A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page xxv
... On the formation of caustics .... 486 323 , 324. Caustic by reflexion of systems of parallel rays 487 325. General properties of such caustics 491 PRICE , VOL . I. d 326. Particular case of the caustics by reflexion at a OF CONTENTS . XXV.
... On the formation of caustics .... 486 323 , 324. Caustic by reflexion of systems of parallel rays 487 325. General properties of such caustics 491 PRICE , VOL . I. d 326. Particular case of the caustics by reflexion at a OF CONTENTS . XXV.
Page xxvii
... parallel to a given plane 538 SECTION 2. - On surfaces generated by 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 ...
... parallel to a given plane 538 SECTION 2. - On surfaces generated by 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 ...
Page 13
... parallel . This then is a case where we cannot compare two geometrical distances , on ac- count of the immensity of one of them . Considering then the 400 millions of miles to be a finite quantity , the distance of the star is infinite ...
... parallel . This then is a case where we cannot compare two geometrical distances , on ac- count of the immensity of one of them . Considering then the 400 millions of miles to be a finite quantity , the distance of the star is infinite ...
Page 49
... parallel to the tan- gent at the vertex o . Let OM = x ) MP = ys ' OA = ar AB = bS ; .. the equation to the curve is y2 b2 = x . a Let AB be divided into n equal parts , and through the several points of division let lines be drawn parallel ...
... parallel to the tan- gent at the vertex o . Let OM = x ) MP = ys ' OA = ar AB = bS ; .. the equation to the curve is y2 b2 = x . a Let AB be divided into n equal parts , and through the several points of division let lines be drawn parallel ...
Page 230
... parallel to the axis of x , and is therefore a dia- meter conjugate to the diameter which is parallel to the axis of a . Similarly , if ( 7 ) = 0 , ( 52 ) has no term involving the x . dr dk dr of and therefore ( 17 ) = 0 , which is y ...
... parallel to the axis of x , and is therefore a dia- meter conjugate to the diameter which is parallel to the axis of a . Similarly , if ( 7 ) = 0 , ( 52 ) has no term involving the x . dr dk dr of and therefore ( 17 ) = 0 , which is y ...
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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