Articles liés à An Introduction to Projective Geometry
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Conic Sections on modern lines. During recent years increasing space has been allowed, in University syllabuses and courses of instruction, to the more powerful and general projective methods, as opposed to the more special methods of what is still known as Geometrical Conies. The line of cleavage between the two has, however, been sharply maintained, with the result that the already much overworked matiiematical student has to learn his theory of Conic Sections three times over: (1) analytically; (2) according to J]uclidean methods; (3) according toP rojective methods. The difficulty has been to reconcile theE uclidean and Projective definitions of the curve; in fact to bring in tlie focal properties into Projective Geometry at a sufficiently early stage. The practice has usually been, in order to pass from the projective to the focal definitions, to introduce the theory of involution. But the latter requires for its fullest and cleare.st treatment the employment of imaginary elements. It seems undesirable that the more fundamental focal properties of the conies, e.g. tlie sum (r ditference of the focal distances and the angles made by tlie.sc with the tangent and normal, should appear to depend upon properties of imaginary points and lines, even though this might introduce greater rapidity of treatment. The University of London has recognized thi.s, for, while admitting Projective Geometry into its syllabuses for the Final Examination for a Pass Degree, it has excluded involution. Many teacliers iiave felt that this exclusion amounted to a rigorous enforcement of the line of cleavage mentioned above. In the present book the difficulty has been met, it is hopcil, successfully.
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