Analytical Geometry: With the Properties of Conic Sections, and an Appendix, Constituting a Tract on Descriptive GeometryLongman, Brown, Green and Longmans, 1846 - 202 páginas |
Dentro del libro
Resultados 1-5 de 38
Página xxii
... obtained by the intersection of a plane with an ellipsoid ; the plane having any position a . Nature of the section of an hyperboloid and of a parabo- loid · - 209. PROP . VII . To find the equation for a plane touching a curve surface ...
... obtained by the intersection of a plane with an ellipsoid ; the plane having any position a . Nature of the section of an hyperboloid and of a parabo- loid · - 209. PROP . VII . To find the equation for a plane touching a curve surface ...
Página 13
... obtain the expressions of these particular values of x , y , in terms of a ' , b ' , a " , b " , the given quantities in the equations of the two lines , from yax + b ' subtract y = a " x + b " ·· . ( a ' — a ' ) x = b ' — b ' ' . b ...
... obtain the expressions of these particular values of x , y , in terms of a ' , b ' , a " , b " , the given quantities in the equations of the two lines , from yax + b ' subtract y = a " x + b " ·· . ( a ' — a ' ) x = b ' — b ' ' . b ...
Página 16
... obtain from the value of tan . at ( b ) in that Article , α tan . + a'a tan . ø + ( a ' + a ) tan . cos . w = ( a ' - a ) sin . w : hence a { sin . w + ( a + cos . w ) tan . } = a ' sin . w− ( 1+ a ' cos . w ) tan . or a = a ' sin . w ...
... obtain from the value of tan . at ( b ) in that Article , α tan . + a'a tan . ø + ( a ' + a ) tan . cos . w = ( a ' - a ) sin . w : hence a { sin . w + ( a + cos . w ) tan . } = a ' sin . w− ( 1+ a ' cos . w ) tan . or a = a ' sin . w ...
Página 18
... obtained , x - x = y , -y = ( a ' + cos . w ) ( y ' — a'x ' —b ′ ) . 1+ a22 + 2 a ' cos . w ; ( 1+ a'cos.w ) ( y ' — a'x ' —b ' ) 1+ a22 + 2 a ' cos . w Substituting these values of x , -x ' , y , -y ' in the formula , D = √ { ( x , ...
... obtained , x - x = y , -y = ( a ' + cos . w ) ( y ' — a'x ' —b ′ ) . 1+ a22 + 2 a ' cos . w ; ( 1+ a'cos.w ) ( y ' — a'x ' —b ' ) 1+ a22 + 2 a ' cos . w Substituting these values of x , -x ' , y , -y ' in the formula , D = √ { ( x , ...
Página 29
... obtained for the point P " . In the two equations thus formed let k ' and k " be the quantities to be determined ; then , since the equations are quadratic , and that the two values of each of the roots k ' and k " are , by hypothesis ...
... obtained for the point P " . In the two equations thus formed let k ' and k " be the quantities to be determined ; then , since the equations are quadratic , and that the two values of each of the roots k ' and k " are , by hypothesis ...
Contenido
1 | |
12 | |
17 | |
18 | |
26 | |
28 | |
34 | |
47 | |
102 | |
104 | |
106 | |
114 | |
116 | |
122 | |
139 | |
140 | |
50 | |
51 | |
53 | |
54 | |
60 | |
65 | |
66 | |
71 | |
78 | |
88 | |
90 | |
91 | |
96 | |
98 | |
145 | |
147 | |
153 | |
159 | |
161 | |
172 | |
173 | |
179 | |
185 | |
190 | |
193 | |
198 | |
10 | |
Otras ediciones - Ver todas
Analytical Geometry: With the Properties of Conic Sections, and an Appendix ... John Narrien Sin vista previa disponible - 2023 |
Analytical Geometry: With the Properties of Conic Sections, and an Appendix ... John Narrien Sin vista previa disponible - 2018 |
Términos y frases comunes
asymptotes bisected centre chord co-ordinate axes co-ordinate planes coefficients cone conjugate axes conjugate diameters conjugate hyperbola consequently cos.² curve line curve surface directrix distance double ordinate draw drawn parallel ellipse or hyperbola equation becomes equivalent excentricity figure find the equation foci focus given line given point imagine let OA let the co-ordinates line be drawn line drawn meet nates oblique origin parabola parallelepiped parameter perpen perpendicular to ox plane in space plane XOY plane zox point of contact produced projected lines projections on zox PROPOSITION rectangle represented respectively right angles Scholium second member semi-conjugate semi-transverse axis square straight line substituting tangent be drawn transverse axis triangles Trigon values whence zero
Pasajes populares
Página 1 - The Debater ; a Series of Complete Debates, Outlines of Debates, and Questions for Discussion. *By F. ROWTON. Fcp.
Página 4 - Diamond Latin-English Dictionary. A Guide to the Meaning, Quality, and right Accentuation of Latin Classical Words. Royal 32mo.
Página 12 - ELEMENTS OF NATURAL HISTORY, For the use of Schools and Young Persons : comprising the Principles of Classification, interspersed with amusing and instructive original Accounts of the most remarkable Animals. By Mrs. R. LEE (formerly Mrs. TE BOWDICH), Author of "Taxidermy," "Memoirs of Cuvier,
Página 9 - BLAIR'S CHRONOLOGICAL AND HISTORICAL TABLES, From the Creation to the present time : with Additions and Corrections from the most authentic Writers ; including the Computation of St. Paul, as connecting the Period from the Exode to the Temple. Under the revision of Sir HENRY ELLIS, KH, Principal Librarian of the British Museum.
Página 14 - MAUNDER.- THE UNIVERSAL CLASS-BOOK : A new Series of Reading Lessons (original and selected) for Every Day in the Year ; each Lesson recording some important Event in General History, Biography, &c. which happened on the day of the month under which it is placed, or detailing, in familiar language, interesting facts in Science ; also a variety of Descriptive and Narrative Pieces, interspersed with Poetical Gleanings : Questions...
Página 9 - Blair's Chronological and Historical Tables, from the Creation to the present time : With Additions and Corrections from the most authentic Writers; including the Computation of St. Paul, as connecting the Period from the Exode to the Temple.
Página 15 - Walker's Dictionary Epitomised. Walker's Pronouncing Dictionary of the English Language, Epitomised on a plan which allows of full Definitions to the leading Words, and large additions to the Terms of Modern Science: with a Key to the Pronunciation of Greek, Latin, and Scripture Proper Names.
Página 14 - An Explanatory Pronouncing Dictionary of the French Language, in French and English ; wherein the exact Sound of every Syllable is distinctly marked, according to the method adopted by Mr.