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The Syllabus of Geometrical Conics

Published online by Cambridge University Press:  15 September 2017

Extract

The Sixth General Meeting of the Association for the Improvement of Geometrical Teaching appointed a Committee for Geometrical Conies, and one for “Higher Plane Geometry, including such subjects as Transversals, Projection, Anharmonic Eatio, etc.”

Dr. Hirst in his Presidential Address has said of the latter subjects, “Until these notions become more familiar ones, I, for my part, believe that Geometrical Conies will always remain in its present unsatisfactory condition. . . . It will be, of course, a question for this Association to decide whether, pending the introduction of the more thorough treatment based on the notions to which I have alluded, some improvement may not be introduced into the subject of Geometrical Conies, as at present understood, with a view of enabling examiners at all events to examine with greater facility and purpose. At present the definitions are so multiform and the sequence of propositions so varied in different text-books, that it is found to be an exceedingly difficult task to examine satisfactorily in the subject at all.”

Type
Research Article
Copyright
Copyright © Mathematical Association 1895

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References

page 37 note * Note that the square of the true conjugate axis of a hyperbola is negative, and therefore less than the square of the transverse axis.

page 37 note † The expression “normal” is a convenient substitute for “perpendicular,” and there is precedent for its use in this sense.

page 38 note * Later writers have taken them (with the proof that SG = e. SP) in the form in which they found them in my Geometrical Conics (1863). But see the preface to Mr. Richardson’s Geometrical Conics.

page 39 note * Another form of the proof is as follows. Complete the parallelogram TCtK, and let x, y denote its sides. Then CK2 – Tt 2 = x 2 + y 2 + 2xy cos C – (x 2 + y 2 – 2xy cos C), which is constant when xy and C are given.