A Treatise on Infinitesimal Calculus ... |
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Page xxix
... circles , geodesic parallels , geodesic conics .. 343. Examples of geodesics on a sphere and on a cylinder 344. Geodesics on the surface of an ellipsoid ; Joachimsthal's theorem 476 477 478 479 480 481 .. 483 485 345 , 346. Theorems ...
... circles , geodesic parallels , geodesic conics .. 343. Examples of geodesics on a sphere and on a cylinder 344. Geodesics on the surface of an ellipsoid ; Joachimsthal's theorem 476 477 478 479 480 481 .. 483 485 345 , 346. Theorems ...
Page 198
... circle ; see fig . 3 . Let the centre be the origin ; and let the arc APμ , whose length is required , begin at A , and be measured from A towards B ; so that , if APS , Oм = x , x decreases as s increases ; let oм1 = xi then since 2+ ...
... circle ; see fig . 3 . Let the centre be the origin ; and let the arc APμ , whose length is required , begin at A , and be measured from A towards B ; so that , if APS , Oм = x , x decreases as s increases ; let oм1 = xi then since 2+ ...
Page 200
... circle . Since ( 11 ) expresses a general relation between the length of an arc of the cycloid measured from the vertex and the abscissa to the extremity of that arc , it may be and frequently will be employed hereafter as the equation ...
... circle . Since ( 11 ) expresses a general relation between the length of an arc of the cycloid measured from the vertex and the abscissa to the extremity of that arc , it may be and frequently will be employed hereafter as the equation ...
Page 202
... circle referred to the centre as origin be ex- pressed by the two equations x = a cos 0 , y = a sin 0 ; then a sin o de , dy = a cos e do ; dx = .. ds = a do ; 8 = a ( 0-0 ) , ( 21 ) if s is the length of the arc between the points to ...
... circle referred to the centre as origin be ex- pressed by the two equations x = a cos 0 , y = a sin 0 ; then a sin o de , dy = a cos e do ; dx = .. ds = a do ; 8 = a ( 0-0 ) , ( 21 ) if s is the length of the arc between the points to ...
Page 210
... vectores is equal to the projection of the length of the curve between the corresponding points on a line to which it is inclined at the constant angle . Ex . 3. The Circle , the extremity of a 210 [ 162 . RECTIFICATION OF PLANE CURVES .
... vectores is equal to the projection of the length of the curve between the corresponding points on a line to which it is inclined at the constant angle . Ex . 3. The Circle , the extremity of a 210 [ 162 . RECTIFICATION OF PLANE CURVES .
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A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2015 |
Common terms and phrases
a₁ a₂ angle application axis Beta-function bx dx consequently convergent series coordinates cosec cx² cycloid definite integral denoted determined differential double integral dx a² dx dx dx dy dx Ex dx² dy dx dy² e-ax element-function ellipse equal evaluation expressed find the area finite and continuous fraction function Gamma-function geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation involute left-hand member length let us suppose limits of integration multiple integrals plane curve polar coordinates preceding proper fraction radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variable x-integration x₁ x²)¹ x²)³ αξ πα