1. A point is that which has no parts, or which has no magnitude. 2. A line is length without breadth. 3. The extremities of a line are points. 4. A straight line is that which lies evenly between its extreme points. 5. A superficies is that which has only length and breadth. 6. The extremities of a superficies are lines. 7. A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. 8. A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction. 9. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line. 10. When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
11. An obtuse angle is that which is greater than a right angle. 12. An acute angle is that which is less than a right angle. 13. A term or boundary is the extremity of any thing. 16. And this point is called the centre of the circle. 17. A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. 18. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter. 19. A segment of a circle is the figure contained by a straight line and the circumference which it cuts off. 29. An acute-angled triangle is that which has three acute angles. 34. All other four-sided figures besides these are called trapeziums. Note. The terms oblong and rhomboid are not often used. Practically the following definitions are used. Any four-sided figure is called a quadrilateral. A line joining two opposite angles of a quadrilateral is called a diagonal.
A quadrilateral which has its opposite sides parallel is called a parallelogram. The words square and rhombus are used in the sense defined by Euclid; and the word rectangle is used instead of the word oblong. 3. And that a circle may be described from any centre, at any distance from that centre. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal. 3. If equals be taken from equals the remainders are equal. 4. If equals be added to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 9. The whole is greater than its part.
10. Two straight lines cannot enclose a space. 11. All right angles are equal to one another. 12. If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles, these straight lines, being continually produced, shall at length meet on that side on which are the angles which are less than two right angles. To describe an equilateral triangle on a given finite straight line. Let AB be the given straight line; it is required to describe an equilateral triangle on AB. From the centre A at the distance AB describe the circle BCD. From the centre B, at the distance BA, describe the circle ACE. ABC shall be an equilateral triangle. Because the point A is the centre of the circle BCD, Balance Bloom CBD AC is equal to AB. And because the point B is the centre of the circle ACE, BC is equal to BA.