Note: Since these definitions are from the first book of the Elements, we shall denote them by a "I." followed by their number. We also broke some of the original definitions into parts to facilitate the memorization.
Definition I.1. A point is that of which there is no part: no length and no breadth.
Definition I.2. A line is a length without breadth.
Definition I.3. The extremities of a line are points.
Definition I.4. A straight line is one which lies evenly with points on itself.
Definition I.5. A surface is that which has length and breadth only.
Definition I.6. The extremities of a surface are lines.
Definition I.7. A plane surface is one which lies evenly with the straight-lines on itself.
Definition I.8. A plane angle is the inclination of the lines to one another, when two lines in a plane meet one another, and are not lying in a straight-line.
Definition I.9. An angle is called rectilinear when the lines containing it are straight.
Definition I.10a. When a straight-line stood upon another straight-line makes adjacent angles which are equal to one another, each of the equal angles is a right-angle.
Definition I.10b. When a straight-line stood upon another straight-line makes adjacent angles which are equal to one another, the two straight-lines are said to be perpendicular to one another.
Definition I.11. An obtuse angle is one which is greater than a right-angle.
Definition I.12. An acute angle is one which is less than a right-angle.
Definition I.13. A boundary is that which is the extremity of something.
Definition I.14. A figure is that which is contained by some boundary.
Definition I.15a. A circle is a plane figure contained by a single line, called circumference, such that all of the straight-lines radiating towards the circumference from one point amongst those lying inside the figure are equal to one another.
Definition I.15b. The circumference of a circle is the boundary of the circle.
Definition I.16. The center of a circle is the point lying inside the circle such that all of the straight-lines from it to the circumference are equal to one another.
Definition I.17a. The radius of a circle is a straight-line from the center of the circle to a point on the circumference.
Definition I.17b. The diameter of a circle is a straight-line between two points on the circumference that passes through the center of the circle.
Definition I.18. A semi-circle is one of the two halves of a circle bounded by the circumference and a diameter.
Definition I.19a. A rectilinear figure is a figure contained by straight-lines.
Definition I.19b. A triangle is a rectilinear figure with three sides.
Definition I.19c. A quadrilateral is a rectilinear figure with four sides.
Definition I.20a. An equilateral triangle is a triangle having three equal sides.
Definition I.20b. An isosceles triangle is a triangle having only two equal sides.
Definition I.20c. A scalene triangle is a triangle having three unequal sides.
Definition I.21a. A right-angled triangle is a triangle having a right-angle.
Definition I.21b. A obtuse-angled triangle is a triangle having an obtuse angle.
Definition I.21c. A acute-angled triangle is a triangle having three acute angles.
Definition I.22a. A square is a quadrilateral having four right-angles and four equal sides.
Definition I.22b. A rectangle is a quadrilateral having four right-angles, but that is not a square.
Definition I.22c. A rhombus is a quadrilateral having four equal sides, but that is not a square.
Definition I.22d. A rhomboid is a quadrilateral having opposite sides and angles equal to each other, but that is not a square, a rectangle, or a rhombus.
Definition I.22e. A trapezia is a quadrilateral that is not a square, a rectangle, a rhombus, or a rhomboid.
Definition I.23. Parallel lines are straight-lines that, being in the same plane, never meet one another even if prolonged to infinity in each direction.
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