First, he says that it concerns him no more than other men, which is true. I meant it against the whole herd of them who apply their algebra to geometry. Secondly, he says that a bare number cannot be the side of a square figure. I would know what he means by a bare number. Ten lines may be the side of a square figure. Is there any number so bare, as by it we are not to conceive or consider anything numbered? Or, by 10 nothings understands he bare 10? He struggles in vain, his conscience puzzles him. Thirdly, he says 10 squares is the root of 100 square squares. To which I answer, first, that there is no such figure as a square square. Secondly, that it follows hence, that a root is a superficies, for such is 10 squares. Lastly, he says that, neither the number 10, nor 10 soldiers, is the root of 100 soldiers; because 100 soldiers is not the product of 10 soldiers into 10 soldiers. This last I grant, because nothing but numbers can be multiplied into one another. A soldier cannot be multiplied by a soldier. But no more can a square figure by a square figure, though a square number may. Again, if a captain will place his 100 men in a square form, must he not take the root of 100 to make a rank or file? And are not those 10 men? TO THE THIRD PAPER. He objects nothing here, but that _the side of a square is not a superficies, but a line_, and that a _square root (speaking of quantity) is not a line, but a rectangle_, is a contradiction. The reader is to judge of that. To his scoffings I say no more, but that they may be retorted in the same words, and are therefore childish. And now I submit the whole to the Royal Society, with confidence that they will never engage themselves in the maintenance of these unintelligible doctrines of Dr. Wallis, that tend to the suppression of the sciences which they endeavour to advance. LETTERS AND OTHER PIECES. LETTERS AND OTHER PIECES. ========== I. A LETTER FROM MR. HOBBS TO MY MR.[2] HONORABLE SIR,