The Geometry of Conics, Part 1 |
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Page xi
... square on a ~ b , the whole figure thus made up will be the square on a + b . or Therefore ( a + b ) 2 = ( a ~ b ) 2 + 4ab , ( a + b ) 3 — ( a ~ b ) 2 = 4ab . The same is proved in Euc . II . 8 , but by an unsym- metrical construction ...
... square on a ~ b , the whole figure thus made up will be the square on a + b . or Therefore ( a + b ) 2 = ( a ~ b ) 2 + 4ab , ( a + b ) 3 — ( a ~ b ) 2 = 4ab . The same is proved in Euc . II . 8 , but by an unsym- metrical construction ...
Page 3
... square of the focal ordinate or semi - latus rectum is equal to 4AS . AS . Hence the latus rectum is equal to 448. Hence also , the ordinate is a mean propor- tional between the abscissa and the latus rectum . 5. Conversely , if P be ...
... square of the focal ordinate or semi - latus rectum is equal to 4AS . AS . Hence the latus rectum is equal to 448. Hence also , the ordinate is a mean propor- tional between the abscissa and the latus rectum . 5. Conversely , if P be ...
Page 22
... square of twice the normal perpendicular to the chord . 68. The locus of the vertex of a parabola which has a given focus and touches a given straight line is a circle . 69. The circle on a focal radius touches the tangent at A. 70. The ...
... square of twice the normal perpendicular to the chord . 68. The locus of the vertex of a parabola which has a given focus and touches a given straight line is a circle . 69. The circle on a focal radius touches the tangent at A. 70. The ...
Page 28
... within the hyperbola . 89. Conics having the same focus and directrix do not meet . Except when P is within the further branch of a hyperbola . 53. PROP . II . The square of the principal 28 CHORD - PROPERTIES OF THE ELLIPSE .
... within the hyperbola . 89. Conics having the same focus and directrix do not meet . Except when P is within the further branch of a hyperbola . 53. PROP . II . The square of the principal 28 CHORD - PROPERTIES OF THE ELLIPSE .
Page 29
Charles Taylor. 53. PROP . II . The square of the principal ordinate PN of any point P on an ellipse whose vertices are A , A ' , varies as AŃ NA ' . ZA P M X A N A Z p Let A'P , PA meet the directrix in Z ' , Z. Then and Compounding ...
Charles Taylor. 53. PROP . II . The square of the principal ordinate PN of any point P on an ellipse whose vertices are A , A ' , varies as AŃ NA ' . ZA P M X A N A Z p Let A'P , PA meet the directrix in Z ' , Z. Then and Compounding ...
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Common terms and phrases
abscissa auxiliary circle bisects the angle Bishop of Carlisle CA² Cambridge CB² CD² centre CN² concyclic Conic Sections conjugate diameters conjugate radii constant ratio CP² CS² CV² draw drawn ellipse equally inclined Fellow of Trinity fixed point focal chord focal perpendicular focal radii focus Geometry Hence intersect J. W. DONALDSON late Fellow latus rectum locus meet the asymptotes meet the curve meet the directrix meets the axis middle point minor axis normal parabola parallel chords parallelogram Pembroke College PN² point Q principal ordinate PROP QV² radius rectangular hyperbola right angles right-angled triangles Second Edition Shew shewn sides SP² St John's College straight line joining subtends a right supplementary angles tangent Third Edition Treatise Trinity College vertex
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