solid problems, and the quinquesection among lineary. But what! are the ancient geometricians to be blamed, who made use of the quadratrix for the finding out of a strait line equal to the arch of a circle? And Pappus himself, was he faulty, when he found out the trisection of an angle by the help of an hyperbole? Or am I in the wrong, who think I have found out the construction of both these problems by the rule and compass only? Neither they, nor I. For the ancients made use of this analysis which proceeds by the powers; and with them it was a fault to do that by a more remote power, which might be done by a nearer; as being an argument that they did not sufficiently understand the nature of the thing. The virtue of this kind of analysis consists in the changing and turning and tossing of rectangles and analogisms; and the skill of analysts is mere logic, by which they are able methodically to find out whatsoever lies hid either in the subject or predicate of the conclusion sought for. But this doth not properly belong to algebra, or the analytics specious, symbolical, or cossick; which are, as I may say, the _brachygraphy_ of the analytics, and an art neither of teaching nor learning geometry, but of registering with brevity and celerity the inventions of geometricians. For though it be easy to discourse by symbols of very remote propositions; yet whether such discourse deserve to be thought very profitable, when it is made without any ideas of the things themselves, I know not. ------------------------------------------------------------------------ [Illustration: C. XX. _of the translation_. _Fig. 1-2_ ] [Illustration: C. XX. _of the translation_. _Fig. 3_ ] [Illustration: C. XX. _of the translation_. _Fig. 4_ ] [Illustration: C. XX. _of the translation_. _Fig. 5-6_ ] ------------------------------------------------------------------------ ------- CHAPTER XXI. OF CIRCULAR MOTION.