The Mathematical Writings of Duncan Farquharson Gregory |
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Page 43
... circle of curvature at any point of a Conic Section , may be readily determined by the following construction . Describe a circle touching the curve at the given point and cutting it in two others , then the chord in the conic section ...
... circle of curvature at any point of a Conic Section , may be readily determined by the following construction . Describe a circle touching the curve at the given point and cutting it in two others , then the chord in the conic section ...
Page 44
... 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 points of intersection coincides with the point of contact , and the line joining ...
... 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 points of intersection coincides with the point of contact , and the line joining ...
Page 45
... circle of curvature at P. 3. In the Cambridge Transactions , Vol . III . , Mr. Morton has demonstrated a number of curious properties of the Conic Sections in relation to the generating cone ; but he does not seem to have noticed the ...
... circle of curvature at P. 3. In the Cambridge Transactions , Vol . III . , Mr. Morton has demonstrated a number of curious properties of the Conic Sections in relation to the generating cone ; but he does not seem to have noticed the ...
Page 49
... circles be touched , two and two , by pairs of tan- gents , the points of intersection of these tangents are in one straight line . But we shall pass on to another problem . 3. If from any point A ( fig . 4 ) in a line of indefinite ...
... circles be touched , two and two , by pairs of tan- gents , the points of intersection of these tangents are in one straight line . But we shall pass on to another problem . 3. If from any point A ( fig . 4 ) in a line of indefinite ...
Page 55
... centre will cut the surface in a circle . The equation to the surfaces without a centre is p'y2 + pz2 = pp'x . Let this be cut by a plane x = m2 + ny , which also cuts the sphere x2 + y2 + z2 SURFACES OF THE SECOND ORDER . 55.
... centre will cut the surface in a circle . The equation to the surfaces without a centre is p'y2 + pz2 = pp'x . Let this be cut by a plane x = m2 + ny , which also cuts the sphere x2 + y2 + z2 SURFACES OF THE SECOND ORDER . 55.
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 |
Common terms and phrases
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