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

363 LETTERS the unit, the square of the diameter AM remaining excluded, which is 14400; and, as a consequence, the duple ratio is excluded. Therefore in AB, besides the two characters or signs given above, namely first of 1/2 infinitely constant; second, always respective, as 1/2, from the harmonic series, one finds the third character, or sign, which is of the prime unit; and the fourth character or sign, which as prime unit in that precise respect excludes from its series the duple ratio. Please take good notice of these four characters, or signs; as precise and intrinsic of AB, and as deduced demonstratively. Now let us go to the third sound and notice its characters and physical signs. This third sound is found infinitely constant in 1/2; first character. It is found respectively, as 1/2, to the precise harmonic series; as when it is not inferred from the precise harmonic series, the third sound is changed into another term in the same way as AB; and it is changed equally into the same identical third sound term, into which AB is demonstratively changed; second character. This third sound is found first unit; third character. The duple ratio is excluded from this third sound; fourth character. Therefore, the third sound is the same identical term AB, considered four characters, or intrinsic and precise and demonstratively inferred signs, the thing, of which they are characters, and from which they are inferred, is different. Nor is it an obstacle in any way that the third sound is physical, AB is demonstrative, and that one does not precisely explain the physical way of the third sound to compare it to the demonstrative way of AB. That the third sound is physical, and that AB is demonstrative, means in philosophical mathematical language that it is the same thing demonstrated physically and mathematically, as it has the same characters. That one does not explain precisely the physical way of the third sound to compare it to the demonstrative way means, in the language of mathematical frankness, that the author does not need this explanation, since it is sufficient for him to have demonstrated that the third sound is the same AB in the area formed by its square. He does not have, then, a higher obligation, and therefore neither does he want to take it, nor can it be given to him with regard to the treatise that is examined. If then, after the full examination of the treatise, Your Reverence and Signor Dottor Balbi will care to see and experience first-hand in what way the third sound and AB are identically the same, the third sound physically, AB mathematically, and how the two volumes of air hitting each other form the above mentioned line precisely (and, as a consequence, the curtain is lifted on a thousand other things), I shall serve you more than willingly. Rather, I shall have the pleasure myself of then breaking down the whole foundation of this system, which is quite large. I warn you though in the present case, and distinctly the most revered Signor Dottor Balbi, that after this explanation it seems impossible that he himself (if he deigns to delve into it for some moments) should not solve the whole mystery by himself, because after such an explanation it remains evidently clear and very easily understood. But the bad thing is that Your Reverence confirms my opinion entirely, and as the fact is such, I say to you again with ever more frankness and truth, that we shall do nothing, because the main and substantial exam pertains