The New Science

...with Archimedean reasoningoriginal: "ragion Archimedane"; referring to the rigorous geometric proofs pioneered by Archimedes of Syracuse, which Tartaglia applied to physics. [I found] that the distance of the aforementioned shot elevated to 45 degrees above the horizon was about ten times the straight path of a shot made along the plane of the horizon, which is called by gunnersoriginal: "bombardieri"; the specialized soldiers who operated heavy cannons or "bombards." "firing at point-blank."original: "ponto in bianco"; literally "point in the white," referring to the center of a target. In this era, it meant aiming the cannon horizontally, directly at the target, without accounting for the arc of the ball’s flight. With this evidence, Magnanimous Duke, I found through geometric and algebraic reasons that a ball fired toward the said 45 degrees above the horizon travels about four times as far in a straight line as that which is fired along the plane of the horizon, which by gunners is called (as I have said) "firing at point-blank." For which reason it is clear, Most Excellent Duke, how a ball fired from the same artilleryoriginal: "artegliaria" travels further in a straight line in one direction than in another, and consequently produces a greater effect.

Furthermore, Most Illustrious Lord, by calculating I found the proportion of the increase and decrease that every piece of artillery makes (in its shots) by raising or lowering it above the plane of the horizon; and similarly (Most Generous Lord), I found the way to reason out and find the variation of said shots in every piece, whether large or small, by means of knowing just one shot (provided that it is always equally charged). Afterwards (Most Prudent Lord), I investigated the proportion and the order of the shots of the mortar,original: "mortaro"; a short-barreled weapon designed to fire projectiles at high trajectories to clear walls or reach into fortresses. and similarly found the way to know how to investigate briefly the variation of said shots, also by means of just a single shot.

Beyond this (Most Bountiful Lord), with most evident reasons I recognized how a piece of artillery could, by two different paths (or elevations), strike in the same place; I also found the way to put such a thing (should it happen) into execution—matters never before heard of (Most Distinguished Lord), nor thought of by any other, ancient or modern. But then I considered (Magnificent Lord) that all these things were of little use to a gunner when the distance of the place where he needed to strike was not known to him. original: "Verbi gratia"; Latin for "For example." For example, occurring...