沿两个方向无定限延长、不论沿哪个方向都不相交的直线。

Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction. obvuUQt+KSQrctqOtdFB119m4TunqLOFtLXkXI9EMwhypuR8tDY+gmsqjemzGuZq