The Doctrine of Fluxions: Not Only Explaining the Elements Thereof, But Also Its Application and Use in the Several Parts of Mathematics and Natural Philosophy
The Doctrine of Fluxions: Not Only Explaining the Elements Thereof, But Also Its Application and Use in the Several Parts of Mathematics and Natural Philosophy
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. 1768 Excerpt: ...the Ordinate at Right Angles, mH is the Radius. 2. In Curves related to a fixed Point, let the Curve 47 AM--z, Ordinate BMzzy, and Mrzzx. Put the Equation of the Curve into Fluxions, and make fome of the firft Fluxions invariable, for which write 1; and ' the Equation being turned into Fluxions again, write 1 for the ...
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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. 1768 Excerpt: ...the Ordinate at Right Angles, mH is the Radius. 2. In Curves related to a fixed Point, let the Curve 47 AM--z, Ordinate BMzzy, and Mrzzx. Put the Equation of the Curve into Fluxions, and make fome of the firft Fluxions invariable, for which write 1; and ' the Equation being turned into Fluxions again, write 1 for the invariable Fluxion, as before: Thus you will determine the other Fluxion and fecond Fluxion, whofe Values being fubjlituted into one of the Forms below which contains that firft and fecond Fluxion, you will have the Radius of Curvature. Forms. # n.n--us--Hence it will easily appear that every Parabola, except the Appolonian, has the Radius of Curvature in the Vertex either infinite or nothing at all. Cor. If ax=yy, bx=.y, cxz=y, dx--y &c. be a Series of Parabolas, then the Angle of Contact (made with the Tangent and Curves at the Vertex of any one is-infinitely greater than the Angle of Contact of the next following one. The Angle of Contact of the first ax=yti is of the fame kind with that of Circles. F f 2 Now FIG. Now it appears that the Angles of Contact of one kind infinitely exceed those of another kind, since the Radius of Curvature of one kind is infinitely greater than that of another; and the Curvature or Angle of Contact is reciprocally as that Radius. Thus in the Curve cx=yt the Radius = = Infinity, and nyy d in the Curve dx--y, the Radius = = Infim 20)! ty, because y--o; and the latter Radius is infinitely greater than she former, for----f--i x---; 2oy nyy zocy and therefore the Angle of Contact of the first infinitely exceeds the Angle of Contact of the last. Therefore a Curve of one kind, how great soever it may be, cannot be interposed at the Point of Contact between the Curve of another kind and its Tangent, however small t...
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New. Trade paperback (US). Glued binding. 482 p. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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