Examples of Analytical Geometry of Three DimensionsMacmillan, 1864 - 84 σελίδες |
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Σελίδα 10
... position , and that the area of its trans- verse section varies as the surface of the sphere . 71. Three edges of a tetrahedron , in length a , b , and c , are mutually at right angles ; prove that if these three edges be taken as axes ...
... position , and that the area of its trans- verse section varies as the surface of the sphere . 71. Three edges of a tetrahedron , in length a , b , and c , are mutually at right angles ; prove that if these three edges be taken as axes ...
Σελίδα 18
... position of the circular sections of an hyperboloid of two sheets , and shew that the same plane will cut the asymptotic cone in a circle . 126. If x , y , 1 ; X q , Y 2 , Z q ; Xz , Y , Z , be the co - ordinates of the extremities of a ...
... position of the circular sections of an hyperboloid of two sheets , and shew that the same plane will cut the asymptotic cone in a circle . 126. If x , y , 1 ; X q , Y 2 , Z q ; Xz , Y , Z , be the co - ordinates of the extremities of a ...
Σελίδα 20
... position of the original point on the surface is changed the locus of the point is an ellipsoid whose semiaxes are a2 - 212 b2 - 2k2 c2 c2 - 2k α b where 1 k2 = + + 1 1 1 143. If two right circular cones whose axes are parallel 20 ...
... position of the original point on the surface is changed the locus of the point is an ellipsoid whose semiaxes are a2 - 212 b2 - 2k2 c2 c2 - 2k α b where 1 k2 = + + 1 1 1 143. If two right circular cones whose axes are parallel 20 ...
Σελίδα 24
... position . Let any tangent plane be drawn to the ellipsoid at a point P ; this will intersect in general the hyperboloid in a plane curve , through which if there be drawn any three tangent planes to the latter surface they will meet in ...
... position . Let any tangent plane be drawn to the ellipsoid at a point P ; this will intersect in general the hyperboloid in a plane curve , through which if there be drawn any three tangent planes to the latter surface they will meet in ...
Σελίδα 26
... position of the globe . 175. In the preceding example , if an ellipsoid having its least axis vertical be substituted for the globe , determine the condition of the shadow of the globe being circular . It may be shewn that the locus of ...
... position of the globe . 175. In the preceding example , if an ellipsoid having its least axis vertical be substituted for the globe , determine the condition of the shadow of the globe being circular . It may be shewn that the locus 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.