PROB. VI. Unto a given Right Line PQ, to draw another Right Line ST, which shall be Parallel to it; and at the Distance of the given Line M. Fig. XV. Practice. F 2. Set one Foot in O, (near to one end of the give Line PQ,) and with the other describe the Arch a a: Also, upon the Point L, (near the other end of the given Line) describe the Arch bb; then, 3. By the Convexity (or Tops) of those Two Arches, if you draw a Right Line ST, it will be Parallel to the given Line PQ, and at the Distance of the Line M. PROB. VII. To a given Line VW, to draw another Right Line Y A, which Fig.XVI. Practice. F Irft, Set one Foot of the Compasses in the given Point R, and with the other describe the Arch ac, fo that it may only touch the given Line V W; and with the same Distance, set one Foot in any Point of the Line VW, as at X, and with the other describe the Arch dd. 2. A Line drawn through the given Point R, by the Convexity of the Arch dd, as the Line YR A, that Line shall be a Parallel to the Line V W. PROB. VIII. A fecond Way to draw a Line Parallel to a given Line A B, which Firft, With the Distance P Fig. Practice. A, upon the Point B, de XVII. 2. With the Distance A B, upon P, describe the Arch ff, croffing the Arch ee in the Point C. 3. A Right Line drawn from the given Point P, through C, shall be Parallel to the given Line A B. PROB. : To make an Angle DFE, equal to a given Angle A B С. Pratice. Upon the Angular Point B, at any Distance, de scribe an Arch gg. Then, Fribe 2. Having drawn another Line, as F E, upon the end F (with the same Distance) describe the Arch bb. 3. Take the Distance g g in your Compasses, and set it from h to h: Then, 4. A Line drawn from F through b, as Fb D, shall make the Angle DFE equal to the Angle AB С. Practice. PROΒ. Χ. To divide an Angle GHK into Two Equal Parts. Fig. XVIII: the Angular Point H (with any Distance Fig. XIX. of the Compaffes) describe an Arch cutting the Two Sides, containing the Angle, in the Points h and s. 2. The Compaffes opened to the same (or any other) Diftance, set one Foot in b, and with the other describe the Archkk; and (with the fame Distance) one Foot fet in s, describe the Arch i i, croffing kk in the Point L. 3. Join H L, and so is the Angle G H K divided into Two Equal Parts, by the Line H L. 36 208 PROBOXIL T ? 4 How to divide a given Right Line MN, into any Number of Practice. First, F Irft, From one end of the given Line, as N, draw the Fig. XX. NO at Pleasure, making the Angle ÓN M. 2. Upon the Point M (by Prob. IX.) make the Angle NMP equal to the Angle ONM; or (by, Prob. VIII.) through the Point M, draw the Line MP Parallel, to the Line O N 3. With any small Distance of the Compasses, one Foot being fet in N, run over Four of those Distances upon the Line N O, ar the Points 1, 2, 3, 4.-Do the like upon the Line MP: Then, C 2 4. If 1. Fig. ΧΧΙ. 4. If you draw the obscure Lines I 4, 23, 3 2, and 4 1, they will cross the given Line M N in the Points d, c, b, a, dividing it into Five Equal Parts, as was required. PROB. ΧΙΙ. To make an Equilateral Triangle ABC, whose Sides Shall be Equal to a given Line O. Practice. M Ake the Side B C equal to the given Line O, and with the fame Distance of the Compasses, fetting one Foot in B, with the other describe the Arch mm; and? set alfo on C, describe the Arch 11, crossing the former Arches in A: Then join A B and AC, fo have you constituted a Triangle A BC, whose Three Sides are severally equal to the given Line O. PROB. ΧΙΙΙ. To make a Triangle G HK, whose Three Sides shall be Equal to the Three given Right Lines D, E, F. D E 2. Take the given Line E in 2. Take the Line F in your Compasses; and setting one Foot in G, with the other describe an Arch 00, croffing the former Arch in the Point K. 4. Join G K and HK; so shall you have conftituted a Triangle; whose Three Sides G H, H.K, and GK, are equal to the Three given Lines D E and F. PROB. XIV. To make'a Geometrical Square BCDE, whose Sides shall be equal to the given Line A. Fic Praffice. First, Make the Line BC for one side of the Square, equal to the given Line A, and on one End thereof, XXIII. as |