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 . Y. GEOMETEIC BEAUTY OF POLYGONS. GEOMETRICAL DESIGN. 47. First. We have seen (Arts. 37-38) that the primaryfigures representing harmony of form are 1st, the right angled,2c?, the equal angled, and StZ, the 36 and 72° acute angled isos-celes triangles. Tlien the corl;esponding^>r^mar2/ rectangles areth
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 . Y. GEOMETEIC BEAUTY OF POLYGONS. GEOMETRICAL DESIGN. 47. First. We have seen (Arts. 37-38) that the primaryfigures representing harmony of form are 1st, the right angled,2c?, the equal angled, and StZ, the 36 and 72° acute angled isos-celes triangles. Tlien the corl;esponding^>r^mar2/ rectangles arethose made by placing the halves of these triangles together bytheir hypothenuses. These rectangles will be the square ; therectangle whose diagonal makes angles of 30° and 60° with itssides; and the rectangle whose diagonal makes angles of 18°and 72° with its sides. Second. We have found (Arts. 40, 41) that from these pri-mary triangles others are derived, and from these, in turn, a cor-responding series of rectangles proceed. 48. It is interesting next to note that most of the regularpolygons, yield simple harmonic ratios, by means of their sub-division into equal triangles, by radii from their centres totheir corners. 49. Thus the equilateral triangle, Fig. 10, divides into three.
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Keywords: ., bo, bookcentury1800, bookdecade1870, booksubjectmechanicaldrawing
