An Introduction to the Doctrine of Fluxions |
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Common terms and phrases
abfcifs AC abfcifs AC=x afymptote alfo alſo Area axis bafe baſe becauſe circle coincide confequently Conftruction Convex Superficies curvilineal ſpace Cycloid decreaſe degree of velocity deſcribed diameter diſtance draw the right drawn equal and parallel equation equation art Evolute EXAMPLE expref expreffion faid fame femicircle fhall fide fimilar fince find the Fluent find the Fluxion find the point firſt flow fore fubftituted fuch fuppofed indefinitely given greateſt Hence increaſe Increment indefinite right line Infinite Series interfecting Involute likewife little right line Logarithm Maximum Method of Fluxions multiplied muſt negative ordinate CB ordinate CB=y PABC point of Inflection progreffion radii Radius of Curvature rectangle reſpectively right line perpendicular ſaid Scholium Second Fluxion ſhall ſubſtituted Subtangent CT ſuppoſed Tangent term CB theſe whofe whoſe xion
Popular passages
Page 188 - JJ/xJV; hence, The sum of the logarithms of any two numbers is equal to the logarithm of their product. Therefore, the addition of logarithms corresponds to the multiplication of their numbers.
Page 199 - ... to the greater, which is impossible : therefore .Fis not the center of the circle ABC. In the same manner it may be shewn, that no other point which is not in CA, is the center ; that is, the center of the circle is in CA.
Page 215 - Tranflated from the Author's Latin Original, not yet made public. To which is fubjoined, a Perpetual Comment upon the whole Work. By JOHN COLSON, MA and FRS Quarto.
Page 214 - the Operations, with fome of the Ufes and Applications of that admirable Method : According to the Scheme prefixed to his Traft of Quadratures, by ( its firft Inventor ) the incomparable Sir Ijaac Newton.
Page 153 - Since the fluxion of the logarithm of any quantity is equal to the fluxion of that quantity divided by the...
Page 5 - However, as the point b is continually nearer to a coincidence with the Tangent...
Page 200 - Now, it is evident, that, at the point of Inflection, the Radius of Curvature muft be Infinité; or, that, on one fide of...
Page 217 - DOCTRINE of FLUXIONS ; not only explaining the Elements thereof, but alfo its Application and Ufe in the feveral Parts of Mathematics and Natural Philofophy.
Page 132 - For then we ihall have as many points in the Evolute; through which, if a Curve line be drawn, it will be. the Evolute fought.