628 PHILOSOPHICAL TRANSACTIONS. [aNNO I67I. 



be 4, this will be 4 times 4 : And so in all other proportions. Of which, 

 if any one doubt, he may believe his own eyes. See figs. 8, Q, 10, 11. 



And this Mr. Hobbes might have been taught by the next carpenter (that 

 knows but how to measure a foot of board) who could have told him, that be- 

 cause the side of a square foot, is 12 inches in length, the plain of it will be 

 12 times 12 inches in squares : Because there will be 12 rows of 12 in a row. 



His third Paper, 



Which came out just as the answer to the two former was going to the press, 

 contains for substance, the same with his second, and the latter part of the 

 first : And so needs no farther answer. — Only I cannot but take notice of his 

 usual trade of contradicting himself. His second paper says, the side of a 

 square is not a superficies, but a line: His third says the quite contrary, (prop. 1 .) 

 A square root, (speaking of quantity) is not a line, but a rectangle. Other 

 faults, falsities, and contradictions, there are a great many.— As for instance : 

 He tells us first, in the natural row of numbers, as 1, 2, 3, 4, 5, 6, &c. every 

 one is the square of some number in the same row ; that is, of some integer 

 number; which is notoriously false. This he contradicts in the very next words, 

 but square numbers, beginning at 1, intermit first two numbers, then four, 

 then six, &c.; so that none of the intermitted numbers is a square number, nor 

 lias any square root. . If these intermitted numbers, between 1, 4, Q, l6, &;c., 

 be not squares, how is it that every one in the whole row is a square, and that 

 of some integer number? But this again is contradicted prop. 2, where 200, 

 one of such intermitted numbers, is made a square, and 14-j-V the root of it. 



Again, in his definition he tells us, that a square root multiplied into itself 

 produces a square: But (prop. 2) he multiplies the root 14-j^^, not into itself, 

 but into 14 (a part thereof,) to make 200, which he will have to be the square 

 of that root. Nor is it a mere slip of negligence in the computation, but his 

 rule directs to it ; any number given is produced by the greatest root multiplied 

 into itself, and into the remaining fraction. Whereof he gives this instance: 

 Let the number given be 200 squares, the greatest root is 14-V squares (he 

 should rather have said lengths ; but that is a small fault with him ;) I say that 

 200 is equal to the product of 14 into itself, which is IpS, together with 14 

 multiplied into -^, which is equal to 4 : that is 14vV nmlti plied into 14. But 

 this calculation is again contradicted in his third proposition, where he calculates 

 the same square otherwise, as we shall see by and by. In the mean time let us 

 consider this alone, and see the contradictions within itself. His rule bids us 

 multiply the greatest root into itself, &c. This greatest root he says is 14-i^ ; 

 yet does he not multiply this, but 14 (a part thereof) into itself, and into the 



