An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
From inside the book
Results 1-5 of 38
Page viii
... Polar 52 53 23 . 24 . Equation of a Line joining Two given Points . Equation of the Tangent at a given Point ib . 54 25 . 26 . 27 . Pole of a given Straight Line . Condition of Tangency . Condition for a Parabola . Co - ordinates of the ...
... Polar 52 53 23 . 24 . Equation of a Line joining Two given Points . Equation of the Tangent at a given Point ib . 54 25 . 26 . 27 . Pole of a given Straight Line . Condition of Tangency . Condition for a Parabola . Co - ordinates of the ...
Page ix
... Polar of a given Point Condition that the Conic may break up into Two Straight Lines . 76 9 . Co - ordinates of the Pole of a given Straight Line 225 ib . ib . 77 10 . Equation of the pair of Tangents , drawn to the Conic from a given ...
... Polar of a given Point Condition that the Conic may break up into Two Straight Lines . 76 9 . Co - ordinates of the Pole of a given Straight Line 225 ib . ib . 77 10 . Equation of the pair of Tangents , drawn to the Conic from a given ...
Page x
... Polar Reciprocal 5 . The degree of a curve is the same as the class of its reciprocal , and vice versa 99 Brianchon's Theorem • · 6 , 7. The polar reciprocal of a conic is a conic 8 . 10 . 12 . Equation of the Polar Reciprocal of one ...
... Polar Reciprocal 5 . The degree of a curve is the same as the class of its reciprocal , and vice versa 99 Brianchon's Theorem • · 6 , 7. The polar reciprocal of a conic is a conic 8 . 10 . 12 . Equation of the Polar Reciprocal of one ...
Page xi
... polar Co - ordinates EXAMPLES 128 129 130 · 132 ib . CHAPTER VIII . ON THE INTERSECTION OF CONICS , ON PROJECTIONS , AND ON THE DETERMINATION OF A CONIC FROM FIVE GIVEN GEOMETRICAL CONDITIONS . 1-3 . Any two conics intersect in four ...
... polar Co - ordinates EXAMPLES 128 129 130 · 132 ib . CHAPTER VIII . ON THE INTERSECTION OF CONICS , ON PROJECTIONS , AND ON THE DETERMINATION OF A CONIC FROM FIVE GIVEN GEOMETRICAL CONDITIONS . 1-3 . Any two conics intersect in four ...
Page 46
... polar of B , and B the pole of CA with respect to the conic . Similarly , C , AB , stand to one another in the relation of pole and polar . Again , since the pole of AB is the point C , and the pole of AC is the point B , it follows ...
... polar of B , and B the pole of CA with respect to the conic . Similarly , C , AB , stand to one another in the relation of pole and polar . Again , since the pole of AB is the point C , and the pole of AC is the point B , it follows ...
Other editions - View all
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 uaČ V'ca values W'ab whence λα
Popular passages
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.
Page 16 - Church, and to point out the relation existing between the amount of evidence for the authenticity of its component parts and the whole mass of Christian literature. Such a method of inquiry will convey both the truest notion of the connexion of the written Word with the living Body of Christ, and the surest conviction of its divine authority.
Page 16 - The author has endeavoured to connect the history of the New Testament Canon with the growth and consolidation of the Church, and to point out the relation existing between the amount of evidence for the authenticity of its component parts, and the whole mass of Christian literature.
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.