In the first place, therefore, if A V be drawn, cutting the arch B H D in X, and the side D C in Z, I desire some analyst would, if he can, give a reason why the strait lines T E and T C should cut the arch B D, the one in Y, the other in X, so as to make the arch B Y equal to the arch Y X; or if they be not equal, that he would determine their difference.
Secondly, if in the side D A, the strait line D a be taken equal to D Z, and V a be drawn; why V a and V B should be equal; or if they be not equal, what is the difference.
Thirdly, drawing Z b parallel and equal to the side C B, cutting the arch B H D in c, and drawing the strait line A c, and producing it to B V in d; why A d should be equal and parallel to the strait line a V, and consequently equal also to the arch B D.
Fourthly, drawing e K the sine of the arch B K, and taking (in e A produced) e f equal to the diagonal A C, and connecting f C; why f C should pass through a (which point being given, the length of the arch B H D is also given) and c; and why f e and f c should be equal; or if not, why unequal.
Fifthly, drawing f Z, I desire he would show, why it is equal to B V, or to the arch B D; or if they be not equal, what is their difference.
Sixthly, granting f Z to be equal to the arch B D, I desire he would determine whether it fall all without the arch B C A, or cut the same, or touch it, and in what point.
Seventhly, the semicircle B D g being completed, why g I being drawn and produced, should pass through X, by which point X the length of the arch B D is determined. And the same g I being yet further produced to D C in h, why A d, which is equal to the arch B D, should pass through that point h.
Eighthly, upon the centre of the square A B C D, which let be k, the arch of the quadrant E i L being drawn, cutting e K produced in i, why the drawn strait line i X should be parallel to the side C D.
Ninthly, in the sides B A and B C taking g l and B m severally equal to half B V, or to the arch B H, and drawing m n parallel and equal to the side B A, cutting the arch B D in o, why the strait line which connects V l should pass through the point o.
Tenthly, I would know of him why the strait line which connects a H should be equal to B m; or if not, how much it differs from it.