Giuseppe Tartini - Lettere e documenti / Pisma in dokumenti / Letters and Documents - Volume / Knjiga / Volume II

375 LETTERS The objection proposed many times by you, and precisely relating to what I have said, is the necessary information about the physical way in which the third sound is produced. I have always answered that nothing matters to me about the way, but the fact alone is sufficient for me, and I am sure I am right. But we can easily agree in general. Let it be the eighth figure, and let the lines A 1/2, A 1/3, A 1/4, A 1/5 etc. be conceived as sounding lines. By playing the two sounding lines A 1/2, A 1/3, the third sound is in unison with A 1/2. By playing A 1/4, A 1/5, the same, etc. Therefore, from the motion of the two spherical volumes of air is formed a radius always equal to A 1/2. If they collide, the two volumes intersect, the two following respective spheres are composed between them, whether by vibrations or by oscillations, or however one wants, it is always true, and always beyond dispute, that if the sound is in unison, it must be that the radius is the same. Now, please forgive me; this is more than enough for the purpose. Here then is the fundamental principle of my system. The physical sounding lines, from which I infer by harmonic series the third sound always constant in 1/2, are equal to the lines in the plane of the diameter harmonically divided, and the third sound is a physical sounding line unfailingly equal to the semidiameter and formed by two circles in the plane, by two spheres in the solid. Given this foundation, the inseparability of the two methods, physical and demonstrative, is more than evident. The remainder (inferred in such a way) will be in another letter, when the replies to the questions which I ask in this one have been absorbed. If you will deign to answer me with the precision with which I ask the question, you will see that we shall come directly to the conclusion. But meanwhile, you send me objection upon objection (forgive me) which are always falsely supposed because you believe that I wish to arrive at the demonstration of the squaring through quantity, which is made known by means of the common or geometrical or numerical sciences, or others if there are any. This mortifies me infinitely, because the treatise is in your hands to be examined. It cannot be examined if one does not read it. If one has read it, how was it not seen, or noticed, that I claim to square the circle without assigning (confessed to be impossible) the quantity of Ax Figure XIII, and I claim to square it by force of reason, and never by force of quantity? If on your part it were objected how the notion of a ratio without the notion of the two terms composing the ratio can be possible, this objection would be reasonable and to the point. But you continuously make objections on what I do not say, nor have ever dreamed of saying: please consider the effect such a thing produces in me. Right from the start I declare the squaring of the circle by force of a science presently unknown. Either I am mad, deviating from my science to those commonly known to infer from these my main foundation (and I certainly do not do this) or the objections raised against me have nothing to do with my treatise. Please deign to reflect whether hitherto a single word has been said on your part on the use which I make and the way in which I mean the discrete geometric proportions, with all of what I infer from them. Nonetheless, this