A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page xx
... equations .. 210. The number of the points of intersection of two curves of the mth and nth degree ; the theorems of Newton and Cotes 320 322 324 325 211. The number of given points through which a curve XX ANALYTICAL TABLE.
... equations .. 210. The number of the points of intersection of two curves of the mth and nth degree ; the theorems of Newton and Cotes 320 322 324 325 211. The number of given points through which a curve XX ANALYTICAL TABLE.
Page 314
... points of intersection is the Lemniscata . Let x and У be the current coordinates of the lines PQ and OP ; and let x ' , y ' be the coordinates to Q , the point on the hyperbola at which the tangent is drawn ; the equations to the ...
... points of intersection is the Lemniscata . Let x and У be the current coordinates of the lines PQ and OP ; and let x ' , y ' be the coordinates to Q , the point on the hyperbola at which the tangent is drawn ; the equations to the ...
Page 325
... points in which the two curves intersect ; the points in which they intersect , I say ; because if all the roots are real , the curves will intersect in mn points in the plane of reference ; and if the roots are imaginary , the points of ...
... points in which the two curves intersect ; the points in which they intersect , I say ; because if all the roots are real , the curves will intersect in mn points in the plane of reference ; and if the roots are imaginary , the points of ...
Page 329
... intersection of u = 0 and of v = 0 , and therefore n ( n + 3 ) clearly passing through the -1 given points ; and as 2 k is undetermined , the number of ... points also pass through three other given points 211. ] 329 ALGEBRAICAL CURVES .
... intersection of u = 0 and of v = 0 , and therefore n ( n + 3 ) clearly passing through the -1 given points ; and as 2 k is undetermined , the number of ... points also pass through three other given points 211. ] 329 ALGEBRAICAL CURVES .
Page 330
Bartholomew Price. thirteen given points also pass through three other given points . n ( n + 3 ) Hence also it ... intersection of two curves of the nth degree : n ( n + 3 ) but -1 of them being given , the remainder , viz . 2 ( n - 1 ) ( n ...
Bartholomew Price. thirteen given points also pass through three other given points . n ( n + 3 ) Hence also it ... intersection of two curves of the nth degree : n ( n + 3 ) but -1 of them being given , the remainder , viz . 2 ( n - 1 ) ( n ...
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according algebraical angles applicable assume axis becomes Calculus called changes sign Chapter circle coefficients consider constant continuous corresponding curve derived derived-functions determine differential dimensions direction divided drawn dx dy dy dx elimination equal equation examples expression factors finite function geometrical given gives greater Hence homogeneous function increases independent infinite infinitesimal infinity involved less limit maxima maximum means method minima minimum value negative observed origin partial particular pass plane positive powers preceding properties quantity relation replaced represent respectively result roots sides similar Similarly singular value straight line substituted successive suppose symbols tangent Theorem tion true values vanish variables variation vary whence zero