An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page 21
... become , and the greater , therefore , the distance from the point to the line ; which is in accordance with the remark made in Art . ( 14 ) . EXAMPLES . 1. Find the equation of the straight line joining the middle points of two sides ...
... become , and the greater , therefore , the distance from the point to the line ; which is in accordance with the remark made in Art . ( 14 ) . EXAMPLES . 1. Find the equation of the straight line joining the middle points of two sides ...
Page 39
... become a perfect square , as may be ascertained by sub- stitution , and the conic will degenerate into a straight line , or rather into two coincident straight lines . Taking then the double signs all negatively , and writing CONIC ...
... become a perfect square , as may be ascertained by sub- stitution , and the conic will degenerate into a straight line , or rather into two coincident straight lines . Taking then the double signs all negatively , and writing CONIC ...
Page 40
... becomes L3a2 + M2ß2 + N3y2 – 2MNßî — 2NLyα — 2LMɑß = 0 , which is equivalent to ± ( La ) 3 ± ( MB ) 3 ± ( Ny ) * = 0 . It may be remarked , that the condition that the point ( l , m , n ) should lie in the above conic , is the same as ...
... becomes L3a2 + M2ß2 + N3y2 – 2MNßî — 2NLyα — 2LMɑß = 0 , which is equivalent to ± ( La ) 3 ± ( MB ) 3 ± ( Ny ) * = 0 . It may be remarked , that the condition that the point ( l , m , n ) should lie in the above conic , is the same as ...
Page 43
... . 8. Thus , let it be required to find the ratios of L , M , N in order that the conic may become the in- scribed circle . At the centre of this circle we have , as we know , a = ẞ = y . This gives , by the result of Art . 8.
... . 8. Thus , let it be required to find the ratios of L , M , N in order that the conic may become the in- scribed circle . At the centre of this circle we have , as we know , a = ẞ = y . This gives , by the result of Art . 8.
Page 49
... becomes a2 b2 c2 + + L2 M2 N2 = 0 . 18. To find the co - ordinates of the centre . Let B , B , be the points in which the conic is cut by CA , then , if B , B , be bisected in Q , the line BQ will pass through the centre . Now , let f ...
... becomes a2 b2 c2 + + L2 M2 N2 = 0 . 18. To find the co - ordinates of the centre . Let B , B , be the points in which the conic is cut by CA , then , if B , B , be bisected in Q , the line BQ will pass through the centre . Now , let f ...
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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.