Elements of conic sections deduced from the coneAt the Clarendon Press, 1818 - 125 pages |
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Common terms and phrases
absciss APPEN article 66 axes base bisected bola BOOK CA² CD² centripetal force circle circumference conic section conical superficies conjugate axis conjugate diameters Conjugate Hyperbolas Consequently diameter A B double ordinate ellipse or hyperbola foci focus Hence hyperbolic sector hyperbolic segments last article let a plane let it cut let it meet let the straight meet the curve meet the tangent opposite cones opposite hyperbolas opposite superficies parabola parabolic segments parallel to A B parallelogram parameter perbola perpendicular plane passing point of concourse point of contact PROP rallel rectangle rest remaining right angles Scholium secant parallel segments side similar triangles square straight line drawn straight line parallel tangent ticle touch the conical touch the section transverse axis velocity vertex
Popular passages
Page 82 - In an ellipse, the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the axes.
Page 4 - In that case the line determined by the vertex and the center of the base is called the axis of the cone. If...
Page 17 - In the octets there is a remarkably regular arrangement of markings, in that the mid-couplet pauses between the first and second, the third and fourth, the fifth and sixth, and the seventh and eighth lines are always marked by a double punctus.
Page 4 - Any straight line drawn through the vertex of the cone to the circumference of the base is called a Side of the Cone.
Page 4 - The word tetrahedron is now often used to denote a solid bounded by any four triangular faces, that is, a pyramid on a triangular base ; and when the tetrahedron is to be such as Euclid defines, it is called a regular tetrahedron. Two other definitions may conveniently be added. A straight line is said to be parallel to a plane when they do not meet if produced. The angle made by two straight lines which do not meet is the angle contained by two straight lines parallel to them, drawn through any...
Page xi - Sectionum Conicarum, libri septem ; accedit, Tractatus de Sectionibus Conicis, et de Scriptoribus qui earum doctrinam tradiderunt.
Page 11 - ... termed the changes of form, must be confined, if we wish to avoid giving the material a set, or, in the case of variable strains, if we wish to avoid giving it a continuous succession of sets which would gradually bring about its destruction ; that these two elastic limits are usually situated one on the one side and the other on the opposite side of the position which the material assumes when subject to no external strain, though they may be both on the same side of this position of relaxation*...
Page 54 - The segment of a diameter between its vertex and an ordinate is called an Absciss of that diameter.
Page 38 - ... the segments of the third tangent between its point of contact and the parallel tangents, is equal to the square of the semi-diameter to which it is parallel.
Page 105 - VI // several bodies revolve about one common centre, and the centripetal force is inversely as the square of the distance...