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

373 LETTERS 102. Tartini to G.B. Martini At last, from Your Reverence’s last letter, I have completely understood that we do not understand each other. I suspected this, but I am now certain of it. Having found the problem, one can find the remedy; but both Your Reverence and the Most Esteemed Signor Dottor Balbi should remember well and observe that in the present case, precision in terms and of things is more than necessary; as well as memory, to remember what has been concluded whether physically or demonstratively. Let us now go back to the beginning. Firstly, I shall grant to the Most Revered Signor Dottor Balbi all that he says about the impossibility of arriving geometrically at the squaring of the circle: not with sines, not with chords, not with the proportion between sines and chords, not with trigonometric tables. In conclusion, in no geometric way. May this be said forever; and let us remember it forever, so that there should never again be reason to waste time. It was therefore superfluous for me to write it now, because I know that I have written it before. Secondly, I shall say that my expression in geometrical rigour does not mean with the rigour of geometric science, that is to say with the rigour of geometric propositions. I would be a madman if this were what I intended. Moreover, that I do not mean this is explained itself in the first words of my treatise. Please read it again, without my having to transcribe; indeed not in the common particular way deduced by the physical harmonic science, of which there is no knowledge, I intend to say by means of a science which is, at present, quite new, but which has the same demonstrative force as geometry; and it has even more because it connects the demonstrative to the physical. Therefore, in geometrical rigour means as I intend it, with the geometric demonstrative method. Now it is up to you to retort that there is no other demonstrative science if not geometry alone. This is true. That the physical harmonic science uses geometry up to that point to which it can use it, this is true and clearly appears in my treatise, where I patently use the geometric way of approximation to the squaring of the circle both with Archimedes’ geometric positions, and with the trigonometric position of Ceulen, 55 but never to square the circle in such a way. I know for sure that I wrote to you before that geometry serves as a measuring stick for the physical harmonic science, and if I did not write this exact word measuring stick I wrote a synonym. So, ad quid perditio haec ? If the way is new, and I clearly stated it by saying not with the common way but with a new science, how come you object in a geometric sense? May this again be finished for all time. 55 Van Ceulen, Ludolph (1540-1610). Dutch mathematician of German origin. See “Ludolph van Ceulen”, in Enciclopedia Italiana online, Treccani, http://www.treccani.it/enciclopedia/ludolph-van-ceulen/) .