Zechino or Sequin, shares in proportion, 2 6 2.16,0 2.31,0 Ducat, double and half in proportion, 2 52 2.12,5 2.26,7 SECTION LXXV. GEOMETRY. DEFINITIONS. 1. A point is that which has position, but no magnitude nor dimensions; neither length, breadth, nor thickness. 2. A line is length, without breadth or thick ness. 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; viz. length, breadth, and thickness. 5. Lines are either right or curved, or mixed of these two. 6. A right or straight line lies all in the same direction between its extremities, and is the 100 shortest distance between two points. When a line is mentioned simply, it means a right line. 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 perpendicular distance, and never meet, though ever so far produced. 10. Oblique lines change their distance from each other, 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 the one side than the other, or when the angles on both sides of it are equal. 12. An angle is the inclination, or opening of two lines having different directions, and meeting in a point. 13. Angles are right or oblique, acute or obtuse. 14. A right angle is that which is made by one line perpendicular to another; or, when the angles on each side are equal to one another, they are right angles. 15. An oblique angle is one which is made by two oblique lines, and is either less or greater than a right angle. 16. An acute angle is less than a right angle. 19. A plane superficies, or plane, is that with which a right line may every way coincide; or, if the line touch the plane in two points, it will touch it in every point; but if not, it is curved. 20. Plane figures are bounded either by right lines or curves. 21. Plane figures, that are bounded by right lines, have names according to the number of their sides, or of their angles; for they have as many sides as angles, the least number being three. 22. A figure of three sides and angles is called a triangle; and it receives particular denominations from the relations of its sides and angles. 23. An equilateral triangle is that whose three sides are equal. 24. An isosceles triangle is that which has two sides equal. 25. A scalene triangle is that whose three sides are unequal. 26. A right-angled triangle is that which as one right angle. 27. Other triangles are oblique-angled, and are either acute or obtuse. 28. An obtuse-angled triangle has one obtuse angle. 29. An acute-angled triangle has its three angles acute. 30. A figure of four sides and angles is called a quadrangle, or a quadrilateral. 31. A parallelogram is a quadrilateral, which has both its pairs of opposite sides parallel; and it takes the following particular names; viz. rectangle, square, rhombus, and rhomboid. 32. A rectangle is a parallelogram, having a right angle. 33. A square is an equilateral rectangle, having its length and breadth equal. 34. A rhomboid is an oblique-angled parallelogram, whose opposite sides are equal. 35. A rhombus is a parallelogram, having all its sides equal, but its angles oblique. 36. A trapezium is a quadrilateral, which has neither two of its opposite sides parallel. 37. A trapezoid has only one pair of its opposite sides parallel. 38. A diagonal is a line joining any two opposite angles of a quadrilateral. 39. Plane figures that have more than four sides are in general called polygons; and they receive other particular names according to the number of their sides or angles. Thus, 40. A pentagon is a polygon of five sides; a hexagon, of six sides; a heptagon, of seven; an octagon, of eight; a nonagon, of nine; a decagon, of ten; an undecagon, of eleven; and a dodecagon, of twelve sides. 41. A regular polygon has all its sides and all its angles equal. If they are not both equal, the polygon is irregular. |