A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page 346
... points . As four conditions determine a parabola , so a parabola is determinate if it touches two given straight ... intersection of ( 52 ) with the original curve : that is , there may be n ( n − 1 ) tangents drawn from a given point to a ...
... points . As four conditions determine a parabola , so a parabola is determinate if it touches two given straight ... intersection of ( 52 ) with the original curve : that is , there may be n ( n − 1 ) tangents drawn from a given point to a ...
Page 347
... point in its plane . A tangent meets a curve in two coincident points ; and as a straight line drawn from a given point cannot cut a curve in more than n points , so the number of pairs of points of intersection of the line with the ...
... point in its plane . A tangent meets a curve in two coincident points ; and as a straight line drawn from a given point cannot cut a curve in more than n points , so the number of pairs of points of intersection of the line with the ...
Page 349
... points of intersection of the straight line with the curve . The extreme point ( x , y , z ) of this cutting line is not fixed ; it may therefore be any point in the plane of the curve : let us assume it to be on the curve : then it is ...
... points of intersection of the straight line with the curve . The extreme point ( x , y , z ) of this cutting line is not fixed ; it may therefore be any point in the plane of the curve : let us assume it to be on the curve : then it is ...
Page 353
... point of intersection of these two lines is the centre of the conic . See Ex . 2 , Art . 141 . If F ( x , y , z ) is of three dimensions , ( 74 ) is the equation to a conic ; and therefore the six points in a curve of the third degree ...
... point of intersection of these two lines is the centre of the conic . See Ex . 2 , Art . 141 . If F ( x , y , z ) is of three dimensions , ( 74 ) is the equation to a conic ; and therefore the six points in a curve of the third degree ...
Page 355
... points of intersection of normals with the curve as there are points of intersection of ( 81 ) with the original curve : that is , the number of points is n2 : therefore from a given point ( § , ŋ ) n2 normals may be drawn to a curve ...
... points of intersection of normals with the curve as there are points of intersection of ( 81 ) with the original curve : that is , the number of points is n2 : therefore from a given point ( § , ŋ ) n2 normals may be drawn to a curve ...
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Common terms and phrases
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