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

376 is my main foundation for arriving at the squaring, and for demonstrating the two centres (Figure XIII), inside which the so much sought-after ratio is hidden. This is such a fundamental point that I regard it as the very first in relation to the demonstration, which decides everything. I openly declare in the treatise (and I hereby confirm it) that of the discrete geometric proportions nothing more than the pure material is known, but that their maximum significance is not known in the slightest. I make use of them from the beginning to the end; I make them inseparable from the physical (which is precisely their importance, and in that sense they pertain to the physical harmonic science alone); I conclude with them; and of this no one has ever spoken, either for or against. Yet here is my main force, and it does not take much effort to detect that it is so. To sum up, having added up what has happened between us in a year and a half, I find that if we except the requested explanations, which I too have seen to have been necessary many times, I have hitherto not heard even one objection derived specifically from the intrinsic nature of my system.They have all been inferred extrinsically from the other known sciences, which in truth have nothing to do with this one which I deal with, if not in that they are of use to it as a measure and plumb line. The physical harmonic science deals with the reasons of things, and not the things, and when it deals with quantity, it deals with the reason it must be that certain quantity, and not how much. Therefore, for the true examination one must necessarily change one’s approach, otherwise it is useless. And if you wish to have the kindness of continuing it, please do allow me to ask questions, as I have done in this letter, and please answer me precisely, asking for an explanation of what you do not understand. Any other way in our case is impossible, and please deign to believe me once and for all, because the evidence of a year and a half is more than sufficient. The letter has been extremely long, but necessary. Please consider it carefully, and you will see many needs at once. I submit to both of you my most deferential regards, and I remain more and more Your Reverence’s most humble, devoted and obliged servant Giuseppe Tartini Padua, 22 September 1752 103. Tartini to G.B. Martini Deprived as I was of a reply for a long time, Your Reverence may well imagine the size of my torment. I fear some health problem; I fear I have written something offensive (surely with no intention on my part). To sum up, whatever doubt comes to