Examples of Analytical Geometry of Three DimensionsMacmillan, 1864 - 84 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 6.
Σελίδα 2
... Interpret the equation x2 + y2 + z2 = ( x cos a + y cos B + z cos y ) 2 , where cos2 a + cos2 B + cos2 y = 1 . 13. Find the angle between the line х y 2 = = and 2 √ / 3 √ / 2 ' X the line = √ / 3 y , z = 0 . 14. Find the equation to ...
... Interpret the equation x2 + y2 + z2 = ( x cos a + y cos B + z cos y ) 2 , where cos2 a + cos2 B + cos2 y = 1 . 13. Find the angle between the line х y 2 = = and 2 √ / 3 √ / 2 ' X the line = √ / 3 y , z = 0 . 14. Find the equation to ...
Σελίδα 4
... Interpret a2 = y2 = 22 . 29. Find the condition that must hold in order that the equations x = cy + bz , y = az + cx , z = bx + ay may represent a straight line ; and shew that the equations to the line then are х y = 2 √ ( 1 − a3 ) ̄ ...
... Interpret a2 = y2 = 22 . 29. Find the condition that must hold in order that the equations x = cy + bz , y = az + cx , z = bx + ay may represent a straight line ; and shew that the equations to the line then are х y = 2 √ ( 1 − a3 ) ̄ ...
Σελίδα 8
... Interpret the equation x2 + y2 + z2 = ( lx + my + nz ) 2 . 59. A , B , C are three fixed points , and P a point in space such that PA + PB2 = PC2 ; find the locus of P , and explain the result when ACB is a right or obtuse angle . 60 ...
... Interpret the equation x2 + y2 + z2 = ( lx + my + nz ) 2 . 59. A , B , C are three fixed points , and P a point in space such that PA + PB2 = PC2 ; find the locus of P , and explain the result when ACB is a right or obtuse angle . 60 ...
Σελίδα 49
... Interpret Aa + BB + Cy + Dd a constant . Aa + BB + Cy = 0 . 303. If a = 0 , 80 , y = 0 be the equations to three ... interpret the equation T. A. G. √ ( ~ 1 ) + √ ( ~~ ) + √√ ( ~ ) = = 0 . 4 306 . Also interpret Au ̧ ̧ + Bu ̧μ ̧ + СÙ ...
... Interpret Aa + BB + Cy + Dd a constant . Aa + BB + Cy = 0 . 303. If a = 0 , 80 , y = 0 be the equations to three ... interpret the equation T. A. G. √ ( ~ 1 ) + √ ( ~~ ) + √√ ( ~ ) = = 0 . 4 306 . Also interpret Au ̧ ̧ + Bu ̧μ ̧ + СÙ ...
Σελίδα 50
Isaac Todhunter. 306 . Also interpret Au ̧ ̧ + Bu ̧μ ̧ + СÙ‚μ ‚ = 0 . 307. If u , v , w are linear functions of x , y , z shew that uvw represents a conical surface ; and shew that the equa- tion to the tangent plane is Xu - 2λw + v = 0 ...
Isaac Todhunter. 306 . Also interpret Au ̧ ̧ + Bu ̧μ ̧ + СÙ‚μ ‚ = 0 . 307. If u , v , w are linear functions of x , y , z shew that uvw represents a conical surface ; and shew that the equa- tion to the tangent plane is Xu - 2λw + v = 0 ...
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.