Examples of Analytical Geometry of Three DimensionsMacmillan, 1864 - 84 σελίδες |
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Σελίδα 9
... ellipses , the area of one of which is double that of the other ; and if I be the latus rectum of the parabola , 1 , 1⁄2 of the sections AC , BC , prove that 1 1 1 = + · 63. Tangent planes are drawn to an ellipsoid from a given external ...
... ellipses , the area of one of which is double that of the other ; and if I be the latus rectum of the parabola , 1 , 1⁄2 of the sections AC , BC , prove that 1 1 1 = + · 63. Tangent planes are drawn to an ellipsoid from a given external ...
Σελίδα 10
... ellipse . 69. Determine the radii of the spheres which touch the co - ordinate planes and the plane x + y + z = h . 70. An ellipsoid is intersected in the same curve by a variable sphere , and a variable cylinder ; the cylinder is ...
... ellipse . 69. Determine the radii of the spheres which touch the co - ordinate planes and the plane x + y + z = h . 70. An ellipsoid is intersected in the same curve by a variable sphere , and a variable cylinder ; the cylinder is ...
Σελίδα 14
... which have the same given ellipse as base . 97. Find the axes of the section of the ellipsoid х to y2 z2 + 1 made by the plane lx + my + nz = 0 . 98. The semiaxes of an ellipsoid are a , b 14 SURFACES OF THE SECOND ORDER .
... which have the same given ellipse as base . 97. Find the axes of the section of the ellipsoid х to y2 z2 + 1 made by the plane lx + my + nz = 0 . 98. The semiaxes of an ellipsoid are a , b 14 SURFACES OF THE SECOND ORDER .
Σελίδα 16
... ellipse x2a2 — + y2b2 ( a2 — c2 ) 2 + ( b2 — c2 ) 2 - - h2 = 1 -- 108. All the normals to the ellipsoid in Ex . 107 meet the plane of ( x , y ) within an ellipse whose equation is a2x2 b2y 2 + ( a2 - c2 ) 2 c2 ) 2 + ( b2 - c2 ) 2 = 1 ...
... ellipse x2a2 — + y2b2 ( a2 — c2 ) 2 + ( b2 — c2 ) 2 - - h2 = 1 -- 108. All the normals to the ellipsoid in Ex . 107 meet the plane of ( x , y ) within an ellipse whose equation is a2x2 b2y 2 + ( a2 - c2 ) 2 c2 ) 2 + ( b2 - c2 ) 2 = 1 ...
Σελίδα 20
... ellipses which touch each other and the edges . 140. Two similar and similarly situated ellipsoids are cut by a series of ellipsoids similar and similarly situated to the two given ones , so that the planes of intersection of any one of ...
... ellipses which touch each other and the edges . 140. Two similar and similarly situated ellipsoids are cut by a series of ellipsoids similar and similarly situated to the two given ones , so that the planes of intersection of any one of ...
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Examples of Analytical Geometry of Three Dimensions Isaac Todhunter Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Examples of Analytical Geometry of Three Dimensions Isaac Todhunter Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
Algebra Arithmetic ax² axis by² Calculus centre circle cloth co-ordinate planes Collection of Examples Conic Sections conical surface conjugate diameters constant contains cos² Crown 8vo curve of intersection cylinder determined developable surface differential equation distance ELEMENTARY ellipse ellipsoid English Find the equation find the locus fixed point fixed straight lines given plane given point hyperbolic hyperboloid John's College late Fellow Latin line of intersection Morocco numerous Examples origin osculating plane parabola paraboloid plane parallel plane passing plane which passes planes are drawn points of contact principal radii principal sections radii of curvature represent right angles right cone Second Edition second order shew sphere ST JOHN'S COLLEGE student surface of revolution surface whose equation tangent plane tetrahedron tions Treatise vertex volume x² y² y² z² y²+z²
Δημοφιλή αποσπάσματα
Σελίδα 15 - PROCTER— A HISTORY OF THE BOOK OF COMMON PRAYER, with a Rationale of its Offices. By FRANCIS PROCTER, MA Thirteenth Edition, revised and enlarged. Crown 8vo. loг. 6d. PROCTER AND MACLEAR— AN ELEMENTARY INTRODUCTION TO THE BOOK OF COMMON PRAYER.
Σελίδα 5 - New Edition. Crown 8vo. $s. KEY TO PLANE TRIGONOMETRY. Crown 8vo. los. 6d. A TREATISE ON SPHERICAL TRIGONOMETRY. New Edition, enlarged. Crown 8vo. 4-?. 6d. PLANE CO-ORDINATE GEOMETRY, as applied to the Straight Line and the Conic Sections. With numerous Examples.
Σελίδα 7 - Calculus — a connection which in some instances involves far more than a merely formal analogy. The work is in some measure designed as a sequel to Professor Boole's Treatise on Differential Equations.
Σελίδα 9 - Ferrers. — AN ELEMENTARY TREATISE ON TRILINEAR CO-ORDINATES, the Method of Reciprocal Polars, and the Theory of Projectors. By the Rev. NM FERRERS, MA, Fellow and Tutor of Gonville and Caius College, Cambridge.