An Elementary Treatise on Conic Sections |
From inside the book
Results 1-5 of 85
Page viii
... chord of a conic is cut harmonically by a point and its polar 195 Diameters of a conic 196 Condition that two given ... chords of a conic 198 • Pairs of common chords of a circle and a conic are equally inclined to the axes of the conic ...
... chord of a conic is cut harmonically by a point and its polar 195 Diameters of a conic 196 Condition that two given ... chords of a conic 198 • Pairs of common chords of a circle and a conic are equally inclined to the axes of the conic ...
Page x
... chord of contact 298 The circle with respect to which the triangle of reference is self - polar 298 The nine - point circle 299 Pascal's theorem . [ See also 328. ] 299 Brianchon's theorem 301 • AREAL CO - ORDINATES 302 TANGENTIAL CO ...
... chord of contact 298 The circle with respect to which the triangle of reference is self - polar 298 The nine - point circle 299 Pascal's theorem . [ See also 328. ] 299 Brianchon's theorem 301 • AREAL CO - ORDINATES 302 TANGENTIAL CO ...
Page 58
... chord of the circles will cut the line on which the points lie in the required centre . * 62 . If any number of points be in involution the cross ratio of any four points is equal to that of their four con- jugates . Let P , Q , R , S ...
... chord of the circles will cut the line on which the points lie in the required centre . * 62 . If any number of points be in involution the cross ratio of any four points is equal to that of their four con- jugates . Let P , Q , R , S ...
Page 64
... chord becomes the tangent at ( x , y ) . The equation of the tangent at ( x ' , y ' ) is there- fore obtained by putting a " = x ' , and y'y ' in equation ( iii ) ; the result is ( x − x ' ) x ' + ( y — y ' ) y ' = 0 , - or xx ' + yy ...
... chord becomes the tangent at ( x , y ) . The equation of the tangent at ( x ' , y ' ) is there- fore obtained by putting a " = x ' , and y'y ' in equation ( iii ) ; the result is ( x − x ' ) x ' + ( y — y ' ) y ' = 0 , - or xx ' + yy ...
Page 67
... chord is still on the axis of y . The locus of the middle points of parallel chords of a circle is therefore the straight line through the centre which is perpendicular to the chords : the locus need not however be supposed to be ...
... chord is still on the axis of y . The locus of the middle points of parallel chords of a circle is therefore the straight line through the centre which is perpendicular to the chords : the locus need not however be supposed to be ...
Other editions - View all
Common terms and phrases
2hxy a² b2 angular points asymptotes ax² axes bisect by² Cambridge centre circumscribing coefficients College confocal conics conjugate diameters conjugate hyperbola constant corresponding cross ratio Crown 8vo curve diagonals directrix distance eccentric angles Edition ellipse envelope equal angles Extra fcap fcap find the equation find the locus fixed point fixed straight line foci focus four points given points given straight line harmonic Hence imaginary inscribed latus rectum Let the co-ordinates Let the equation line joining line whose equation meet middle point nine-point circle normals pair of conjugate parabola pass pencil perpendicular point of intersection point Q points at infinity points of contact polar pole Professor projection prove quadrilateral radical axis rectangular hyperbola required equation right angles shew sides square subtend tangents triangle of reference values vertex zero
Popular passages
Page 49 - EUROPEAN HISTORY. Narrated in a Series of Historical Selections from the Best Authorities. Edited and arranged by EM SEWELL and CM YONGE. First Series, 1003 — 1154. Third Edition. Crown 8vo. 6s. Second Series, 1088—1228. Crown 8vo. 6s. Third Edition. " We know of scarcely anything which is so likely to raise to a higher level the average standard of English education.
Page 31 - ON SOUND AND ATMOSPHERIC VIBRATIONS. With the Mathematical Elements of Music. Designed for the Use of Students in the University. Second Edition, revised and enlarged. Crown 8vo.
Page 12 - THE REPUBLIC OF PLATO. Translated into English, with an Analysis and Notes, by J.
Page 46 - Stands alone as the one general history of the country, for the sake of which all others, if young and old are wise, will be speedily and surely set aside. " — Academy. Analysis of English History, based on Green's " Short History of the English People.
Page 100 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 26 - HEMMING— AN ELEMENTARY TREATISE ON THE DIFFERENTIAL AND INTEGRAL CALCULUS, for the Use of Colleges and Schools. By GW HEMMING, MA, Fellow of St. John's College, Cambridge. Second Edition, with Corrections and Additions. 8vo.
Page 55 - Sonnenschein and Meiklejohn. — THE ENGLISH METHOD OF TEACHING TO READ. By A. SONNENSCHEIN and JMD MEIKLEJOHN, MA Fcap. 8vo. COMPRISING : THE NURSERY BOOK, containing all the Two-Letter Words in the Language, id. (Also in Large Type on Sheets for School Walls. 5*.) THE FIRST COURSE, consisting of Short Vowels with Single Consonants.
Page 54 - HISTORICAL OUTLINES OF ENGLISH ACCIDENCE, comprising Chapters on the History and Development of the Language, and on Word-formation. New Edition.
Page 22 - Prize Essay for 1877. 8vC. &r. 6d. SMITH— Works by the Rev. BARNARD SMITH, MA, Rector of Glaston, Rutland, late Fellow and Senior Bursar of St. Peter's College, Cambridge. ARITHMETIC AND ALGEBRA, in their Principles and Application ; with numerous systematically arranged Examples taken from the Cambridge Examination Papers, with especial reference to the Ordinary Examination for the BA Degree.
Page 55 - TAYLOR— WORDS AND PLACES; or, Etymological Illustrations of History, Ethnology, and Geography. By the Rev. ISAAC TAYLOR, MA Third and cheaper Edition, revised and compressed. With Maps. Globe 8vo. 6s.