File:Perspective and geometrical drawing adapted to the use of candidates for second and third-class teachers' certificates (1887) (14782797362).jpg

Identifier: perspectivegeome01mcgu (find matches)
Title: Perspective and geometrical drawing adapted to the use of candidates for second and third-class teachers' certificates
Year: 1887 (1880s)
Authors: McGuirl, Thomas H. (from old catalog)
Subjects: Geometrical drawing Perspective
Publisher: Toronto, W. Briggs
Contributing Library: The Library of Congress
Digitizing Sponsor: The Library of Congress

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nit, lying on G.P. directly in front. 14. Represent a hexagon, side 3, half buried vertically inthe ground, one side parallel to G.P.; hexagon __;_ to P.P.and 3 within it, 4^ to left. 54 DRAWINv The Octagon. The drawing of an octagon diflfers but little from that ofthe hexagon, we shall, therefore, merely show the plan. Thefollowing are methods of drawing the plan:— C A OS D H v% \ v^ P K <) N i L Af^ F Fig. 31. Let AB = given side (on B.L.); bisect AB in O, and drawOG _J_ to OA and equal it, and describe semicircle AGB; THE OCTAGON. OD join AG and GB; with centres A, B, and distances equal toAG, describe arcs to cut AB produced in C and D; on CDdescribe square CDFE. With centre A and distance ABdescribe arc to cut CE in H; find P similarly; with centresH and P and distances equal to PIA, describe arcs to cut CEand DF in K and N respectively, and with same distancesdescribe arcs to cut EF in L and M; join AH, KL, MN andBP, which will complete the octagon, (Fig. 31.)Another way: a
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56 DRAWING. Let AB = given side; take centre O, and with distance AOdescribe circle AGD; draw diameter CD _J_ to AB. JoinCA and produce it. With centre A and distance AB describearc to cut CA produced in E; then draw EF _J_ to BA pro-duced, and produce FE, making EG = EA, etc. (Fig. 32.) Note.—In parallel perspective a hexagon or an octagonmust be supposed to have a side parallel or perpendicular to,the picture plane. THE CIKCLE. 57 The Circle. Hitherto we have been dealing exclusively with straightlines, in so far as the appearance of figures is concerned; wenow proceed to represent curved lines in perspective. It isevident that a curve cannot be correctly represented, withoutthe aid of straight lines. There is only one -position in which a circle will appear trueto the eye, and that is, when the eye is in a line exactly per-pendicular to its plane, at its centre. In all other positions itwill appear an ellipse, varying from a circle to a line. If, forinstance, we place a hoop on t

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