626 PHILOSOPHICAL TRANSACTIONS. [aNNO 16/ 1. 



self, as the mathematicians do, with supposed infinites ; for his infinites, and 

 more than infinites, of years, days, and hours, already past, must be real in- 

 finities, and which have actually existed, and whereof the last is given ; and yet 

 there are more to follow. Mr. Hobbes shall do well for his exercise, to solve 

 these, before he propose more quaeries of infinites. And this I say, to show 

 that Mr. Hobbes is, as much as any, concerned to solve the quasries by him- 

 self proposed. 



In the latter Part of his Jirst Paper, 



He gives us, out of his Roset, prop. 5, this attempt of squaring the circle. 

 Suppose DT be -I- DC, and DR a mean proportional between DC and DTi 

 the semidiameter DC will be equal to the quadrantal arc RS, and DR to TV. 

 PI. 14, fig. 7. 



That the thing is false, is already shown on another occasion. As he has it 

 in his present publication, his demonstration is peccant in these words, " There- 

 fore — the arc on TV, the arc on RS, the arc on CA, cannot be in continual 

 proportion;" with all that follows; there being no ground for such conse- 

 quence. 



And the thing is manifest ; for since that, by his construction, 

 DC, CA, arc on CA extended -ff- ~] are in the same continual pro- 

 DR, RS, arc on RS extended -H- \ portion, of the semidiameter to 

 DT, TV, arc on TV extended -H- J the quadrantal arc; 

 Let that proportion be what you will; suppose as 1 to 2; and consequently 

 DC to CA being as 1 to 2, it will be to the arc on CA, as 1 to 4: And by the 

 same reason DR to the arc on RS, and DT to the arc on TV, must also be as 

 1 to 4 : And therefore the arcs on TV, on RS, on CA; that is 4 DT, 4 DR, 

 4 DC, will be in the same proportion to one another, as their singles, DT, 

 DR, DC: But these, by construction, are in continual proportion ; therefore 

 those arcs also, as they ought to be. Indeed if, by changing some one of the 

 terms, you destroy, contrary to the hypothesis, the continual proportion of 

 DT, DR, DC, you will destroy that of the arcs also, which are still proportional 

 to these: but so long as DT, DR, DC, be in any continual proportion, whe- 

 ther that by him assigned or any other, those will be in the same continual pro- 

 portion with them. As if for DT, DR, DC, be taken Dt, Dr, DC, in any 

 continual proportion, either greater, less, or equal to his, the arcs on tv, on rs, 

 on CA, extended, will be in the same continual proportion. 



But, which is the common fault of Mr. Hobbes's demonstration, if this de- 

 monstration were good, it would serve as well for any proposition as that for 

 which he brings it. For if, instead of f, he had said, a, \y -^^^ or what else 



