Elements of plane and solid free-hand geometrical drawing, with lettering; and some elements of geometrical ornamental design, including the principals of harmonic angular ratios, etcIn three parts ..for draughtsmen and artisans; and teachers and students of industrial and mechanical drawing . But if the side, OA, of the right angle, be taken as such radius, as indicatedby the arc Aa, the other side, AB, will be the natural tangent of the sameangle. OUKVILINEAE GEOMETKIC BEAUTY. 109 5°. The triangle 11 a 0. Here,. Oa= 1 — i/s and a11 = ^ ,__. Then to find the an^le at 0 to a radius of
Elements of plane and solid free-hand geometrical drawing, with lettering; and some elements of geometrical ornamental design, including the principals of harmonic angular ratios, etcIn three parts ..for draughtsmen and artisans; and teachers and students of industrial and mechanical drawing . But if the side, OA, of the right angle, be taken as such radius, as indicatedby the arc Aa, the other side, AB, will be the natural tangent of the sameangle. OUKVILINEAE GEOMETKIC BEAUTY. 109 5°. The triangle 11 a 0. Here,. Oa= 1 — i/s and a11 = ^ ,__. Then to find the an^le at 0 to a radius of 1, 1we must proceed as in 4°, whence \.—\ 1/3 : 1 :: ^ — : tang. aOir. 1 1That is, tang, a 0 11 = - ^^ _ VS ?^ l-iy3 2-1/3 24/3-3 — = the natural tangent of 65° : 6 + . Hence the tri-angle 0 a 11 is not a very close approximation to one of22°: 30, 67° : 30, 90°. 66. Proceeding in like manner, beginning with a rectanglecomposed of two triangles of the third order of symmetry 18°,72°, 90° (Art. 39), we should find like curious and interestingresults. Thus 0, 2, 10, Fig. 16, will then become an equila-teral triangle, or its half, one of 30°, 60°, 90° ; 0, 3, d willbecome a triangle of 18°, 72°, 90°, and 0 4 cl\ one of 10°, 80°,90°, etc. And, in general, the triangle on 2, 10 of a series ofellipses thus formed, will be of the same form as the one on3 g 9 of the next preceding ellipse, and so on ; the one on 4 8being of
Size: 1863px × 1341px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bo, bookcentury1800, bookdecade1870, booksubjectmechanicaldrawing
