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

367 LETTERS then be necessary to form a sort of solid ellipse, etc., in which his proposition, which is of a greater speed in the stronger sounds, lesser in those less strong, shall be verified; but it will also be noted that the less strong (that is, less high) will have a greater arc; the stronger (that is, the higher) a smaller arc. It will furthermore be verified that any sound of the chords AF, AE, AD shall propagate in AB, which is the common arc; and to sum up, too many further things will be verified in due time. But onwards indeed with the examination. I am absolutely stunned that the rest of the chocolate, which I sent a month and a half ago, has not arrived to you yet. But I shall look into it. I submit to you my regards, and I remain Your Reverence Most Reverend’s most humble, devoted and obliged servant Giuseppe Tartini Padua, 15 July 1752 100. Tartini to G.B. Martini May formalities between us be banished forever; nor do I wish to be thanked for a whimsy. I am pleased that you have received the remainder of the chocolate, and both Your Reverence and the Most Illustrious Signor Dottor Balbi, whose hands I kiss, must allow me the full freedom to do what I wish to do of this nature, for as long as I live; nor should any words be spoken upon this point ever again. I shall come to Your Reverence’s last letter. I grant unconditionally to the most esteemed Signor Dottor Balbi that it is impossible to determine and realise the quality of the straight line which squares the circle, which one cannot get close to, if not by approximation alone. In this, all the sciences are the same; arithmetic, geometry, algebra, the physical harmonic science; and if there are other ones, or other ones are possible, it will always be the same. Therefore, we all agree on this point. Nevertheless, I say again, and confirm, that only the physical harmonic science has the privilege of being able to square the circle demonstratively and physically; I mean to say, when I say demonstratively, in a rigorously geometric manner. I shall then try to explain myself in the present letter as well as I can, and if it does not suffice (I am writing in proximity of the imminent departure of the post, not having had any other time), I shall carry on writing until I am understood. Two straight lines are required for the squaring of the circle. If, for example, one side of the square circumscribed is 14, one quarter of the circumference of the circle inscribed is found as 11 (by Archimedes), but is found by approximation. If the side itself (by mean) is 452, one finds one quarter of the circumference as 355, but by approximation, albeit greater;