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 . r, and thus appearing to coincide withits diameter A B, which is supposed to be in the surface of thepaper. Then A OB will represent this semi-circle, after re-volving it over into the paper, about its fixed diameter A B asan axis. ISText, let A O B be an isosceles right-angled triangle,inscribed in this
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 . r, and thus appearing to coincide withits diameter A B, which is supposed to be in the surface of thepaper. Then A OB will represent this semi-circle, after re-volving it over into the paper, about its fixed diameter A B asan axis. ISText, let A O B be an isosceles right-angled triangle,inscribed in this semi-circle, and produce its sides at this triangle into any other, as tf O (^, in which onevertex shall remain at O, and the altitude shall still coincidewith O C, and make the angles at a and h with any simple ratioto each other. In the figure, this ratio is \, the angles at a and5 being respectively of 30° and 60°. So much being done, mark the points b, C, a on the edge ofa slip of paper, and then adjust the position of the slip by trial. 114 FREE-HAND GEOMETRICAL DRAWING. wliicli can easily be done, so tliat the distances a 0 and h C shallbe included, as shown at a^ c, and -h^ Cj, between the lines O Aand O C, and O B and O C, the lines distingnished by Then, assuming any points, as n and ^, equidistant from C forconvenience, draw n m and^ r perpendicular to A B ; and drawO n and O^, and note their intersections, n^ and j?i with a^ h^.Also note c,. Finally, at n^ c^, J9, draw perpendiculars to a^ b^,and make n^)n^ = nm; c^Oj = CO ; p^ r^=^jpr. Then the curvea^ Oj ^1 will be that semi-oval which circumscribes the trianglea, O, h^ of 30°, 60°, 90° derived from the triangle A O B as de-scribed, that is, so that O D hisects the angle A O B. 78. Variations from Fig. 22. These may be made in threeways.* 1°. By dividing the angle A O B equally, or otherwise. 2°. By making the ratio of the angles, a and h, of the trans-formed triangle a Oh, either
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Keywords: ., bo, bookcentury1800, bookdecade1870, booksubjectmechanicaldrawing
