A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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Page 1
... distance from the fixed point is equal to the distance from the fixed line , that is , when SP is equal to PM , the Conic Section is K ' called a Parabola . S ( 2. ) When the distance from the fixed point is less than the distance from ...
... distance from the fixed point is equal to the distance from the fixed line , that is , when SP is equal to PM , the Conic Section is K ' called a Parabola . S ( 2. ) When the distance from the fixed point is less than the distance from ...
Page 2
... distance from the fixed point is greater than the distance from the fixed line , that is , when the ratio which SP bears to PM is greater than unity , the Conic Section is called an Hyperbola . 2. The reason of the term Conic Sections ...
... distance from the fixed point is greater than the distance from the fixed line , that is , when the ratio which SP bears to PM is greater than unity , the Conic Section is called an Hyperbola . 2. The reason of the term Conic Sections ...
Page 4
... distance on both sides of the axis . COR . 2. The parabola may be described practically in the following manner . K M Α S x Let S be the focus and KX be the directrix ; and let a rigid bar QM , having a string of the same length as ...
... distance on both sides of the axis . COR . 2. The parabola may be described practically in the following manner . K M Α S x Let S be the focus and KX be the directrix ; and let a rigid bar QM , having a string of the same length as ...
Page 5
... distance from the directrix ; and the distance of any point outside the parabola from the focus is greater than its distance from the directrix . Q Р M X X A ( 1. ) Let Q be a point inside the parabola . Draw QM at right angles to the ...
... distance from the directrix ; and the distance of any point outside the parabola from the focus is greater than its distance from the directrix . Q Р M X X A ( 1. ) Let Q be a point inside the parabola . Draw QM at right angles to the ...
Page 8
... distance SP , and the perpendicular PM on the directrix . K Р M Z X A S M ' R K Let the tangent at P meet the directrix in the point Z ; join SZ ; then since the angle ZSP is a right angle , ( Prop . IV . ) : . ZS2 + SP2 = PZ2 . Also ...
... distance SP , and the perpendicular PM on the directrix . K Р M Z X A S M ' R K Let the tangent at P meet the directrix in the point Z ; join SZ ; then since the angle ZSP is a right angle , ( Prop . IV . ) : . ZS2 + SP2 = PZ2 . Also ...
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Common terms and phrases
AC² angle ZSP auxiliary circle BC² BERNARD DRAKE bisects the angle CA² Cambridge CD be conjugate CD² centre circle be described circle described circle of curvature cloth CO.'S PUBLICATIONS cone Conic Sections conjugate diameters conjugate hyperbola CP² Crown 8vo curve cutting plane drawn at right drawn parallel ellipse Euclid Fcap Fellow of St Fellow of Trinity focal chord focus intersect John's College join SP late Fellow latus rectum let the tangent M.A. Fellow MACMILLAN & CO.'S major axis mean proportional meet CD meet the axis meet the directrix meet the ellipse meeting the asymptotes pair of tangents parabola parallelogram perpendicular PN² produced to meet Prop prove QV² radius right angles Second Edition triangle Trinity College University of Cambridge vertex
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