Various Questions and Inventions

as it is elevated minute by minute, so also minute by minute it goes on increasing its travel in a straight line. The same will also happen at the points, and in greater quantity: that is, when elevated to the first point of the quadrant, it will travel much more in a straight line than it will in the site of equality, that is, when leveled. And elevated then to the second point of said quadrant, it will travel much more in a straight line than it will when elevated to the first point. And so elevated to the third point, it will travel even more in a straight line than it will at the second, and so successively to the fourth, it will travel more than at the third, and at the fifth more than at the fourth, and at the sixth (mentioned above) it will travel more than at the fifth. And if it could be elevated further by degrees, its travel in a straight line would go on increasing: that is, at the 7th point, it will travel more in a straight line than at the 6th, and at the 8th more than at the 7th, and at the 9th more than at the 8th, and at the 10th more than at the 9th, and at the 11th more than at the 10th, and at the 12th its entire shot will be in a straight line, because it will be perpendicular above the horizon. This one will be more perfectly straight than any of the aforementioned, because in truth the transit, or moto violento violent motion (forced motion) of an equally heavy body that is outside the perpendicular of the horizon, can never have any part that is perfectly straight (as was said above regarding the second supposition of the second book of our Nuova Scientia).

Duke: Why then do you say "in a straight line," if it is not perfectly straight?

N. Niccolò Tartaglia: To be understood by the common people, because that part which is almost insensibly curved, we call straight, and that which is evidently curved, they call curved.

Duke: Continue.

N. Niccolò Tartaglia: Now, to return to our purpose, I say therefore that if the height of the aforementioned fortress were such that from there to the artillery pieces which were on the plain of the mountain were 760 paces, and that from the same fortress to those artillery pieces which were on the summit of the mountain were only 130 paces, in this case, I say that the aforementioned colubrine would have a greater effect on the walls of said fortress while standing on the summit of the mountain than it would while standing at the foot of the mountain. The cause is that the said colubrine (standing leveled) shoots about 200 paces in a straight line (as was said above). Therefore, being 130 paces from the wall (as was supposed), it would come to strike the said wall about 70 paces before the end of its travel in a straight line. But standing at the foot of the mountain (from which place to the said wall it has been supposed to be diametrically 760 paces), and elevating it to the elevation of 45 degrees (that is, to the 6th point of our quadrant), it will shoot about 800 paces in a straight line (as was said above), whence it would come to strike the said wall only about 40 paces before the end of its travel in a straight line, that is, before its sensible declination. And because that ball which, in its striking, has to traverse a longer space (finding no resistance) will have a greater effect on such resistance (for the reasons brought forth in the 4th proposition of the first book of our Nuova Scientia), therefore, because the ball fired from the summit of the mountain in its striking would still have to go 70 paces in a straight line, and that fired from the plain, in its striking, would have to proceed only 40 paces in a straight line, for these reasons it would be concluded in such a case that the said colubrine would have a greater effect on said wall while standing on the summit of the mountain than it would standing on the plain, or foot of the mountain, at the elevation of the said 6th point of the...