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they met RS, forming the right-angled triangles MPR, MQR, 

 MTR, MUR, MVR, and MSR. He then shewed, that as the angles 

 at the vertex of each of these triangles, contained respectively 

 45°, 30°, 22° 30', 18°, 15°, 12° 51' 26", 11° 15', they related to 

 the right angle, as the harmonics of sound, expressed by the signs 

 c, g, c^ e", g, bb, and c^ relate to the fundamental note C, pro- 

 duced by the string of the monochord. These triangles he combined 

 in the following manner upon a line AB (figure 2, of the annexed 

 Plate), which he said might be of any given length according to 

 the size of the figure to be formed. From B at an angle of 11° 15' 

 with AB he drew the line Bg indefinitely, and from A at an angle 

 of 15° with AB the line Ar, also indefinitely, and cutting Bg in K. 

 Through K he drew KL at right angles with AB, forming the tri- 

 angles ALK and KLB. Through K he drew the line pO parallel 

 to AB. From A at an angle of 12° 51' 26" with AB he drew AV, 

 cutting pO in M, and drew MN at right angles with AB, forming 

 the triangle AMN. From A at an angle of 18° with AB, he drew 

 Au, cutting pO in H, and drew HI at right angles with AB, form- 

 ing the triangle AHI. From A at an angle of 22° 30' with AB, 

 he drew At, cutting pO in F, and drew FG at right angles with 

 AB, forming the triangle AFG. From A at an angle of 30° with 

 AB he drew As, cutting pO in C, and drew CD at right angles with 

 AB, forming the triangle ACD. From C at an angle of 45° with 

 AB and CD he drew CE, forming the triangle CDE. Thus, he ob- 

 served, were the triangles arising from the harmonic angles con- 

 structed upon AB in the same relative proportions to each other, 

 that they were when formed upon the line RS, figure 1. Upon the 

 other side of AB he constructed similar triangles forming the equila- 

 teral triangle ACC ; the right-angled isosceles triangle ECC, and 

 the acute-angled isosceles triangles AFF, AHH, AKK, AMM, and 

 BKK. Within this diagram he shewed that the human skeleton 

 could be formed in the most perfect proportions, determining, at the 

 same time, the centres of all the various motions of the joints ; and 

 also that the symmetrical beauty of the external form, whether in 

 a front or profile view, was governed by these angles ; thus en- 

 deavouring to prove that an application of the laws of numerical 

 harmonic ratio in the practice of the sculptor and painter would give 

 these imitative arts a more scientific character than they at present 

 possess, and, so far from retarding the efibrts of genius, would 

 rather tend to facilitate and assist them. 



