OF th£ discoveries of

96

that the curve described by the ball would bethat of a parabola* Tartalia had before re-marked, without assigning any good reason forhis assertion, that a ball would be thrown to thegreatest distance, when the piece made an angleof forty-five degrees with the horizon; this rulewas not only confirmed by Galileo, but extend-ed still further, by his proving that at all anglesequally distant from forty-five degrees, the rangewould be the fame.

The next subject, which engaged hi attention*was the phænomenon of falling bodies, and thelaw of their acceleration. Every attentive mindmust have observed that a stone, or any otherheavy body, in falling from a certain height, ac-quires a greater velocity the nearer it approachesthe earth; but before the time of Galileo, nophilosopher had been able to ascertain the exactproportion of its celerity, in the different instantsof its descent. He was the first who determinedthat the velocities are always proportional to thetimes; and the spaces passed through to thesquares of those times: that is, in a doubletime, the body will have acquired a double ve-locity ; in a triple time, a triple velocity, &c.and likewise, in a double time, the body willhave run through a space four times as great asin a single time; in a triple time, through aspace nine times as great, and so on.

Galileo