Chnp.VI. ANTIENT METAPHYSICS. 419 



was a Power which urged the Body downward, and made a cur- 

 vllineal Motion of that which otherwife would have been redili- 

 neal ; and he made the fame fuppofition with refpeft to the Motion 

 of the Planets, and maintained that they are defledled from the 

 RediUneal Motion by the fame Power which makes a ftone fall to 

 the ground: And thus he compounded the Motion of the Planets, 

 likewife, of two Motions, the one of which he, called the Projedlile 

 Motion, ftill carrying on the comparifon with Projediles, and the 

 other the Centripetal. By the one of thefe, the Body is carried on 

 in its Orbit, fo that it may be called the Progreflive Motion ; and 



G g g 2 by 



St the end of the fecond iiiftant, have acquired a double Velocity ; and fo on, during 

 the continuance of the Motion. 



Thus far Giiileo went, and no farther; for he did not know that, at the end of 

 the fecond inftant, the Body had acquired a further degree of Velocity by its being 

 fo much nearer tl,e Centre. Nor was it poflibie that he could difcover this by his 

 method of experiment, as no fpacc, through which we can let a Body fall here on 

 Earth, can have any fenfible proportion to the diftance from the Earth's Centre. But 

 Sir Ifaac having difcovered, as I faid, that the primary Planets, in their defcent to- 

 wards the Sun, were accelerated as the Square of the Diftance reciprocally, did by a 

 moft h^ppy conjecture fuppofe, that the fame Rule might take place in falling Bodies 

 here on earth ; fo that their Motion was accelerated two ways, firft, in the Ratio of 

 the Time, and then as the Square of the Diftance decreafcs. 



Further, Galileo did not know with what Force the falling Body begins to be 

 moved. Neither could this be difcovered by any experiment ; for, as Time and Space 

 are infinitely divilible, fuppofe we certainly knew with what Velocity a Body is 

 moved after having fallen the io,oooth part of a Second of Time, or the lo.oooth- 

 part of an irch of Space, we could not, for that, know with what Velocity it fet 

 out. But Sir Ifaac, having fo happily conjei£\ured that the motion was accelerated 

 in the Ratio above mentioned to (he Diftance, would very naturally fuppofe that 

 the Motion began witli a Velocity t'lat was in the fame Ratio to the Diftance from 

 the Centre. But this difcovery, of the Velocity of the Motion, both in its continu- 

 ation and beginning, was no more, I imagine, than a moft fagacious aiiJ happy 

 conjeiSture, till it was veiified by applying it to the Defcent of the Moon from her 

 Tangent, without the oblcrvation of which it appears to me impoflible that ever the 

 theory ot Gravitation could have been completed. But now it is perfcdly com- 

 plete, becaufe it is known with what Velocity the Body fets out in its fall, — how that 

 Vtlocity is increafed,_and what Space it gots through in what Time. 



