An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page xiv
... we get aa + bB + cy = 2A . Next , suppose P to lie between AB , AC produced , and on the side of BC remote from A ( fig . 2 ) . Fig . 2 . Then a will be negative , while B , y are positive . Hence 2 MODERN GEOMETRY .
... we get aa + bB + cy = 2A . Next , suppose P to lie between AB , AC produced , and on the side of BC remote from A ( fig . 2 ) . Fig . 2 . Then a will be negative , while B , y are positive . Hence 2 MODERN GEOMETRY .
Page 1
... produced backwards ( fig . 3 ) , so that ß , y are negative while a is positive . Twice Fig . 3 . P B the areas of PBC , PCA , PAB , are now represented by bß , -cy respectively , so that we still have aa , - aa + bB + cy = 2A . In all ...
... produced backwards ( fig . 3 ) , so that ß , y are negative while a is positive . Twice Fig . 3 . P B the areas of PBC , PCA , PAB , are now represented by bß , -cy respectively , so that we still have aa , - aa + bB + cy = 2A . In all ...
Page 22
... produced . 2 6. On the sides BC , CA , AB of the triangle ABC , respectively , pairs of points are taken , B , C ,; C , A .; A , B2 ; such that the points of intersection of BC with BC ,, of CA with C4 , and of AB with AB , lie in a ...
... produced . 2 6. On the sides BC , CA , AB of the triangle ABC , respectively , pairs of points are taken , B , C ,; C , A .; A , B2 ; such that the points of intersection of BC with BC ,, of CA with C4 , and of AB with AB , lie in a ...
Page 26
... produced to any point P ' , and let the angle P'OR be bisected by OS , then sin POQ = sin QOR , sin POS sin P'OS = sin ROS ; sin POQ . sin ROS 1 . sin POS . sin QOR Hence the truth of the proposition . 23. PROP . If ABC be the triangle ...
... produced to any point P ' , and let the angle P'OR be bisected by OS , then sin POQ = sin QOR , sin POS sin P'OS = sin ROS ; sin POQ . sin ROS 1 . sin POS . sin QOR Hence the truth of the proposition . 23. PROP . If ABC be the triangle ...
Page 28
... produce them to meet in E. Join AE , then AE shall be the fourth harmonic required . For , let ABC be the triangle of reference , and let the equation of AD be B - ky - 0 . Let the equation of B'C ' be λa + B ― ky = 0 . Then that of BC ...
... produce them to meet in E. Join AE , then AE shall be the fourth harmonic required . For , let ABC be the triangle of reference , and let the equation of AD be B - ky - 0 . Let the equation of B'C ' be λa + B ― ky = 0 . Then that of BC ...
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Common terms and phrases
aa+bB+cy angular points anharmonic ratio asymptotes auxiliary conic b₁ b₂ C₁ Cambridge centre Chap chord circle cloth co-ordinates coefficients coincide common tangents conic passing conic section conics intersect Crown 8vo denoted determine directrix find the condition find the equation fixed point fixed straight line four points given conic given point given straight line hyperbola internal bisectors investigated Let the equation line at infinity line joining locus meets the conic obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points of contact PQRS projection prove represented respect second degree shewn Similarly sin POS tangents tangents drawn theorem three points three straight lines tion touch the conic touches the line Treatise triangle of reference ua² V'ca values W'ab whence λα
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Page 6 - The earlier sections of each chapter contain that kind of matter which has usually been thought suitable for the beginner, while the latter ones are devoted either to an account of recent discovery, or to the discussion of such deeper questions of principle as are likely to present themselves to the reflective student in connection with the methods and processes of his previous course.
Page 11 - For really ripe scholarship. extensive acquaintance with Latin literature, and familiar knowledge of continental criticism, ancient and modern, it is unsurpassed among English editions.
Page 17 - Our Year. A Child's Book, in Prose and Verse. By the Author of
Page 8 - In order to spare astronomers and observers in natural philosophy the confusion and loss of time which are produced by referring to the ordinary treatises embracing both branches of probabilities (the first...
Page 8 - ... which can be altered only by the changes of entire units or integral multiples of units in the fundamental conditions of the problem ; the other concerning those chances which have respect to insensible gradations in the value of the element measured), the present tract has been drawn up.
Page 150 - SNOWBALL — THE ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY; with the Construction and Use of Tables of Logarithms. By JC SNOWBALL, MA New Edition.
Page 8 - It is of importance that those who wish to cultivate any subject may be able to ascertain what results have already been obtained, and thus reserve their strength for difficulties which have not yet been conquered. The Author has endeavoured in this work to ascertain distinctly what has been effected in the Progress of the Calculus, and to form some estimate of the manner in which it has been effected.
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Page 2 - Routh. — AN ELEMENTARY TREATISE ON THE DYNAMICS OF THE SYSTEM OF RIGID BODIES. With Numerous Examples. By EDWARD JOHN ROUTH, MA, late Fellow and Assistant Tutor of St. Peter's College, Cambridge; Examiner in the University of London. Second Edition, enlarged. Crown 8vo. cloth.