THE ELEMENTS OF GEOMETRY. BOOK I DEFINITIONS. 1. A Solid is that which has length, breadth and thickness. 2. A Superficies is one of the bounds of a folid, and has length and breadth without thickness. 3. A Line is one of the bounds of a fuperficies, and has length without breadth or thickness. 4. A Point is one of the extremities of a line, and has neither length, breadth, nor thickness. 5. A right line is that which has all its parts lying in the fame direction. 6. A plane fuperficies is that which is every where perfectly flat and even. 7. A plain rectilineal angle is the inclination or opening of two right lines which meet in a point. 8. One right line is faid to be perpendicular to another, when it makes the angles on both fides of it equal to each other. 9. A right angle is that which is made by two right lines that are perpendicular to each other. 10. An obtufe angle is that which is greater than a right angle. 11. An acute angle is that which is less than a right angle. 12. A figure is that which is inclosed by one or more boundaries. 13. A circle is a plane figure, contained by one line, called the circumference, which is every where equally diftant from a point within the figure, called the centre. О 14. Rectilineal figures are those which are contained by right lines. 15. All plane figures, bounded by three right lines, are called triangles. 16. An equilateral triangle, is that which has all its fides equal to each other. 17. An ifofceles triangle, is that which has only two of its fides equal to each other. A 18. A right-angled triangle, is that which has one right angle; the fide which is opposite to the right angle being called the hypothenuse. 19. An obtufe-angled triangle, is that which has one obtufe angle. 20. Parallel right lines are fuch as are in the fame plane, and which, being produced ever fo far both ways, will never meet. 21. Every plane figure, bounded by four right lines, is called a quadrangle, or quadrilateral. 22. A parallelogram, is a quadrangle whofe oppofite fides are parallel. 23. The diagonal of a quadrangle, is a right line joining any two of its oppofite angles. 24. The base of any figure is that fide upon which it is supposed to stand; and the vertical angle is that which is oppofite to the base. NOTE, When an angle is expressed by means of three letters, the one which ftands at the angular point, must always be placed in the middle. POSTULATES. 1. Let it be granted that a right line may be drawn from any one given point to another. 2. That a terminated right line, may be produced to any length in a right line. 3. That a circle may be defcribed from any point as a centre, at any distance from that centré. 4. And that a right line, which meets one of two parallel right lines, may be produced till it meets the other. AXIOM S. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals the wholes will be equal. 3. If equals be taken from equals the remainders will be equal. 4. If equals be added to unequals the wholes will be unequal. |