The New Science

...to hit a visible place when the distance to it was unknown to him. What would it profit him (O Magnanimous Duke) in this case if he knew that his piece fired at such an elevation reaches 1356 pacesoriginal: "passa"; a unit of measurement used in Italian ballistics, roughly equivalent to 1.5 meters or 5 feet., and at another [elevation] 1468 paces, and at yet another 1574 paces, and so on, degree by degree? Certainly it would profit him nothing; for not knowing the distance, he would even less know at what mark or elevation he should set his piece of artilleryoriginal: "artegliaria" so that it might strike the desired location.

It follows then (Most Invincible Lord) that there are two principal skills necessary for a royal gunneroriginal: "bombardiero"; a specialist in operating heavy cannons or bombards. (wishing to fire with reason and not by chance), of which the one without the other is almost of no use. The first is that he roughly knows how to recognize and calculate (by sight) the distance to the place he needs to hit. The second is that he knows the range of the shots of his artillery according to its various elevations. Knowing these things, he will not err much in his shots; but lacking one of them, he cannot fire (by any account) with reason, but only by guesswork. And if by chance he strikes the place at the first shot, or near the place he desires, it is more by luck than by science (especially in long-distance shots).

For which reason (Most Illustrious Lord), I found a new way to investigate briefly the heights, the hypotenuseoriginal: "ypothumissale"; Tartaglia is using a localized version of the Greek term for the diagonal distance between the observer and a high point. or diagonal distances, and also the horizontal distances of visible things. This is not entirely a new thing, because in truth, EuclidA Greek mathematician (c. 300 BCE) known as the "Father of Geometry." in his Opticsoriginal: "prospettiua"; referring to Euclid's work on the geometry of vision. briefly teaches it theoretically in part; similarly Johannes Stoeffleroriginal: "Giouanne Stoflerino"; a German mathematician and astronomer (1452–1531)., Oronce Finéoriginal: "Orontio"; a French mathematician and cartographer (1494–1555)., Pietro Lombardo, and many others have given rules for such matters—some using the sun, some with a mirror, some with the quadrantAn instrument used to measure angles up to 90 degrees., some with the astrolabeAn ancient astronomical instrument used for solving problems relating to time and the position of the Sun and stars., some with two rods, some with a staff (titled Jacob’s stafforiginal: "baculo de Iacob"; a tool used to measure angles between the horizon and a celestial body or between two landmarks.), and in many other various ways. But I say (Most Distinguished Lord) that I found a new way, expedient and quick and easy for everyone to understand, and with less error...