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 . ciples of beauty founded, as before shown, on the numbers2, 3, and 5. Only, if it be plainly seen, that musical harmony is expressed byratios founded on these numbers, it wiU more readily appear that geometricbeauty may be similarly founded. CHAPTEE lY. APPLICATION TO TKIANGLES AND RECTANGLES. Triangles.
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 . ciples of beauty founded, as before shown, on the numbers2, 3, and 5. Only, if it be plainly seen, that musical harmony is expressed byratios founded on these numbers, it wiU more readily appear that geometricbeauty may be similarly founded. CHAPTEE lY. APPLICATION TO TKIANGLES AND RECTANGLES. Triangles. 36. Proceeding from, linear to superficial heauty, and bear-ing in mind the principle of Arts. (16) and (17) we shall findits simplest geometrical expression in triangular figures whoseangles have simple ratios to each other, founded on the num-bers 2, 3, 5. And, of these triangles, right angle ones are thesimplest in relation to our present subject, since they contain inthemselves the standard angle of comparison for the other twoangles. (26) Formal beauty, thus founded upon the numbers 2, 3, 5, maybe said to be of the first, second and third orders respectively. 37. The simplest geometric heauty of the first order will berepresented by the isosceles right-angled triangle, Fig. 4, in. which the equal acute angles are to each other as 1 : 1, and tothe right angle, as 1 : 2. Also this triangle can, as shown atA « 0 and a 5 B, be indefinitely divided into triangles similarto the whole one, ABC. It thus geometrically represents theprinciple of 38. The simplest geometric beauty of the second order is APPLICATION TO TRIANGLES AND EECTANGLES. 91 that of the equilateral triangle. For such a triangle, ABC,Fig. 5, is divided by its altitude CD into right angled trianglesof 30°, 60°, 90°, giving the ratios i, i, |, thus illustrating^ byits exhibition of the number 3, in connection with 2, the firsfiprinciple of varieti/. Ao sX &\^ S Go^ cX 39. The simplest geome
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Keywords: ., bo, bookcentury1800, bookdecade1870, booksubjectmechanicaldrawing
