Examples of Analytical Geometry of Three DimensionsMacmillan, 1864 - 84 σελίδες |
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Σελίδα 2
... contains the line whose equations are 15 . Ax + By + Cz = D , A'x + B'y + C'z = D ' , and the point ( a , ß , y ) ... containing them is 2 , ; = 0 ; ( 1 − 1 ) x + ( m ̧ — m2 ) y + ( n ̧ — n ̧ ) z = - - and the equation to the other plane ...
... contains the line whose equations are 15 . Ax + By + Cz = D , A'x + B'y + C'z = D ' , and the point ( a , ß , y ) ... containing them is 2 , ; = 0 ; ( 1 − 1 ) x + ( m ̧ — m2 ) y + ( n ̧ — n ̧ ) z = - - and the equation to the other plane ...
Σελίδα 3
... contains a given line and is perpendicular to a given plane . 20. Shew that if the straight lines х α - y 2 B - γ ' lie in one plane , then = = X y 2 a2 a b2ß c2 y X ī = y m = / m - ( b2 — c2 ) + В n ( c2 — a2 ) + — ( a2 — b2 ) = 0 ...
... contains a given line and is perpendicular to a given plane . 20. Shew that if the straight lines х α - y 2 B - γ ' lie in one plane , then = = X y 2 a2 a b2ß c2 y X ī = y m = / m - ( b2 — c2 ) + В n ( c2 — a2 ) + — ( a2 — b2 ) = 0 ...
Σελίδα 4
... contains a given straight line , and makes a given angle with a given plane . 27. A straight line makes an angle of 60 ° with one axis , and an angle of 45 ° with another ; what angle does it make with the third axis ? 2 28. Interpret ...
... contains a given straight line , and makes a given angle with a given plane . 27. A straight line makes an angle of 60 ° with one axis , and an angle of 45 ° with another ; what angle does it make with the third axis ? 2 28. Interpret ...
Σελίδα 8
... containing the mean axis , shew that the perpendiculars from the centre on the tangent planes at every point of the ... contain the least axis ; find the locus of the foci of the sections . 56. Find the locus of a point which is ...
... containing the mean axis , shew that the perpendiculars from the centre on the tangent planes at every point of the ... contain the least axis ; find the locus of the foci of the sections . 56. Find the locus of a point which is ...
Σελίδα 9
... contains a given right line . Shew also that if the point of contact be not given , and if the plane of section always contain a given point , the centre of the sphere C ' will always be upon a given paraboloid . 62. If A , B , C be ...
... contains a given right line . Shew also that if the point of contact be not given , and if the plane of section always contain a given point , the centre of the sphere C ' will always be upon a given paraboloid . 62. If A , B , C be ...
Άλλες εκδόσεις - Προβολή όλων
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.