The Mathematical Writings of Duncan Farquharson Gregory |
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Page 43
... axis of x and the tangent that of y , when x = 0 the two values of y must also = 0 , and therefore D = 0 , which reduces the equation to y2 + Bxy + Cx2 + Ex = 0 . The equation to a circle touching the curve at the given point , that is ...
... axis of x and the tangent that of y , when x = 0 the two values of y must also = 0 , and therefore D = 0 , which reduces the equation to y2 + Bxy + Cx2 + Ex = 0 . The equation to a circle touching the curve at the given point , that is ...
Page 44
... axis of x is determined by the ratio 1 - C B ; and as this is independent of the circle , the line will В remain parallel to one position , as the circle varies in size . But when the circle becomes the circle of curvature , one of the ...
... axis of x is determined by the ratio 1 - C B ; and as this is independent of the circle , the line will В remain parallel to one position , as the circle varies in size . But when the circle becomes the circle of curvature , one of the ...
Page 45
... axis of the cone as the axis of x2 the equation to the cone will be x2 + y2 = m * z * . And if we suppose the cutting plane to be perpendicular to the plane of xz , its equation will be z cosa + x sina = r ; where r is the radius of the ...
... axis of the cone as the axis of x2 the equation to the cone will be x2 + y2 = m * z * . And if we suppose the cutting plane to be perpendicular to the plane of xz , its equation will be z cosa + x sina = r ; where r is the radius of the ...
Page 46
Duncan Farquharson Gregory, Robert Leslie Ellis William Walton. the axis of z . we get Eliminating between the two ... axes of the projection , m2 2.2 2 m2r2 cos2 a 12 12 a 29 ( cos2a - m2 sin2a ) 2 cos2a — m2 sin2 a If a , b be the axes ...
Duncan Farquharson Gregory, Robert Leslie Ellis William Walton. the axis of z . we get Eliminating between the two ... axes of the projection , m2 2.2 2 m2r2 cos2 a 12 12 a 29 ( cos2a - m2 sin2a ) 2 cos2a — m2 sin2 a If a , b be the axes ...
Page 47
... axes of x and y . Let OB = a , OA = -a , OD = b , OC = -c . The equations to BD and AC are α X y h + 2/2 = 1 , y + - 1 . a C At their intersection the equations may be combined in any manner ; therefore , subtracting them , 3 ( 1 − 1 ) ...
... axes of x and y . Let OB = a , OA = -a , OD = b , OC = -c . The equations to BD and AC are α X y h + 2/2 = 1 , y + - 1 . a C At their intersection the equations may be combined in any manner ; therefore , subtracting them , 3 ( 1 − 1 ) ...
Other editions - View all
The Mathematical Writings of Duncan Farquharson Gregory (Classic Reprint) Duncan Farquharson Gregory No preview available - 2019 |
The Mathematical Writings of Duncan Farquharson Gregory William Walton,Robert Leslie Ellis,Duncan Farquharson Gregory No preview available - 2015 |
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a₁ applied arbitrary constants arithmetical asymptotes axis becomes binomial theorem C₁ Cambridge Mathematical Journal centre coefficients commutative commutative operations conic section consider cosine cosne curve determine Differential Calculus differential equations dt² dx dx dx dy dx² dy² Edition equal expression factor Finite Differences fraction functional equation geometrical given Hence infinite integral intersection inverse operation John Herschel laws of combination linear logarithms maxima and minima method motion multiplying negative original P₁ parabola pendulum perpendicular plane of xy point of suspension principles quantity represent residue result right angles roots sides singular point solution subtraction suppose surface symbols of operation tangent Taylor's theorem term theory tion triangle u₂ values variables whence