A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page x
... circle we know that the 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 ...
... circle we know that the 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 ...
Page xxiii
... circle , and the epicycloid SECTION 2. - Tangents and normals to polar curves . 412 414 269. The values of ds , and ... circles 422 SECTION 4. - Direction of curvature and points of inflexion . 276. The convexity or concavity of a curve ...
... circle , and the epicycloid SECTION 2. - Tangents and normals to polar curves . 412 414 269. The values of ds , and ... circles 422 SECTION 4. - Direction of curvature and points of inflexion . 276. The convexity or concavity of a curve ...
Page xxiv
... circle 281. Definition of radius of curvature and of circle of curvature . 282. Mathematical values of radius of curvature 432 433 434 436 283. Illustrative examples 284. The angle of contingence , and its relation to the radius of ...
... circle 281. Definition of radius of curvature and of circle of curvature . 282. Mathematical values of radius of curvature 432 433 434 436 283. Illustrative examples 284. The angle of contingence , and its relation to the radius of ...
Page xxv
... circle can have contact of the third order ... 468 312. Contact of curves with given curves . 469 SECTION 2. - The theory of envelopes . 313. Explanation of the subject of envelopes , families of curves , variable parameters . . . . 471 ...
... circle can have contact of the third order ... 468 312. Contact of curves with given curves . 469 SECTION 2. - The theory of envelopes . 313. Explanation of the subject of envelopes , families of curves , variable parameters . . . . 471 ...
Page xxvii
... circles . 369-371 . Surfaces of revolution 539 372-374 . Tubular surfaces 542 CHAPTER XVII . CURVATURE OF CURVES IN SPACE . 375. Mode of measuring absolute curvature ; angle of contingence 547 376. Mode of measuring torsion ; radius of ...
... circles . 369-371 . Surfaces of revolution 539 372-374 . Tubular surfaces 542 CHAPTER XVII . CURVATURE OF CURVES IN SPACE . 375. Mode of measuring absolute curvature ; angle of contingence 547 376. Mode of measuring torsion ; radius of ...
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Common terms and phrases
a₁ algebraical angles b₁ Calculus change of sign changes sign circle coefficients constant curve d2F d2F d²u d²x d²y d2y dx2 d³u d³y derived determine differential equation dr dr dx dx dx dy dx² dy dx dy dy dy dz dy² equal equicrescent explicit function expression F(xo F(xo+h factors finite quantity func geometrical given Hence homogeneous function increases increments indeterminate form infinitesimal Infinitesimal Calculus infinity involved Let f(x logarithm Maclaurin's maxima and minima maximum or minimum minimum value negative partial derived-functions particular values plane positive primitive equation proper fraction real roots replaced result right-hand member Similarly singular value straight line Sturm's Theorem substituting suppose symbols Taylor's Series Theorem tion vanish variables variation versin whence zero
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