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

459 LETTERS 175. Tartini to G.B. Martini May Your Reverence be well assured that for as long as I live, my care and diligence to keep you supplied with good tobacco, according to your needs, will be extraordinary. But likewise you should also understand that, in spite of the universal use which is made here of that sort of tobacco, luck is needed to find the type that is really good. Moreover, the diligence of those particular amateurs who make it for themselves is useless, and it goes bad in the heat. The present stock has a bad leaf, and this is the reason. We are close to the new stock, and let us hope it is better. I shall come to what I mentioned to you in the other letter of mine, and Your Reverence, in reply, must let me know whether it is appreciated. But in my opinion, I do not see how what I am about to tell you could be profitable to the history; it would be to the doctrine, but it would require the whole doctrine, which is impossible in a letter, and inconvenient in a history. I shall then explain nothing more than the language in general of the Platonic and, as a consequence, Pythagorean doctrine, for in this respect Pythagoras and Plato are in complete agreement. I ask Your Reverence to observe in Plato’s dialogue of the universe (i.e. the Pythagorean Timaeus explained by Plato) the formation of the world soul. The doctrine contained there substantially says that parts are removed from a given continuous geometric proportion and are carried forward to the mean, so that a discrete geometric proportion is formed and deduced, which certainly can no longer preserve the ratio of the geometric extremes, because having had a part removed in order to place them in the mean, the extremes of the second discrete geometric proportion must be in a lesser ratio to the extremes of the continuous geometric ratio. Here is the example in figures. Given the continuous subduple = 1·2·4, when the unit is cut or subtracted at the extreme = 4, there remains the extreme = 3. With this, the subsesquitertian ratio is subtracted, which is = 3·4, and this must be carried forward to the mean, which means to say in relation to the mean = 2, which was the geometric with regard to the extremes = 1·4, and is arithmetical with regard to the extremes 1·3, which remain after the subtraction of the unit of the extreme = 4 in the term = 3 which becomes extreme. After transforming therefore the four terms 1; 1: ½, 2, 3 into integers 2: 3: 4: 6, it will be generally accepted that the term subtracted from the continuous geometrical extreme and carried forward to the discrete geometrical mean is always the harmonic mean of the extremes of the discrete geometrical proportion, and that the geometric mean of the continuous proportion is always converted into the arithmetical mean of the discrete relation. Therefore, given the sesquialter continuous extremes = 4·6·9, after subtracting a unit at the extreme 9, 8 is left as an extreme, and since 8: 9 is the subsesquioctavian ratio, this must be carried forward to the mean, relative to the term that was the geometric mean of the extremes