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Page 34 - ... the shortest the nature of the thing admits of, for a general one,) I can compare them. And so, if any two figures expressed by such equations be propounded, I can by the same rule compare them, if they may be compared. This may seem a bold assertion, because it is hard to say a figure may or may not be squared or compa[red] with another, but it is plain to me by the fountai[n I] draw it from. thou[gh] I will not undertake to prove it to others.
Page 34 - I say there is no such curve line, but I can, in less than half a quarter of an hour, tell whether it may be squared, or what are the simplest figures it may be compared with, be those figures conic sections or others. And then, by a direct and short way, (I dare say the shortest the nature of the thing admits of, for a general one,) I can compare them. And so, if any two figures expressed by such equations be propounded, I can...
Page 34 - ... not excepting the method of reducing roots to fractions. The advantage of the way I follow you may guess by the conclusions drawn from it, which I have set down in my answer to M. Leibnitz ; though I have not said all there. For there is no curve line expressed by any equation of three terms, though the unknown quantities affect one another in it, or the indices of their dignities be surd quantities, A ft.