A treatise on solid geometry, by P. Frost and J. Wolstenholme1863 |
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Page xiv
... angles between them . Diametral plane for a system of chords of non - central conicoids .. any Diametral plane for a system of chords of any conicoid Principal planes of The three principal planes of any conicoid are at right angles ...
... angles between them . Diametral plane for a system of chords of non - central conicoids .. any Diametral plane for a system of chords of any conicoid Principal planes of The three principal planes of any conicoid are at right angles ...
Page xxii
... right circular cylinder Geodesic on right cone 449 450 Number of geodesics on cone Geodesic on surface of revolution ... angles with the line of 459 Locus of intersection of perpendicular geodesic tangents to two lines of cur- vature ...
... right circular cylinder Geodesic on right cone 449 450 Number of geodesics on cone Geodesic on surface of revolution ... angles with the line of 459 Locus of intersection of perpendicular geodesic tangents to two lines of cur- vature ...
Page 18
... right angle ; .. PQ2 = PN2 + NQ2 = PM2 + MN2 + NQ2 ; .. 1 = l2 + m2 + n2 , which is the relation required . Hence the three angles of in- clination cannot all be assumed arbitrarily . 26. To find the angle between two straight lines in ...
... right angle ; .. PQ2 = PN2 + NQ2 = PM2 + MN2 + NQ2 ; .. 1 = l2 + m2 + n2 , which is the relation required . Hence the three angles of in- clination cannot all be assumed arbitrarily . 26. To find the angle between two straight lines in ...
Page 21
... right angle ; .. MN = PL = PQ cos QPL , and MN is the projection of PQ on AB , < QPL = the inclination of PQ to the plane , whence the proposition . Projection of a Plane Area upon a Plane . 33. DEF . The orthogonal projection of a ...
... right angle ; .. MN = PL = PQ cos QPL , and MN is the projection of PQ on AB , < QPL = the inclination of PQ to the plane , whence the proposition . Projection of a Plane Area upon a Plane . 33. DEF . The orthogonal projection of a ...
Page 25
... right angles , the direction- cosines are l + l ' + l " √3 m + m2 + m " / 3 n + n + n " " √3 ( 11 ) Find the direction - cosines of the two straight lines which are equally inclined to the axis of z , and are perpendicular to each ...
... right angles , the direction- cosines are l + l ' + l " √3 m + m2 + m " / 3 n + n + n " " √3 ( 11 ) Find the direction - cosines of the two straight lines which are equally inclined to the axis of z , and are perpendicular to each ...
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Common terms and phrases
asymptotic ax² axes axis by² circular sections cone conicoid constant corresponding cos² cosines curve of intersection cylinder determined developable surface directing planes direction-cosines directrix drawn dx dy ellipse ellipsoid envelope equal find the equation fixed plane fixed point focal conic focal curve geodesic given plane given point given straight line Hence hyperbolic paraboloid hyperboloid infinite distance infinite number Let the equation line joining line of curvature line of intersection locus normal nth degree obtain osculating plane P₁ parabola perpendicular plane containing plane curve plane of xy plane passing plane section plane whose equation points of intersection polar plane pole principal planes projection radius ratio reciprocal right angles satisfy the equation second degree shew sin² sphere tangent plane tetrahedron values vertex x² y²
Popular passages
Page 472 - THE FIRST THREE SECTIONS OF NEWTON'S PRINCIPIA, With Notes and Illustrations. Also a collection of Problems, principally intended as Examples of Newton's Methods. By PERCIVAL FROST, MA Third Edition.
Page 475 - Mr. Smith's Work is a most useful publication. The Rules are stated with great clearness. The P^xamples are well selected and worked out with just sufficient detail without being encumbered by too minute explanations ; and there prevails throughout it that just proportion of theory and practice, which is the crowning excellence of an elementary work.
Page 98 - The hyperboloid of one sheet may be generated by the motion of a variable ellipse, which moves so that its plane is always parallel to a fixed plane, and which changes its form so that its vertices always lie in two hyperbolas traced on planes perpendicular to each other and to the fixed plane, these hyperbolas having a common conjugate axis.
Page 135 - Conic, is the locus of a point which moves so that its distance from a fixed point is in a constant ratio to its distance from a fixed straight line.