The Geometry of Conics, Part 1 |
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Page vi
... Salmon's inexhaustible works . April , 1872 . * The triangles pCN , dCR in Arts . 72 , 212 differ only in relative position . + See page 38 . Arts . 53 , 202 . CONTENTS . CHAPTER I. CHORD - PROPERTIES OF THE PARABOLA vi PREFACE .
... Salmon's inexhaustible works . April , 1872 . * The triangles pCN , dCR in Arts . 72 , 212 differ only in relative position . + See page 38 . Arts . 53 , 202 . CONTENTS . CHAPTER I. CHORD - PROPERTIES OF THE PARABOLA vi PREFACE .
Page x
... triangle , always in the same plane , by the point of a pencil or sharp instrument at P. Then as P moves in such a way as to keep the string stretched it describes an ellipse . It is evident that if S , S ' be made to coincide the ...
... triangle , always in the same plane , by the point of a pencil or sharp instrument at P. Then as P moves in such a way as to keep the string stretched it describes an ellipse . It is evident that if S , S ' be made to coincide the ...
Page xi
... triangles QuZ , Q'vZ ' , vZ = vZ ' , QM – Ov = Ov — Q'M ' . Therefore QM + Q'M ' = 20v . If the figure be drawn as on p . 66 , where O bisects Qq , it may be shewn in like manner that QM — qm = 2OL . If the parallels drawn as above be ...
... triangles QuZ , Q'vZ ' , vZ = vZ ' , QM – Ov = Ov — Q'M ' . Therefore QM + Q'M ' = 20v . If the figure be drawn as on p . 66 , where O bisects Qq , it may be shewn in like manner that QM — qm = 2OL . If the parallels drawn as above be ...
Page 6
... without assuming Prop . II .: In the right - angled triangles MQO , SQO , which have MQ , QO = SQ , QO , the side OMOSOM ' , similarly . Hence Qv = Q'v . 12. PROP . IV . the parabola , then If 6 CHORD - PROPERTIES OF THE PARABOLA .
... without assuming Prop . II .: In the right - angled triangles MQO , SQO , which have MQ , QO = SQ , QO , the side OMOSOM ' , similarly . Hence Qv = Q'v . 12. PROP . IV . the parabola , then If 6 CHORD - PROPERTIES OF THE PARABOLA .
Page 7
... triangles OYV , QDV . 2 2 But QD2 = OM2 = OY- SY2 , as in Art . 7 . Therefore Also Therefore and QV2 = OV2 - v V2 . Pv = SP = PO , as in Art . 10 . OV = PV + SP , ~ V = PV ~ SP . Therefore OV2 — v V2 = 4SP.PV. Hence [ Introd . QV2 = 4SP ...
... triangles OYV , QDV . 2 2 But QD2 = OM2 = OY- SY2 , as in Art . 7 . Therefore Also Therefore and QV2 = OV2 - v V2 . Pv = SP = PO , as in Art . 10 . OV = PV + SP , ~ V = PV ~ SP . Therefore OV2 — v V2 = 4SP.PV. Hence [ Introd . QV2 = 4SP ...
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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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