, 4 'ATnalftif BODIES. Chap. 2. 



parts, mnft be at the leaft a line. This line thus made, cannot be 

 conceived to be divided into more parts then into three ; fincc 

 doing fo you reduce it into the indivisibles that compofed it. 

 But Euclidc hath demonstratively proved beyond all cavill ( in 

 the tenth proportion of his fixth book of Elements ) that any 

 line vvhatfoever may be divided into wbatfcever number of 

 parts; fo that if this bea line, it muft be divisible into a hundred 

 or a thoufand, or a million of parts : which l.-ing importable in 

 a line, that being divided into three parts onely, every one of 

 thofe three is incapable of further division : it is evident, that 

 neither a line, nor any Quantity vvhatfoever, is competed or 

 made of a determinate number of indivifibles. 



And fince that this capacity of being divifible into infinite 

 parts, is a property belonging to all cxcenfion ( tor Euclides de- 

 monftration is univerfall ) we muft needs conftfle that it is the 

 nature of indivifibles, when they are j'oyned together, to be 

 drowned in one another , for otherwise there would refult a 

 kind of extenfion out of them, which would not have that pro- 

 perty; contrary to what Euclide hath demonftrated. And from 

 hence it followeth that Quantity cannot be compoied of an in- 

 finite multitude of fiich indivifibles; for if this be the narure of 

 indivifibles, though you put never fc great a number of them 

 together, they will ftill drown thcmfelves all in one indivihble 

 point. For what difference can their being infinite, bring to 

 them, of fuch force as to deftroy their eflence and propcrcy ? If 

 you butconfider how the eflentiall compofition of any multi- 

 tude whatfbever, is made by the continuall addition of unities, 

 till that number arife; it is evident in our cafe that the infinity of 

 indivifibles muft alfo arife , out of the continued addition 

 of ftiJl one indivifible to the indivifibles prefuppofed : then lee 

 us apprehend a finite number of indivifibles, which ( according 

 us we have proved ) do make no extenfion, but are all of them 

 drowned in the firft; and obferving how the progreife unto an 

 infinite multitude, gocth on by the (reps of one and one, added 

 ftill to this prefuppoicd number : we fhall fee that every in- 

 divifible added , and confequcndy the whole infinity, will be 

 drowned in the fiift number , as that was in the firft indivi- 

 fible. 



Which will be yet plainer, if we confider that the nature of 



extenfion 



