Various Questions and Inventions

A circular diagram represents principles of ballistics. The circle contains a coordinate system and various labeled points: E at the top, F at the bottom, A on the left, and R on the right. Other points labeled include B, L, G, M, T, Q, S, H, K, O. Two small circles, labeled I and V, are positioned on lines within the larger circle, possibly representing projectiles at different elevations. The center of the circle is marked with mathematical or symbolic notations.

Duke: What do you mean to infer by this?

N. Niccolò Tartaglia: I wish to infer this: that every piece of artiglieria artillery, when leveled, is understood to be in the site of equality. The ball fired from it, when released in such a site, exits the piece heavier than when elevated or separated from that site of equality in any other way (for the reasons stated above). Therefore, in such a site, the ball travels with more difficulty and much sooner begins to decline downward, that is, toward the earth; it declines in greater quantity than when elevated in any other way. That is to say (as is said among bombardiers), it travels much less in a straight line than when elevated in any other way. Consequently, the effects of shots made in such a site will be less vigorous, or of lesser effect, than in any other. It is true that Your Excellency might say, and reasonably, "From your reasons I am clear that at equal distances it will have less effect, but at unequal distances I remain doubtful." This is because, in our inquiry, we see that those artillery pieces positioned on a plain or at the foot of a mountain are much farther from the fortress than those on the summit of the mountain. Such a difference could be much greater than the difference in its firing in a straight line, or the difference of its effects at equal distances. Being so, those on the summit of the mountain would come to have a greater effect than those placed on the plain. Regarding this doubt, I answer that it is indeed true that the distance of those stationed on the plain could sometimes be so greatly different from that of those on the summit of the mountain that what we have said or doubted above would follow.

Duke: Give me an example in a figure, if you wish for me to understand you.

N. Niccolò Tartaglia: To exemplify this thing figuratively, we will suppose a colubrina colubrine (a type of long cannon) of 20 pounds of ball weight. This colubrine (according to that experiment which was conducted at Verona, narrated at the beginning of our Nuova Scientia New Science to Your Excellency) I find that such a colubrine in the site of equality (that is, standing leveled) will shoot on aim, or in a straight line, about 200 paces. And at the elevation of 45 degrees, that is, at the sixth point or at the 72 minutes of our squadra gunner's quadrant, such a colubrine (for the reasons brought forth in the last proposition of the second book of our Nuova Scientia) will shoot on aim, or in a straight line, in that direction, about 800 paces.

Duke: Therefore, firing the said colubrine at such an elevation, it will shoot about 800 paces in a straight line, and firing it leveled, it will not shoot more than about 200 paces?

N. Niccolò Tartaglia: Reason affirms this.

Duke: That seems like a great difference to me.

N. Niccolò Tartaglia: This happens because such an elevation is still very different from the site of equality, because if...