## An Elementary Treatise on Pure Geometry: With Numerous Examples |

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### Common terms and phrases

ABCD asymptotes axes bisects centre circular points circumcircle circumscribed coincide collinear common chord common points common tangents confocal conic passes conic touching conjugate diameters conjugate lines conjugate points constant corresponding points cross ratio cut the conic directrix double contact double lines double points draw drawn ellipse envelope figure fixed line fixed point foci focus four points given conic given line given point harmonic triangle Hence homographic ranges homology homothetic imaginary points inscribed intersection involution pencil line at infinity line joining locus middle point nine-point circle orthocentre orthogonal pair of conjugate pairs of points parabola parallel perpendicular plane point at infinity points of contact polar pole projection Prove quadrangle quadrilateral radical axis rays reciprocal rectangular hyperbola right angle segment straight line subtend system of conics theorem transversal triangle ABC vanishing line vertex

### Popular passages

Page 373 - Also in three volumes, crown 8vo, price 12s. each. Seventeen Lectures on the Study of Mediaeval and Modern History and kindred subjects, 1867-1884.

Page 378 - The entire work in 26 vols., cloth £5 net, morocco back £6 6s. net. The 4 vols. of ' The Indian Empire' separately, cloth 6s. net each, morocco back 7s. 6d. net; Atlas, cloth 15s. net, morocco back 17s. 6d. net; the remaining 21 vols., cloth £4 4s. net, morocco back £5 5s. net. Vol. I. Descriptive. Vol. II. Historical. Vol. III. Economic. Vol. IV. Administrative. Vol.

Page 331 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.

Page 381 - Grueber. Lex Aquilia. The Roman Law of Damage to Property : being a Commentary on the Title of the Digest 'Ad Legem Aquiliam

Page 376 - Crown 8vo. 7s. 6d. Geography of the Dominion of Canada and Newfoundland. By the same author. With ten maps. 1891. Crown 8vo. 6s. Geography of Africa South of the Zambesi. By the same author. With maps. 1892. Crown 8vo. 7s. 6d. The Claims of the Study of Colonial History upon the attention of the University of Oxford.

Page 383 - CSI (1907.) Crown 8vo. 5s. net. Land-Systems of British India, being a manual of the LandTenures, and of the systems of Land-Revenue administration. By the same.

Page 370 - WACE. 8vo. 10s. 6d. net Catalogue of the Greek Vases in the Ashmolean Museum. By P. GARDNER. Small folio, linen, with 26 plates. £3 3s. net The Cults of the Greek States. By LR FARNELL.

Page 352 - The nine-point circle of any triangle touches the inscribed and escribed circles. Let ABC be a triangle, / the inscribed circle touching BC in Q, and E the escribed circle opposite to A touching £C in Q'. Bisect BC, CA in M and M...

Page 164 - Two vertices of a triangle self-conjugate for a given conic move on fixed lines ; show that the locus of the third vertex is a conic passing through the intersections of the given lines with the given conic and through the poles of the given lines for the given conic. Ex. 6. A A' are a pair of opposite vertices of a quadrilateral whose sides touch a conic at L, M, N, R.

Page 303 - To find the locus of the centre of a circle which passes through a given point and touches a given straight line.