A Geometrical Treatise on Conic Sections, with a copious collection of examples |
From inside the book
Results 1-5 of 18
Page
... conjugate diameters in the ellipse , and of the asymptotes in the hyperbola , and the proof that QV2 = 4SP . PV in the parabola ; while many important theorems admitting of an easy geo- metrical solution are introduced . 2 ( 6. ) A full ...
... conjugate diameters in the ellipse , and of the asymptotes in the hyperbola , and the proof that QV2 = 4SP . PV in the parabola ; while many important theorems admitting of an easy geo- metrical solution are introduced . 2 ( 6. ) A full ...
Page 51
... conjugate semi - diameters , and PN , DR be the ordinates of the points P and D ; then ( 1. ) CN2 + CR2 = AC2 , ( 2. ) PN2 + DR2 = BC2 . ( 3. ) CP2 + CD2 = A C2 + BC2 , T N C R T ' Produce NP , RD E 2 CONIC SECTIONS . 51 .. the triangle ...
... conjugate semi - diameters , and PN , DR be the ordinates of the points P and D ; then ( 1. ) CN2 + CR2 = AC2 , ( 2. ) PN2 + DR2 = BC2 . ( 3. ) CP2 + CD2 = A C2 + BC2 , T N C R T ' Produce NP , RD E 2 CONIC SECTIONS . 51 .. the triangle ...
Page 54
... conjugate diameters is equal to the rectangle contained by the axes of the ellipse . Let PCP ' , DCD ' be a pair of conjugate diameters , and let a parallelogram be formed by drawing tangents at the points P , P ' , D , D ' . Ꭲ ...
... conjugate diameters is equal to the rectangle contained by the axes of the ellipse . Let PCP ' , DCD ' be a pair of conjugate diameters , and let a parallelogram be formed by drawing tangents at the points P , P ' , D , D ' . Ꭲ ...
Page 55
... conjugate diameters , and PF be drawn at right angles to CD meeting CA in G , then PF . PG t = B BC " . P n D G A ' A S ' N F K D ' Draw the ordinate PN , and produce it to meet CD ' in K. Also draw Pn at right angles to CB , and let ...
... conjugate diameters , and PF be drawn at right angles to CD meeting CA in G , then PF . PG t = B BC " . P n D G A ' A S ' N F K D ' Draw the ordinate PN , and produce it to meet CD ' in K. Also draw Pn at right angles to CB , and let ...
Page xxii
... conjugate diameters is equal to the rectangle contained by the axes of the ellipse . Let PCP ' , DCD ' be a pair of conjugate diameters , and let a parallelogram be formed by drawing tangents at the points P , P ' , D , D ' . R - ~ T Р ...
... conjugate diameters is equal to the rectangle contained by the axes of the ellipse . Let PCP ' , DCD ' be a pair of conjugate diameters , and let a parallelogram be formed by drawing tangents at the points P , P ' , D , D ' . R - ~ T Р ...
Other editions - View all
Common terms and phrases
AC² angle ZSP auxiliary circle BC² BERNARD DRAKE bisects the angle CA² Cambridge CD be conjugate CD² centre circle be described circle described circle of curvature cloth CO.'S PUBLICATIONS cone Conic Sections conjugate diameters conjugate hyperbola CP² Crown 8vo curve cutting plane drawn at right drawn parallel ellipse Euclid Fcap Fellow of St Fellow of Trinity focal chord focus intersect John's College join SP late Fellow latus rectum let the tangent M.A. Fellow MACMILLAN & CO.'S major axis mean proportional meet CD meet the axis meet the directrix meet the ellipse meeting the asymptotes pair of tangents parabola parallelogram perpendicular PN² produced to meet Prop prove QV² radius right angles Second Edition triangle Trinity College University of Cambridge vertex
Popular passages
Page 8 - THE SEVEN KINGS OF ROME. An Easy Narrative, abridged from the First Book of Livy by the omission of Difficult Passages; being a First Latin Reading Book, with Grammatical Notes and Vocabulary.
Page 7 - THRUPP.— Antient Jerusalem : a New Investigation into the History, Topography, and Plan of the City, Environs, and Temple. Designed principally to illustrate the records and prophecies of Scripture. With Map and Plans. By JOSEPH FRANCIS THRUPP, MA 8vo. cloth, lis. THRUPP.— Introduction to the Study and Use of the Psalms. By the Rev. JF THRUPP, MA 2 vols. Svo. 21*.
Page 7 - The fitness of Holy Scripture for Unfolding the Spiritual Life of Man : Christ the Desire of all Nations ; or, the Unconscious Prophecies of Heathendom.
Page 2 - Prelector of St. John's College, Cambridge. AN ELEMENTARY TREATISE ON MECHANICS. For the Use of the Junior Classes at the University and the Higher Classes in Schools.