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 . per-pendiculai- to wJc^ are the limit between all acute and allobtuse angles. That is, the right angle, being of necessarilyfixed size, is the standard of comparison for all other angles. 27. Beginning now with known principles, from which toproceed to the unknown, the first illustration of beauty sensi-
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 . per-pendiculai- to wJc^ are the limit between all acute and allobtuse angles. That is, the right angle, being of necessarilyfixed size, is the standard of comparison for all other angles. 27. Beginning now with known principles, from which toproceed to the unknown, the first illustration of beauty sensi-bly derived from the divisions of a line, sh dl be the beauty of GENERAL APPLICATIONS OF THE IDEA OE BEAUTY IN EATIOS. 85 sound,OGca-sioned by the notes given out by the divisions of avibrating string. By showing that the long and well established laws of musi-cal harmony, or beauty of sound, are based upon the numbers2, 3, 5, and their multiples, it will be more readily apparenttliat the abstract principles of beauty already described in con-nection with these numbers, are also as truly the bases of geo-metrical harmony, or beauty of geometrical form. That the musical terms employed may be better understood,a sketch of a portion of a piano or organ keyboard is heregiven. Fig 2. ^-. B^ c P e r G A B c, D, E, F, q, Aj 28. A note occasioned by a certain number of vibrations persecond (fixed upon by agreement), whether of a stretchedstring, as in a viol, harp, or piano, or of a column of air, as inan organ pipe, is adopted as a standard of comparison, anddesignated by the letter C. A string one-half as long. Fig. 3,vibrates twice as fast, and gives a note designated as Cj, whicliis described as an octave above C. In other words, the differ-ence in sound between these notes is called the interval of anoctave. Fig^S Again: f of the lengtli of the string will vibrate three timeswhile the whole string vibrates twice, that is f times while thewhole string vibrates once, and will yie
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Keywords: ., bo, bookcentury1800, bookdecade1870, booksubjectmechanicaldrawing
