To the tenth you object for almost three leaves together, against these words of mine, _because_, in the sixth figure, _B C is to B F in triplicate proportion of C D to F E, therefore inverting, F E is to C D in triplicate proportion of B F to B C_. This you objected then. But now that I have taught you so much geometry, as to know _that of three quantities, beginning at the least, if the third be to the first in triplicate proportion of the second to the first, also by conversion the first to the second shall be in triplicate proportion of the first to the third_; if it were to do again, you would not object it. My eleventh article you would allow for demonstrated, if my second had been demonstrated, upon which it dependeth. Therefore seeing your objections to that article are sufficiently answered, this article also is to be allowed. The twelfth also is allowed upon the same reason. What falsities you shall find in such following propositions as depend upon the same second article, we shall then see when I come to the places where you object against them. To the thirteenth article you object, “_that the same demonstration may be as well applied to a portion of any conoeides, parabolical, hyperbolical, elliptical, or any other, as to the portion of a sphere_.” By the truth of this let any man judge of your and my geometry. Your comparison of the sphere and conoeides, so far holds good, as to prove that the superficies of the conoeides is greater than the superficies of the cone described by the subtense of the parabolical, hyperbolical, or elliptical line. But when I come to say, that _the cause of the excess of the superficies of the portion of the sphere above the superficies of the cone, consists in the angle D A B, and the cause of the excess of the circle made upon the tangent A D, above the superficies of the same cone, consists in the magnitude of the same angle D A B_, how will you apply this to your conoeides? For suppose that the crooked line A B (in the seventh figure) were not an arch of a circle, do you think that the angles which it maketh with the subtense A B, at the points A and B, must needs be equal? Or if they be not, does the excess of the superficies of the circle upon A D above the superficies of the cone, or the excess of the superficies of the portion of the conoeides above the superficies of the same cone, consist in the angle D A B, or rather in the magnitude of the two unequal angles D A B, and A B A? You should have drawn some other crooked line, and made tangents to it through A and B, and you would presently have seen your error. See how you can answer this; for if this demonstration of mine stand firm, I may be bold to say, though the same be well demonstrated by Archimedes, that this way of mine is more natural, as proceeding immediately from the natural efficient causes of the effect contained in the conclusion; and besides, more brief and more easy to be followed by the fancy of the reader.