Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 σελίδες |
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Σελίδα 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.
Σελίδα 13
... common and are similar . Therefore SK : SN = SG : SP = = SA : AX . [ Prop . IX . Alternando SK : SA = also SN : AX , SP : SA = NX : AX . [ Def.and alternando . Therefore PK : SA = SX : AX . [ 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 = also SN : AX , SP : SA = NX : AX . [ Def.and alternando . Therefore PK : SA = SX : AX . [ Euc . v . , 24 , Cor . 1 . But SE : SA = SX ...
Σελίδα 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 N Then △ 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 N Then △ SPT = MPT ...
Σελίδα 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 ...
Σελίδα 30
... directrix , meet QR in T. Then , in the triangles MPR , SPR , the side MP is equal to SP , and PR is common . Also 4 MPR = SPR . [ Prop . II . Therefore the remaining angles are equal , each to each 30 THE PARABOLA . QV2 = 4SP.
... directrix , meet QR in T. Then , in the triangles MPR , SPR , the side MP is equal to SP , and PR is common . Also 4 MPR = SPR . [ Prop . II . Therefore the remaining angles are equal , each to each 30 THE PARABOLA . QV2 = 4SP.
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Geometrical Conics: Including Anharmonic Ratio and Projection, with numerous ... Charles Taylor Περιορισμένη προεπισκόπηση - 2022 |
Geometrical Conics: Including Anharmonic Ratio and Projection, with numerous ... Charles Taylor Περιορισμένη προεπισκόπηση - 2022 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD abscissa Alternando asymptotes auxiliary circle axis in G bisects the angle CA² Cambridge CB² CD² centre chord of contact chord of curvature chord PQ chords parallel cone Conic Sections conjugate diameters conjugate hyperbola 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 Lemma Let the tangent locus major axis meet the axis meet the directrix meet the minor meets the curve middle point minor axis opposite sides ordinate parabola parallel chords parallelogram pass pencil perpendicular plane point of intersection point Q points of contact polar produced projection Prop prove quadrilateral rectangular hyperbola right angles semi-diameter semi-latus rectum similar triangles Similarly straight line drawn touches vertex
Δημοφιλή αποσπάσματα
Σελίδα 226 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools.