A Treatise on Fluxions: In Two Volumes, Volume 2W. Baynes, 1801 - Calculus |
Contents
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Common terms and phrases
acquired algebraic algebraic quantities angle arch axis bisected body CA² CD² centre of gravity centrifugal force circle circular arks compound ratio computed conic sections curve density described determined diameter direction distance earth ellipse equal successive differences equator expressed figure fluxion of AA follows force EK given hyperbola increase or decrease increment integer invariable inversely last article likewise line of swiftest logarithm manner maxima and minima measured meet method of fluxions minimum motion multiplied ordinate parallel perpendicular plane proportion quadratic divisors quantity radius ray of curvature rectangle represented resolved respective right line sine Sir Isaac Newton solid sphere spheroid ADBE square supposed equal surface swiftest descent tangent theorem tion uniform vanish velocity
Popular passages
Page 1 - Magnitudes were supposed to be generated by motion; and, by comparing the increments that were generated in any equal successive parts of the time, it was first determined whether the motion was uniform, accelerated, or retarded. . . . When the motion was accelerated, this increment was resolved into two parts ; that which alone would have been generated if the motion had not been accelerated, but had continued uniform from the beginning of the time, and that which was generated in consequence of...
Page 311 - The Anti-logarithmic Canon. Being a Table of Numbers, Consisting of Eleven Places of Figures corresponding to all Logarithms under 100000. Whereby the Logarithm for any Number, or the Number for any Logarithm, each under Twelve Places of Figures, are readily found. With Precepts and Examples...
Page 311 - ... whereby a person in a few days may instruct himself to write short hand correctly, & by a little practice cannot fail taking down any discourse deliver'd in public.
Page 164 - The logarithm of a product is equal to the sum of the logarithms of the factors : log ab = log a + log b. This follows from the fact that if 10* = a and 10¿ = &, 10z+¿ = a • b.
Page 160 - ... often saves the trouble of distinguishing, and demonstrating separately, the various cases of proportions, and preserves their analogy in view. But as the proportions of lines depend on their magnitude only, without regard to their position ; and motions and forces are said to be equal or unequal, in any given ratio, without regard to their directions; and in general the proportion of quantities relates to their magnitude only, without determining whether they are to be considered as increments...
Page 1 - Among mathematicians, are defined to be infinitely small quantities. In the method of infinitesimals, the element by which any quantity increases or decreases, is supposed to be infinitely small ; and is generally expressed by two or more terms...
Page 160 - Maclaurin observes, that the use of the negative sign, in algebra, is attended with several consequences that at first sight are admitted with difficulty, and has sometimes given occasion to notions that seem to have no real foundation. This sign implies, that the real value of the quantity represented by the letter to which it is prefixed is to be subtracted : and it serves, with the positive sign, to keep in view what elements or parts enter into the composition of quantities, and in what manner,...
Page 160 - ... difficulty, and has sometimes given occasion to notions that seem to have no real foundation. This sign implies, that the real value of the quantity represented by the letter to which it is prefixed is to be subtracted ; and it serves, with the positive sign, to keep in view what elements or parts enter into the composition of quantities, and in what manner, whether as increments or decrements, that is, whether by addition or subtraction, which is of the greatest use in this art.
Page 100 - ... of the squares of any two conjugate diameters is equal to the difference of the squares of the axes.
Page 40 - ... the sum of the two products of each body multiplied by its distance from that point is equal to the product of the sum of the bodies multiplied by the distance of their common centre of gravity from the same point.