A point is that which has no part.
点是没有部分的东西。
A line is breadthless length.
线是没有宽度的长度。
The extremities of a line are points.
线的端是点。
A straight line is a line which lies evenly with the points on itself.
直线是同它上面的点平直相处的线。
A surface is that which has length and breadth only.
面只有长度和宽度。
The extremities of a surface are lines.
面的端是线。
A plane surface is a surface which lies evenly with the straight lines on itself.
平面是同它上面的直线平直相处的面。
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.
平面角是在同一平面内相交而不成一直线的两条线彼此倾斜所成。
And when the lines containing the angle are straight, the angle is called rectilineal.
如果成角的两条线都是直线，这个角叫直线角。
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.
一条直线立在另一条直线上，使相邻两角相等，则这两个角都是直角，立着的线叫作垂线。
An obtuse angle is an angle greater than a right angle.
大于直角的角叫钝角。
An acute angle is an angle less than a right angle.
小于直角的角叫锐角。
A boundary is that which is an extremity of anything.
界是某物的端。
A figure is that which is contained by any boundary or boundaries.
图形是被一个或多个界围成的东西。
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;
圆是一个平面图形，由一条线围成；从图形内某一点到这条围线的所有直线都相等。
And the point is called the centre of the circle.
这个点叫圆心。
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.
直径是过圆心并在两端落到圆周上的任一直线；它也把圆分成两半。
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.
半圆是由直径和被直径截下的圆周围成的图形；半圆的圆心同原圆的圆心相同。
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.
直线形是由直线围成的图形：三边形由三条直线围成，四边形由四条直线围成，多边形由四条以上直线围成。
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.
在三边形中，三边相等的是等边三角形，只有两边相等的是等腰三角形，三边都不相等的是不等边三角形。
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 acuteangled triangle that which has its three angles acute.
在三边形中，有一个直角的是直角三角形，有一个钝角的是钝角三角形，三个角都是锐角的是锐角三角形。
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.
在四边形中，四边相等且四角都是直角的是正方形；四角都是直角但四边不全相等的是长方形；四边相等但角不是直角的是菱形；对边和对角相等但四边不全相等且角不是直角的是斜方形；其余四边形叫梯形。
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.
平行直线是在同一平面内、向两端无限延长也不会相交的直线。