The Geometry of Conics, Part 1 |
From inside the book
Results 1-5 of 21
Page 11
... opposite sides of the axis the sum of the ordinates of 1 , 2 is equal to the sum of the ordinates of 3 , 4 , 44. On a chord through a fixed point O there is taken a mean proportional OM to the segments of the chord . Shew that the locus ...
... opposite sides of the axis the sum of the ordinates of 1 , 2 is equal to the sum of the ordinates of 3 , 4 , 44. On a chord through a fixed point O there is taken a mean proportional OM to the segments of the chord . Shew that the locus ...
Page 18
... opposite sides of the axis , then by addition , < PSQ = 2 ( SpP + SqQ ) = 2 ( SpP + pqT ) = 2PTQ . [ Euc . I. 32 . ( ii ) If P , Q lie on the same side of the axis * , then by subtraction , < PSQ = 2 ( SqQ — SpP ) = 2pTq . Therefore in ...
... opposite sides of the axis , then by addition , < PSQ = 2 ( SpP + SqQ ) = 2 ( SpP + pqT ) = 2PTQ . [ Euc . I. 32 . ( ii ) If P , Q lie on the same side of the axis * , then by subtraction , < PSQ = 2 ( SqQ — SpP ) = 2pTq . Therefore in ...
Page 19
Charles Taylor. If P , Q lie on opposite sides of the vertex , then in the preceding figure produce TS to t . Then < PSt = 1⁄2 PSQ [ 29 . = PTQ . [ 30 . Hence by Euc . I. 32 , < STP + SPT = STQ + STP . Therefore < SPT = STQ . And △ TSP ...
Charles Taylor. If P , Q lie on opposite sides of the vertex , then in the preceding figure produce TS to t . Then < PSt = 1⁄2 PSQ [ 29 . = PTQ . [ 30 . Hence by Euc . I. 32 , < STP + SPT = STQ + STP . Therefore < SPT = STQ . And △ TSP ...
Page 21
... opposite side the direction of the crease touches a parabola . 50. Shew how to draw tangents to a parabola from any given external point . 51. If PQ be the chord of contact of tangents from O , then SO2 = SP . SQ . 52. The tangent at ...
... opposite side the direction of the crease touches a parabola . 50. Shew how to draw tangents to a parabola from any given external point . 51. If PQ be the chord of contact of tangents from O , then SO2 = SP . SQ . 52. The tangent at ...
Page 22
... opposite directions intersect at right angles . 61. The perpendicular drawn to a normal from the point in which it meets the axis envelopes an equal parabola . 62. Normals at the extremities of a focal chord intersect on the diameter ...
... opposite directions intersect at right angles . 61. The perpendicular drawn to a normal from the point in which it meets the axis envelopes an equal parabola . 62. Normals at the extremities of a focal chord intersect on the diameter ...
Other editions - View all
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
Popular passages
Page 10 - The Greek Testament : with a critically revised Text ; a Digest of Various Readings ; Marginal References to Verbal and Idiomatic Usage ; Prolegomena ;"and a Critical and Exegetical Commentary. For the Use of Theological Students and Ministers. By HENRY ALFORD, DD, Dean of Canterbury. Vol. I., containing the Four Gospels.
Page 7 - DIFFERENTIAL AND INTEGRAL CALCULUS. An Elementary Treatise on the Differential Calculus. By WH MILLER, MA Third Edition. 8vo. 6*.
Page 10 - COMPANION TO THE GREEK TESTAMENT. For the use of Theological Students and the Upper Forms in Schools. By AC BARRETT, MA, Caius College.
Page 15 - The Mathematical and other Writings of ROBERT LESLIE ELLIS, MA, late Fellow of Trinity College, Cambridge. Edited by WILLIAM WALTON, MA Trinity College, with a Biographical Memoir by the Very Reverend HARVEY GOODWIN, DD Dean of Ely. 8vo. 16*.
Page 9 - Elementary Course of Mathematics. Designed principally for Students of the University of Cambridge. By HARVEY GOODWIN, DD, Lord Bishop of Carlisle.
Page 11 - PEARSON, DD, late Lord Bishop of Chester. Compiled, with some additional matter occasionally interspersed, for the use of the Students of Bishop's College, Calcutta, by WH MILL, DD late Principal of Bishop's College, and Regius Professor of Hebrew in the University of Cambridge.
Page 10 - Annotations on the Acts of the Apostles. Original and selected. Designed principally for the use of Candidates for the Ordinary BA Degree, Students for Holy Orders, &c., with College and Senate-House Examination Papers. By the Rev. TR MASKEW, MA Second Edition, enlarged. 12mo. 5».
Page 2 - Classics," so far as they have been published, will be adopted. These editions have taken their place amongst scholars as valuable contributions to the Classical Literature of this country, and are admitted to be good examples of the judicious and practical nature of English scholarship; and as the editors have formed their texts from a careful examination of the best editions extant, it is believed that no texts better for general use can be found. The volumes are well printed at the Cambridge University...
Page 11 - A Plain Introduction to the Criticism of the New Testament. With 40 facsimiles from Ancient Manuscripts. For the use of Biblical Students. By FH SCRIVENER, MA Trinity College, Cambridge. 8vo.
Page 2 - THIS series is intended to supply for the use of Schools and Students cheap and accurate editions of the Classics, which shall be superior in mechanical execution to the small German editions now current in this country, and more convenient in form. The texts of the " Biblioiheca Classica?1 and " Grammar' School Classics," so far as they have been published, will be adopted.