The second book in ten propositions is devoted to the finding the centres of gravity (I) of a parabolic segment, (2) of the area included between any two parallel chords and the portions of the curve intercepted by them.
A diameter is a line through the centre and terminated by the curve: it bisects all chords parallel to the tangents at its extremities; the diameter parallel to these chords is its conjugate diameter.
A volume might be written on Orlando di Lasso's art of so crossing the voices as to render possible successions of chords which, on a keyed instrument where such crossing cannot be expressed, would be a horrible series of consecutive fifths; the beauty of the device consisting in the extreme simplicity of the chords, combined with the novelty due to the fact that these chords cannot be produced by any ordinary means without incorrectness.
The chords necessary in this part, which with its supporting bass is called the continuo, were indicated by figures; and the evanescent and delicate tones of the harpsichord; lent themselves admirably to this purpose where solo voices and instruments were concerned.
In 1747 he applied his new calculus to the problem of vibrating chords, the solution of which, as well as the theory of the oscillation of the air and the propagation of sound, had been given but incompletely by the geometricians who preceded him.
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