A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page xxi
... tangent 332 215. Modification of the equation in case the function is ( a ) implicit , ( B ) homogeneous .. 333 216. Equation to the tangent , when the equation to the curve is homogeneous and of three variables 334 217. Equation to the ...
... tangent 332 215. Modification of the equation in case the function is ( a ) implicit , ( B ) homogeneous .. 333 216. Equation to the tangent , when the equation to the curve is homogeneous and of three variables 334 217. Equation to the ...
Page xxiii
... Tangents and normals to polar curves . 269. The values of ds , and of lines and quantities connected with the tangent and the normal 412 414 270. Other values of p .... 271. The same quantities in terms of p and r 272. Examples in ...
... Tangents and normals to polar curves . 269. The values of ds , and of lines and quantities connected with the tangent and the normal 412 414 270. Other values of p .... 271. The same quantities in terms of p and r 272. Examples in ...
Page xxv
... tangent intersect or not at the common point , according as the contact is of an even or odd order 461 462 462 464 308. Order of contact dependent on the number of undetermined constants in the equation to a curve 464 309 , 310. Cases ...
... tangent intersect or not at the common point , according as the contact is of an even or odd order 461 462 462 464 308. Order of contact dependent on the number of undetermined constants in the equation to a curve 464 309 , 310. Cases ...
Page xxvi
... tangent plane to a curved surface . . 333. The direction - cosines of the tangent - plane 498 500 501 334 , 335. Modified forms of the equation to the tangent plane , when the equation to the surface is ( a ) explicit , ( B ) homo ...
... tangent plane to a curved surface . . 333. The direction - cosines of the tangent - plane 498 500 501 334 , 335. Modified forms of the equation to the tangent plane , when the equation to the surface is ( a ) explicit , ( B ) homo ...
Page 30
... tangent at any point is the line which coincides with the straight line joining the point and its consecutive point ; that is , the tangent is the element produced . In elementary treatises on conics , the tan- gent to a conic is ...
... tangent at any point is the line which coincides with the straight line joining the point and its consecutive point ; that is , the tangent is the element produced . In elementary treatises on conics , the tan- gent to a conic is ...
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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