Geometrical conic sections |
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Page 6
... propositions serve to connect the diameters and other lines , and the areas , of the known curve with those of its projection . EXAMPLES . 1. If the inclination of two planes be the third of two right angles , and a line of 4 yards in ...
... propositions serve to connect the diameters and other lines , and the areas , of the known curve with those of its projection . EXAMPLES . 1. If the inclination of two planes be the third of two right angles , and a line of 4 yards in ...
Page 14
... proposition , if the tangent at P meets the axis major in T , and PN be the ordinate , CN . CT CA. = 8. The tangents to a circle at the extremities of 14 CONIC SECTIONS . Circumscribing parallelogram Supplemental Chords.
... proposition , if the tangent at P meets the axis major in T , and PN be the ordinate , CN . CT CA. = 8. The tangents to a circle at the extremities of 14 CONIC SECTIONS . Circumscribing parallelogram Supplemental Chords.
Page 15
... proposition of the last Art . these will be the tangents required . 9. The above propositions might equally have been made to take the form , if Qv be the ordinate to CD , and the tangent at Q meet CD in t , and Qv2 : CP2 :: Dv . vd ...
... proposition of the last Art . these will be the tangents required . 9. The above propositions might equally have been made to take the form , if Qv be the ordinate to CD , and the tangent at Q meet CD in t , and Qv2 : CP2 :: Dv . vd ...
Page 24
... propositions : If the circle inscribed in the triangle VAA ' touches the sides at K , S , L ; and the circle that touches AA ' and VA , VA ' produced touches them at H , K ' , L ' , then KK ' = AA ' , and ASA'H . also For the perimeter ...
... propositions : If the circle inscribed in the triangle VAA ' touches the sides at K , S , L ; and the circle that touches AA ' and VA , VA ' produced touches them at H , K ' , L ' , then KK ' = AA ' , and ASA'H . also For the perimeter ...
Page 31
... the angle SPY the angle HPZ ( by the last proposition ) = = the vertical opposite angle KPY . Hence SY KY , and SP = KP : = : . KH = KP + PH = SP + PH = 2AC . And C , Y being the middle points of SH FOCAL PROPERTIES OF THE ELLIPSE . 31.
... the angle SPY the angle HPZ ( by the last proposition ) = = the vertical opposite angle KPY . Hence SY KY , and SP = KP : = : . KH = KP + PH = SP + PH = 2AC . And C , Y being the middle points of SH FOCAL PROPERTIES OF THE ELLIPSE . 31.
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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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