Various Questions and Inventions

that is, standing on the summit of said mound, or standing there to the side at the foot of it.

N. Without a doubt, standing on the level, that is, at the foot of the hill, it would have a greater effect or penetration in said fortress than it would have standing on the summit of the hill.

S.D. And I would judge, and do judge, that it is entirely the contrary, because those that fire from the summit of the hill will be much closer to the walls of that fortress than those that fire from the foot of the hill. And since, by natural reason, the closer the target is to the artillery, the greater the effect the ball should have upon it.

N. If an artillery piece fired equally in every direction, what Your Excellency says would follow. But for effective reasons, I find the entirely opposite, that is, that every piece of artillery will necessarily fire less in a straight line while leveled than it would in any other way of being positioned. Or, to say it better, every piece of artillery will necessarily fire more in a straight line while somewhat elevated in the front than it will while standing level. And the more it is elevated, the more it will fire in a straight line. The same must be understood for being lowered, that is, that it will fire much more in a straight line while somewhat lowered in the front than it will while standing level; and the more it is lowered, the more it will fire in a straight line.

S.D. This that you say seems to me a very strange thing to believe, that is to say, that the same quantity and power of powder should push the same weight of ball more vigorously in one way than in another. Therefore, I would be pleased if you would assign me the reason and cause of this opinion of yours.

N. We demonstrated the reason for this (by the accidents occurring in its shots) in the final proposition of the Second Book of our Nova Scientia New Science. It is true that in such a demonstration, the proximate cause of such an effect is not assigned, which matter I passed over in that place so as not to weary Your Excellency, because such a proximate cause is demonstrated with the science of weights, which is a science of no small speculation, being subalternated both by Geometry and by Natural Philosophy. But if it is not burdensome for you to listen to me, I will endeavor to demonstrate it at present.

S.D. Proceed then, but be brief.

N. To demonstrate this matter correctly, I am forced, wishing to be understood, to send ahead the definition of some opportune terms, and also some suppositions, as is customary in every science. And because all things are better learned by example than by words, I pose as an example the balance or scale a.b. with the two arms a.c. and c.b. equal, and the center upon which it turns is the said point c. And at the extremities of said two arms are joined two equally heavy bodies, which we will name by the same letters, that is, a. and b. These two bodies, being equal in weight by presupposition and hung at equal lengths, that is, at the said two arms a.c. and c.b. of the proposed balance (which are supposed to be equally long), by the first petition brought by Archimedes in the book he wrote on the center of gravity, they will incline equally; that is, they will stand in equilibrium, as appears in the figure below.