Geometrical conic sections |
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Page 10
... meet the curve in two points on opposite sides of AA ' , and at equal distances from it . AA ' is called the axis major of the ellipse , and a line through C its middle point in the plane of the curve at right angles to AA ' limited by ...
... meet the curve in two points on opposite sides of AA ' , and at equal distances from it . AA ' is called the axis major of the ellipse , and a line through C its middle point in the plane of the curve at right angles to AA ' limited by ...
Page 14
... meet therefore when projected these chords are parallel to conjugate diameters of the ellipse : such chords when projected are called supplemental chords ; they form two sides of a triangle the base of which is a diameter , and its ...
... meet therefore when projected these chords are parallel to conjugate diameters of the ellipse : such chords when projected are called supplemental chords ; they form two sides of a triangle the base of which is a diameter , and its ...
Page 15
... meet in the diameter ( produced ) which bisects the chord : and the tangent at the extremity of the diameter when ... meet CD in t , and Qv2 : CP2 :: Dv . vd : CD2 , Cv . Ct CD2 . = As a particular case of the latter , if Pn be the ...
... meet in the diameter ( produced ) which bisects the chord : and the tangent at the extremity of the diameter when ... meet CD in t , and Qv2 : CP2 :: Dv . vd : CD2 , Cv . Ct CD2 . = As a particular case of the latter , if Pn be the ...
Page 16
... meet AA ' produced in the same point as the tangent to the ellipse at P. Hence we shall have А NG.NT - NP2 and NC . NT = NQ2 ; A ' .. NG : NC :: NP : NQ :: BC : AC . 12. By the reasoning of the last article we see that if CP , CD be con ...
... meet AA ' produced in the same point as the tangent to the ellipse at P. Hence we shall have А NG.NT - NP2 and NC . NT = NQ2 ; A ' .. NG : NC :: NP : NQ :: BC : AC . 12. By the reasoning of the last article we see that if CP , CD be con ...
Page 18
... meet the auxiliary circle in Q , and PR parallel to the major axis to meet the circle on the minor axis in R , QR produced will pass through the common centre . 3. A rectilinear figure circumscribing an ellipse and having its sides ...
... meet the auxiliary circle in Q , and PR parallel to the major axis to meet the circle on the minor axis in R , QR produced will pass through the common centre . 3. A rectilinear figure circumscribing an ellipse and having its sides ...
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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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