"Above all things it must be considered, that the motion of descending grave bodies is not uniform, but departing from rest they go continually accelerating.. But this general notion is of no avail, if it be not known according to what proportion this increase of velocity is made; a conclusion that hath been until our times unknown to all PhilosoÂphers; and was first found out & demonstrated by the Academick [Galileo], our common friend, who in some of his writings not yet publishÂed... he proveth, how that the acceleration of the right moÂtion of grave bodies, is made according to the numbers uneven beginning ab unitate [from unity], that is, any number of equal times being assigned, if in the first time the moveable departing from rest shall have passed such a certain space, as for example, an ell, in the seÂcond time it shall have passed three ells, in the third five, in the fourth seven, and so progressively, according to the following odd numbers; which in short is the same, as if... the [sums of] spaces passed are to each other, as the squares of their times."
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Salviati, p. 198.
https://en.wikiquote.org/wiki/The_Systeme_of_the_World%3A_in_Four_Dialogues
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The Systeme of the World: in Four Dialogues
The Systeme of the World: in Four Dialogues is the original 1661 English translation, by Thomas Salusbury, of Galileo Galilei's DIALOGO sopra i due MASSI SISTEMI DEL MONDO (1632). Galileo's publication is more generally recognized under the title of Stilman Drake's English translation, Dialogue Concerning the Two Chief World Systems, published in 1953. A revised and annotated edition of the Salusbury translation was also introduced in 1953 by Giorgio de Santillana under the title Dialogue on the
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