Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 páginas |
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Página 9
... on the tangent at P. So since Tlies on the tangent at Q. Hence , in the right - angled triangles SLT , SMT , the sides SL , SM are equal . But the hypotenuse ST is common . Therefore the angles TSL , TSM are equal , or CONICS . 9.
... on the tangent at P. So since Tlies on the tangent at Q. Hence , in the right - angled triangles SLT , SMT , the sides SL , SM are equal . But the hypotenuse ST is common . Therefore the angles TSL , TSM are equal , or CONICS . 9.
Página 13
... common and are similar . Therefore SK : SN = SG : SP = SA : AX . [ Prop . IX . Alternando SK : SA = SN : AX , also Therefore SP : SA = NX : AX . PK : SA = SX : AX . [ Def.and alternando . [ Euc . v . , 24 , Cor . 1 . But SE : SA = SX ...
... common and are similar . Therefore SK : SN = SG : SP = SA : AX . [ Prop . IX . Alternando SK : SA = SN : AX , also Therefore SP : SA = NX : AX . PK : SA = SX : AX . [ Def.and alternando . [ Euc . v . , 24 , Cor . 1 . But SE : SA = SX ...
Página 26
... common . Hence the remaining angles are equal , each to each , so that L SPR = MPR . Hence also the supplementary angles , which RP produced makes with SP , PM , are equal . Produce PR to meet the axis in T. M R S N Then L SPT = MPT ...
... common . Hence the remaining angles are equal , each to each , so that L SPR = MPR . Hence also the supplementary angles , which RP produced makes with SP , PM , are equal . Produce PR to meet the axis in T. M R S N Then L SPT = MPT ...
Página 29
... common to the right- angled triangles SPR , MPR , therefore RM = RS = = RN similarly . Draw RO parallel to the axis and meeting PQ in R. Then PO = 0Q . Hence PM + QN = 2RO . But SP = PM and SQ = QN . [ Def . Therefore PQ = PM + QN = 2RO ...
... common to the right- angled triangles SPR , MPR , therefore RM = RS = = RN similarly . Draw RO parallel to the axis and meeting PQ in R. Then PO = 0Q . Hence PM + QN = 2RO . But SP = PM and SQ = QN . [ Def . Therefore PQ = PM + QN = 2RO ...
Página 30
... directrix , meet QR in T. Then , in the triangles MPR , SPR , the side MP is equal to SP , and PR is common . Also △ MPR = SPR . [ Prop . II . Therefore the remaining angles are equal , each to each 30 THE PARABOLA . QV4SP.
... directrix , meet QR in T. Then , in the triangles MPR , SPR , the side MP is equal to SP , and PR is common . Also △ MPR = SPR . [ Prop . II . Therefore the remaining angles are equal , each to each 30 THE PARABOLA . QV4SP.
Otras ediciones - Ver todo
Geometrical Conics: Including Anharmonic Ratio and Projection, with numerous ... Charles Taylor Vista previa restringida - 2022 |
Geometrical Conics: Including Anharmonic Ratio and Projection, with numerous ... Charles Taylor Vista previa restringida - 2022 |
Términos y frases comunes
ABCD abscissa asymptotes auxiliary circle axis in G bisects the angle CA² Cambridge CB² CD² centre chord of contact chord of curvature chords parallel cone conic Conic Sections conjugate diameters conjugate hyperbola conjugate points constant ratio corresponding CP² Crown 8vo Draw drawn parallel ellipse equally inclined fixed point fixed straight line focal chord foci focus harmonic Hence inscribed latus rectum Let the tangent locus major axis meet the asymptotes meet the axis meet the curve meet the directrix meet the minor middle point minor axis opposite sides ordinate parabola parallelogram pass pencil perpendicular plane PM perpendicular point of intersection point Q points of contact polar projection Prop prove quadrilateral rectangular hyperbola right angles semi-latus rectum similar triangles Similarly straight line drawn subtends touches vertex
Pasajes populares
Página 226 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools.