Sir Isaac Newton's Two Treatises of the Quadrature of Curves and Analysis by Equations of an Infinite Number of Terms (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1745 Excerpt: ... be propoled, generated by the Rolling of the Circle AHGE upon the Base 1 Drs Cartes calls those Curves, in which the Relation of the Absciss and Ordinate is expressed by an Equation of two Dimensions, Curves of the first Order or Kind, -viz. the Circle, Ellipse, Parabola and Hyperbola: but under Curves of the second Order, he reckons both such, the Relation of whose Absciss and Ordinate is expressed by an Equation of three Dimensions; and likewise those, in which it is expressed by an Equation of four Dimensions. And under Curves of the third Kind or Order, he reckons all those in which the Relation of the Absciss and Ordinate is defined either by an Equation of four or of five Dimensions, and so on. See his Geometry, Sook z. But the Division above, which is Sir Isaac Newton's, is the most simple and natural. See his Enumeratio Linearum tertii Ordinis at the Beginning. And whereas there have been some Differences among learned Men, with respect to what Curves ought to be called geometrical; and as to their Preference in geometrical Constructions of Problems. See our Author's Opinion of this Matter in the Appendix to his Arith. Univ. de Construclione Linear . Where he fliews that the Rule by which to determine the Preference of one Curve to another in Geometry, is the Easiness of the Description; and not the greater Simplicity of the Equation by which it is defined: which last is a Consideration entirely algebraical, otherwise the Parabola ought to be preferred to the Circle in geometrical Constructions: which no one will affirm. The gcner.il Division of Curves by our Author is into geometrically rational, and geometrically irrational. "Curvas geometrici rationales appello, quorum puncla omnia per longitudinet "aquatiombus definitas, i. e. per long...