Geometrical conic sections |
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Page iii
... Hyperbola . This Method is calculated to produce a material simplification in the treatment of those curves and to ... Rectangular Hyperbolas : and in the second place , it naturally divides the properties that may be proved by ...
... Hyperbola . This Method is calculated to produce a material simplification in the treatment of those curves and to ... Rectangular Hyperbolas : and in the second place , it naturally divides the properties that may be proved by ...
Page vi
... rectangular hyperbola 3. Magnitude of the axes · Properties of the rectangular hyperbola : - 4. Asymptotes . • 42 2835 43 46 47 48 · 51 52 5. Intercepts between asymptotes and curve equal . Locus of the middle points of parallel chords ...
... rectangular hyperbola 3. Magnitude of the axes · Properties of the rectangular hyperbola : - 4. Asymptotes . • 42 2835 43 46 47 48 · 51 52 5. Intercepts between asymptotes and curve equal . Locus of the middle points of parallel chords ...
Page 6
... rectangular hyperbola helps us to ascertain the properties of the hyperbola of unequal axes . The preceding propositions serve to connect the diameters and other lines , and the areas , of the known curve with those of its projection ...
... rectangular hyperbola helps us to ascertain the properties of the hyperbola of unequal axes . The preceding propositions serve to connect the diameters and other lines , and the areas , of the known curve with those of its projection ...
Page 43
... hyperbola may be projected from or into an hyperbola whose axes are equal , called an equilateral or rectangular hyperbola . Let DED ' , RPR ' be circular sections of the cone , made by planes at right angles to the axis through C and ...
... hyperbola may be projected from or into an hyperbola whose axes are equal , called an equilateral or rectangular hyperbola . Let DED ' , RPR ' be circular sections of the cone , made by planes at right angles to the axis through C and ...
Page 45
... hyperbola will be rectangular and will have each of its axes equal to AA ' . Let the two hyperbolas be now placed in the same plane with their transverse axes coincident , and let the ordinate NP of the first hyperbola produced if ...
... hyperbola will be rectangular and will have each of its axes equal to AA ' . Let the two hyperbolas be now placed in the same plane with their transverse axes coincident , and let the ordinate NP of the first hyperbola produced if ...
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Common terms and phrases
AC² Algebra ARITHMETIC asymptotes auxiliary circle axis major BC² BEGINNERS bisects the angle Cambridge CD² centre Chap Christ's College cloth Conic Sections conjugate diameters conjugate hyperbola CP² Crown 8vo cutting plane directrix draw drawn parallel ELEMENTARY TREATISE ellipse English equal angles equally inclined Examination Papers Extra fcap extremities fcap focal chord foci focus GEOMETRY given Grammar Greek Hence intersect John's College Latin latus rectum line joining manual Mathematical meet the curve method Metric System middle point MIXED MATHEMATICS parabola parallelogram perpendicular point of contact produced meet Professor projection proposition prove quadrilateral rectangle rectangular hyperbola render revised right angles Schools Second Edition semi-diameters shew sphere straight line subtend tangent touch transverse axis triangles Trigonometry University of Cambridge vertex
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