A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page 50
... hyperbola . ( 4 ) The area of an ellipse is to that of a circle whose radius is the semi - axis major of the ellipse as the axis minor is to the axis major . Many other problems will be introduced hereafter . CHAPTER II . CONSTRUCTION ...
... hyperbola . ( 4 ) The area of an ellipse is to that of a circle whose radius is the semi - axis major of the ellipse as the axis minor is to the axis major . Many other problems will be introduced hereafter . CHAPTER II . CONSTRUCTION ...
Page 309
... hyper- bola whose transverse axis is 2 a , and conjugate axis 2b , and whose asymptotes are as drawn in fig . 30 ; but which hyperbola , when the 1 is introduced , is in the plane containing the line a'oa , and perpendicular to the ...
... hyper- bola whose transverse axis is 2 a , and conjugate axis 2b , and whose asymptotes are as drawn in fig . 30 ; but which hyperbola , when the 1 is introduced , is in the plane containing the line a'oa , and perpendicular to the ...
Page 310
... hyperbola in the plane passing through the line BOB ' and perpendicular to the plane of the paper , and which is delineated by the dotted lines of the figure , viz . SBS ' and TB'T ' ; and the equations to its asymptotes are x = + ...
... hyperbola in the plane passing through the line BOB ' and perpendicular to the plane of the paper , and which is delineated by the dotted lines of the figure , viz . SBS ' and TB'T ' ; and the equations to its asymptotes are x = + ...
Page 311
... hyperbola may be expressed by x = a sec 0 y = b tan e ; x2 y2 a2 62 + = 1 . x2 a2 y2 - 62 = 1 . ( 9 ) ( 10 ) Other examples of the same kind will be found in the sequel . 194. ] The Cissoid of Diocles . Fig . 34 . DEFINITION . - If at ...
... hyperbola may be expressed by x = a sec 0 y = b tan e ; x2 y2 a2 62 + = 1 . x2 a2 y2 - 62 = 1 . ( 9 ) ( 10 ) Other examples of the same kind will be found in the sequel . 194. ] The Cissoid of Diocles . Fig . 34 . DEFINITION . - If at ...
Page 312
... hyperbola having been operated upon in a manner analogous to the circle in the above generation of the curve . The equation will be subsequently completely analysed ; but certain salient points of it are at once evident from the geo ...
... hyperbola having been operated upon in a manner analogous to the circle in the above generation of the curve . The equation will be subsequently completely analysed ; but certain salient points of it are at once evident from the geo ...
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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