GEOMETRY," DEFINITIONS, 1. A POINT is that, which has position, but not magnitude, 2. A line is length, without breadth or thickness. 3. A surface, or superficies, is an extension, or a figure, of two dimensions, length and breadth, but without thickness. 4. A body, or solid, is a figure of three dimensions, namely, length, breadth and thickness. Hence surfaces are the extremities of solids; lines the extremities of surfaces; and points the extremities of lines. 5. Lines * A TUTOR teaches Simson's Edition of EUCLID'S ELE ENTS of GEOMETRY in Harvard College, 5. Lines are either right, or curved, or mixed of these two. 6. A right line, or straight line, lies all in the same direction between its extremities, and is the shortest distance between two points. 7. A curve continually changes its direction between its extreme points. 8. Lines are either parallel, oblique, perpendicular, or tangential. 9. Parallel lines are always at the same distance, and never meet, though ever so far produced, 10. Oblique right lines change their distance, and would meet, if produced, on the side of the least distance. 11. One line is perpendicular to another, when it inclines not more on one side than on the other. 12. One line is tangential, or a tangent, to another, when it touches it without cutting, if both be pro duced. 13. An angle is te inclination, or opening, of two lines, having different directions, and meeting in a point. 14. Angles are right or oblique, acute or obtuse. 15. A right angle is that, which is made by one line perpendicular to an◄ other. Or when the angles on each side are equal to one other, they are right angles. 19. Superficies are either plane or curved. 20. A plane superficies, or a plane, is that, with which a right line may, every way, coincide. But if not, it is curved. 21. Plane figures are bounded either by right lines or curves. 22. Plane figures, bounded by right lines, have names according to the number of their sides, or angles; for they have as many sides as angles; the least number being three. 23. A 23. A figure of three sides and angles is called a trian gle. And it receives particular denominations from the relations of its sides and angles. 24. An equilateral triangle is that, whose three sides are equal. 25. An isosceles triangle is that, which has two sides equal. 26. A scalene triangle is that, whose three sides are all unequal. 27. A right-angled triangle is that, which has one right angle. 28. Other triangles are oblique-angled, and are either obtuse-angled or acute-angled. 29. An |