A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page x
... curvature of a circle is continuous , and that the line joining two points of it , however near together they are , cannot be straight ; and thus our symbols , though representatives of such straight lines , only ap- proximately ...
... curvature of a circle is continuous , and that the line joining two points of it , however near together they are , cannot be straight ; and thus our symbols , though representatives of such straight lines , only ap- proximately ...
Page xxii
... curvature and points of inflexion . 240. Direct proof that a curve is convex or concave downwards 12y dx2 according as is positive or negative ... 367 241. Another proof of the same theorem by means of an expansion 368 242. Examples in ...
... curvature and points of inflexion . 240. Direct proof that a curve is convex or concave downwards 12y dx2 according as is positive or negative ... 367 241. Another proof of the same theorem by means of an expansion 368 242. Examples in ...
Page xxiii
... curvature and points of inflexion . 415 417 417 418 420 421 422 276. The convexity or concavity of a curve towards the pole 423 SECTION 5. - Tracing polar curves . 277 General hints for analysing the equations and tracing the curves ...
... curvature and points of inflexion . 415 417 417 418 420 421 422 276. The convexity or concavity of a curve towards the pole 423 SECTION 5. - Tracing polar curves . 277 General hints for analysing the equations and tracing the curves ...
Page xxiv
... curvature ; definition of curvature of a circle 281. Definition of radius of curvature and of circle of curvature . 282. Mathematical values of radius of curvature 432 433 434 283. Illustrative examples 436 284. The angle of contingence ...
... curvature ; definition of curvature of a circle 281. Definition of radius of curvature and of circle of curvature . 282. Mathematical values of radius of curvature 432 433 434 283. Illustrative examples 436 284. The angle of contingence ...
Page xxvii
... CURVATURE OF CURVES IN SPACE . 375. Mode of measuring absolute curvature ; angle of contingence 547 376. Mode of measuring torsion ; radius of torsion 377,378 . Radius of absolute curvature . 379. Angle of curvature 548 549 551 380 ...
... CURVATURE OF CURVES IN SPACE . 375. Mode of measuring absolute curvature ; angle of contingence 547 376. Mode of measuring torsion ; radius of torsion 377,378 . Radius of absolute curvature . 379. Angle of curvature 548 549 551 380 ...
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Common terms and phrases
a₁ algebraical angles b₁ becomes Calculus change of sign changes sign circle coefficients constant cosec curve d2F d2F d²u d²x d²y d³u d³y derived function determine differential equation dr dr dr dy dx dx dx dy dx² dy dx dy dy dy dz dy² dz dx equal equicrescent explicit function expression F(xo F(xo+h factor finite quantity fraction func given Hence homogeneous function increases increments indeterminate form infinite infinitesimal Infinitesimal Calculus infinity involved logarithms loge Maclaurin's maxima and minima maximum or minimum minimum value negative partial derived-functions positive primitive equation radius replaced result right-hand member roots Similarly sin x singular value Sturm's Theorem substituting suppose symbols Theorem tion vanish variables variation versin whence zero