A Mathematical Treatise; Containing a System of Conic-Sections; With the Doctrine of Fluxions and Fluents, Applied to Various Subjects; Viz. to the Finding the Maximums and Minimums of Quantities; Radii of Evolution, Refraction,

A Mathematical Treatise; Containing a System of Conic-Sections; With the Doctrine of Fluxions and Fluents, Applied to Various Subjects; Viz. to the Finding the Maximums and Minimums of Quantities; Radii of Evolution, Refraction,

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1736 edition. Excerpt: ...the Radius of Evolution DM required. EXAMPLE VIII. Fig. 140. 204. ET PFMB, be the reciprocal Spiral, with such a 1 Property, that the Product of any arch AN (2), of " a Circle described with the pole P as a center, and terminated by the radius PN and the first radius PA, multiplied into the part PM (j) of that radius terminated by the Spiral, be always given. Let the arch AB, terminated by the first radius PA and by the Spiral, be--n, and PN =a-, then will an=yz; and because the radius PN is to the radius PM, as the circular velo Art. 188. city--z of the point N, is to the circular velocity x of the point Mj we shall have--yz =ax; and substituting for--z, its value any into the Fluxion--of the Equation an--yzi it will be yy, . yy. y come ny=yx; andfor=---andr--=jry, or--=j. There ccy cc fore ME (cc--rr--rsy)=z, because r--and cc--rr--yy. y n SECTION IV. The Use of Fluxions in finding of Caujlieks by Refraction and by Refection Tie.. 141, 142. Definition. IF the directions of an infinite number of Rays FA, FxVT, all issuing from the fame luminous Point F, be altered after their concurrence with a Curve AMN, either nearer or farther from the perpendicular DM to it; and if the law of alteration be continually such, that the Sine DE of the angle of incidence DME, be to the Sine DB, of the angle of refraction DMB, in the given ratio of m to n: the Curve KLH, which touches all the the broken or refracted Rays, or their continuations AH, ML, is call'd the Caujlick by Refraction. Corollary 205 T F the Caustick L H, be taken as an Evolute, and the Fic. 141; X Involute A Qbe described from the beginning at A: then if from the center F, the circular arch AP be described, the line QL plus the part LH of the Caustick, will be always "= Art....show more

Product details

  • Paperback | 52 pages
  • 189 x 246 x 3mm | 109g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236885481
  • 9781236885487