An Elementary Treatise on Conic Sections |
From inside the book
Results 1-5 of 32
Page 57
... coincident . Hence the diagonal AC is cut harmonically . We can prove in a similar manner that the other diagonals are divided harmonically . INVOLUTION . * 61 . Def . Let O be a fixed point on a given straight line , and P , P ' ; Q ...
... coincident . Hence the diagonal AC is cut harmonically . We can prove in a similar manner that the other diagonals are divided harmonically . INVOLUTION . * 61 . Def . Let O be a fixed point on a given straight line , and P , P ' ; Q ...
Page 66
... coincident or imaginary . Hence there are two values of x , and the two corre- sponding values of y are found from ( ii ) . So that every straight line meets a circle in two real , coincident , or imaginary points - imaginary points ...
... coincident or imaginary . Hence there are two values of x , and the two corre- sponding values of y are found from ( ii ) . So that every straight line meets a circle in two real , coincident , or imaginary points - imaginary points ...
Page 67
... coincident if ca√1 + m * . Hence the line y = mx + a√1 + m2 will touch the circle x2 + ya2 for all values of m . = Since either sign may be given to the radical √1 + m2 , it follows that there are two tangents to a circle for every ...
... coincident if ca√1 + m * . Hence the line y = mx + a√1 + m2 will touch the circle x2 + ya2 for all values of m . = Since either sign may be given to the radical √1 + m2 , it follows that there are two tangents to a circle for every ...
Page 68
... coincident if the point be on the circle , and imaginary if the point be within the circle . Let the equation of the circle be x2 + y2 = a2 , and let h , k be the co - ordinates of any point . Let x ' , y ' be the co - ordinates of any ...
... coincident if the point be on the circle , and imaginary if the point be within the circle . Let the equation of the circle be x2 + y2 = a2 , and let h , k be the co - ordinates of any point . Let x ' , y ' be the co - ordinates of any ...
Page 69
... coincident , or imaginary according as a'h2 — a2 ( a2 — k2 ) ( h2 + k2 ) - - is greater than , equal to , or less than zero . That is , according as h2 + k2 - a2 ( ? ) is greater than , equal to , or less than zero . That is , according ...
... coincident , or imaginary according as a'h2 — a2 ( a2 — k2 ) ( h2 + k2 ) - - is greater than , equal to , or less than zero . That is , according as h2 + k2 - a2 ( ? ) is greater than , equal to , or less than zero . That is , according ...
Other editions - View all
Common terms and phrases
2hxy a² b2 angular points asymptotes ax² axes bisect by² Cambridge centre coincident common confocal conics conic touching conjugate diameters constant corresponding Crown 8vo curve diagonals director-circle directrix distance eccentric angles Edition ellipse equal angles Extra fcap fcap find the equation find the locus fixed point fixed straight line foci focus four given points four points given conic given straight line imaginary inscribed latus rectum Let the equation line at infinity line joining line whose equation locus meet middle point nine-point circle normals original conic parabola Pascal's Theorem perpendicular point of intersection points at infinity points of contact polar pole Professor prove quadrilateral radical axis radius ratio rectangular hyperbola right angles second degree self-polar shew sides square tangential equation tangents triangle formed triangle of reference Trinity College values vertex vß² x² y² zero
Popular passages
Page 37 - NEWTON'S PRINCIPIA, With Notes and Illustrations. Also a collection of Problems, principally intended as Examples of Newton's Methods. By PERCIVAL FROST, MA Third Edition. 8vo.
Page 23 - Prize Essay for 1877. 8vo. &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 100 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 20 - 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 71 - THE BIBLE IN THE CHURCH. A Popular Account of the Collection and Reception of the Holy Scriptures in the Christian Churches. New Edition.
Page 40 - LESSONS IN ELEMENTARY CHEMISTRY, INORGANIC AND ORGANIC. By HENRY E. ROSCOE, FRS, Professor of Chemistry in Owens College, Manchester. With numerous Illustrations and Chromo-Litho of the Solar Spectrum, and of the Alkalies and Alkaline Earths. New Edition. Fcap. 8vo. 4*. 6d. , '* As a standard general text-book it deserves to take a leading place." — SPECTATOR. *' We unhesitatingly pronounce it the best of all our elementary treatises on Chemistry,
Page 57 - HISTORICAL OUTLINES OF ENGLISH ACCIDENCE, comprising Chapters on the History and Development of the Language, and on Word-formation.
Page 69 - MANUAL; or, the Church Catechism Illustrated and Explained, for the Use of Clergymen, Schoolmasters, and Teachers. By the Rev. ARTHUR RAMSAY, MA New Edition. iSmo. is. 6d. SIMPSON— AN EPITOME OF THE HISTORY OF THE CHRISTIAN CHURCH. By WILLIAM SIMPSON, MA New Edition. Fcap. 8vo. 3*. 6d. TRENCH— By RC TRENCH, DD, Archbishop of Dublin.
Page 138 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 68 - ST. PAUL'S EPISTLES TO THE COLOSSIANS AND TO PHILEMON. A Revised Text, with Introductions, Notes, and Dissertations.