of which there is but one Diameter that divides it equally in two. D. a Volute, which is a Figure or Superficies contained in a fpiral Line. E. a Cylindrical Superficies. F. an irregular culvilinear Figure, compofed of feveral unequal curve Lines. Of Mixed FIGures. A Is a Semi-Circle, which is so much of a Circle as is contained from its Diameter either way. Plate 1. Fig. II. B. a Portion of a Circle, being compofed of a Right Line and Part of a Circle. F. a great Portion of a Circle, containing more than half of it. G. a fmall Portion of a Circle, containing less than half of it. C. A Sector, which is a Figure compofed of two' SemiDiameters, with more or lefs than half of the Circle. D. Concentric Figures, are those whofe Centers are the fame. E. Excentric Figures, are thofe contained in fome measure within each other, but which have not the fame Center. Of Regular and Irregular FIGURes. AA Regular Figure, is that whofe oppofite Sides Plate 1. Fig. are equal and the fame. 12. B. An Irregular Figure, is that compofed of unequal Sides and Angles. EE. Similar Figures are thofe, of which the Lines of one are proportioned to the Lines of the other, tho' one may be greater or leffer than the other. FF. Equal Figures, are those whofe Contents are the fame, and which may be fimilar or diffimilar. C. An Equiangular Figure, has all its Angles equal. EE. One Figure is Equiangular to another, when all the Angles of one are equal to all the Angles of the other. C.D. An Equilateral Figure, is that whofe Sides are all equal. GG. Similar Curvilinear Figures, are thofe in which may be infcribed, or round which may be circumfcribed fimilar Polygons. L 2 AXI Plate 1. Fig. 13. AXIOM S. N Axiom, is fuch a common, plain, felf-evident and received Notion, that it cannot be made more plain and evident by Demonftration, because it is itself better known than any thing that can be brought to Prove it. I. Things equal to one fingle Thing, are in themselves equal. The Lines AC, AC, which are equal to AB, are also equal to themselves. II. If equal Things are added to Things that are equal, the Whole will be equal. The Lines AC, AC, are equal,' The Lines added, CD, CD, are equal, Therefore the Whole, AD, AD, are alfo equal. III. If equal Things are taken from Things that are equal, the Remainder will be equal. From the equal Lines AD, AD. Take away the equal Parts AC, AC. The remaining Parts CD, CD. Are equal. IV. If equal Things are added to Things that are unequal, the Whole will be unequal. Plate 1. If equal Things are taken away from Things Fig. 14. which are unequal, the Remainder will be unequal. From the unequal Lines AE, AE. Take away the equal Parts AD, AD. The Remainder Are unequal. DE, DE. VI. VI. Things which are double the Proportion of another, are in themselves equal. The Right Lines DD, DD. Which are double the Line AD. VII. Things which have but half the Proportion of other equal ings, are in themselves equal. The Lines AD, AD. Which are only half the Length of the Lines DD, DD. What is here faid with regard to Lines, is equally true with respect to Numbers, Superficies and Solids. Refolutions of fome Questions necessary to facilitate the Practice of GEOMETRY. Apply the Ruler even with the Points A and B. Then draw the Line required By drawing your Pen or Pencil along The Side of the Ruler, from the Point AB, A B. Place one of the Points of the Compass in the Point A A And by drawing or turning them round from the Point B BCD IV. To describe a Section from the given Points EF. PRACTIC E. Open the Compaffes at Difcretion, but in fuch a manner nevertheless, that the Distance between its two Points, may be greater than half the Distance between the two given Points E and F. Having opened the Compaffes, From the Point E describe the Arch LM The Section Is what is required. G BOOK |