定义 Definitions[1]
01 / 点是没有部分的东西。
A pointis that which has no part.
02 / 线是没有宽的长。
A lineis breadthless length.
03 / 线之端是点。
The extremities of a line are points.
04 / 直线[2]是其上均匀放置着点的线。
A straightline is a line which lies evenly with the points on itself.
05 / 面是只有长和宽的东西。
A surfaceis 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 surfaceis 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 angleis 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 perpendicularto that on which it stands.
11 / 钝角是大于直角的角。
An obtuse angleis an angle greater than a right angle.
12 / 锐角是小于直角的角。
An acute angleis an angle less than a right angle.
13 / 边界是某个东西的端。
A boundaryis 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 figureis 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 circleis 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 centreof 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 diameterof 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[3]所围成的图形。且半圆的心和圆心相同。
A semicircleis 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 figuresare those which are contained by straight lines, trilateralfigures being those contained by three, quadrilateralthose contained by four, and multilateralthose 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 triangleis that which has its three sides equal, an isosceles trianglethat which has two of its sides alone equal, and a scalene trianglethat 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 triangleis that which has a right angle, an obtuse-angled trianglethat which has an obtuse angle, and an acute-angled trianglethat 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 squareis that which is both equilateral and right-angled; an oblongthat which is right-angled but not equilateral; a rhombusthat which is equilateral but not right-angled; and a rhomboidthat 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 linesare straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.
[1]欧几里得的希腊文本（第一个印刷版于1533年问世）中的定义、公设和公理本来是没有编号的。其定义是连续地叙述出来的，它更像是一篇讨论术语如何使用的序言，而不是充当后续命题的公理基础。这里我们遵循英译者托马斯·希思（Thomas L. Heath）所使用的格式。（译者注）
[2]按照现在的理解，直线是无限的，而希腊人所说的直线却是有限的，本书没有按照现在的理解把“直线”译成“线段”。此外，对于这个“直线”定义，其希腊文原文的含义非常模糊，历史上有着各种不同解读，希思给出的英译文也不够明确。有兴趣的读者可查阅希思所作的解说。（译者注）
[3]按照现在的理解，“圆周”是一个正圆，而希腊人所说的“圆周”却是圆的一部分，相当于现在所说的“弧”。本书没有按照现在的理解把“圆周”译成“弧”。（译者注）

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