A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page 370
Bartholomew Price. dy dx ' that , at a point of inflexion , and therefore the angle T , attains to a maximum or minimum , and is in fact at the point stationary ; that is , is the same for three consecutive points on the curve : the ...
Bartholomew Price. dy dx ' that , at a point of inflexion , and therefore the angle T , attains to a maximum or minimum , and is in fact at the point stationary ; that is , is the same for three consecutive points on the curve : the ...
Page 371
... point of inflexion ; see fig . 41 . In a similar manner it may be shewn that the logarithmic curve and the catenary are both convex downwards . 243. ] And now let us consider the results of the preceding Articles from a geometrical point ...
... point of inflexion ; see fig . 41 . In a similar manner it may be shewn that the logarithmic curve and the catenary are both convex downwards . 243. ] And now let us consider the results of the preceding Articles from a geometrical point ...
Page 373
... point ( x , y ) , then the curve is concave downwards as in fig . 54 ; and if d'y changes its sign at the point by passing through O or , the curve is above the ... points of inflexion when the equation of curve is an implicit function.
... point ( x , y ) , then the curve is concave downwards as in fig . 54 ; and if d'y changes its sign at the point by passing through O or , the curve is above the ... points of inflexion when the equation of curve is an implicit function.
Page 374
Bartholomew Price. dr parallel to the axis of y so that is a point of inflexion . does not vanish , then there dy The condition therefore for a point of inflexion is primarily ( 110 ) . Now this equation is in its present form evidently ...
Bartholomew Price. dr parallel to the axis of y so that is a point of inflexion . does not vanish , then there dy The condition therefore for a point of inflexion is primarily ( 110 ) . Now this equation is in its present form evidently ...
Page 375
... inflexion are the points common to the two curves whose equations are ( 111 ) ... point of in- flexion at a finite distance , but there may be four points of ... inflexion but also other singular points on the original curve , so it has ...
... inflexion are the points common to the two curves whose equations are ( 111 ) ... point of in- flexion at a finite distance , but there may be four points of ... inflexion but also other singular points on the original curve , so it has ...
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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