 | John Henry Pratt - Celestial mechanics - 1836 - 672 pages
...V'li -Qu M" - r-7f 2 sin /j - - ............ (2). ^ Now the conic section is an ellipse, parabola, or hyperbola according as e is less than, equal to, or greater than unity. Heuce, from equation (l), the orbit described is an ellipse, parabola, or hyperbola about the focus... | |
 | John Henry Pratt - Mechanics, Analytic - 1841 - 644 pages
.../} and a(l ~e*) = - = - — ............ (2). /* M Now the conic section is an ellipse, parabola, or hyperbola according as e is less than, equal to, or greater than unity. Hence, from equation (l), the orbit described is an ellipse, parabola, or hyperbola about the focus according... | |
 | John Henry Pratt - Architecture - 1842 - 674 pages
...and a(l ~ e*) = - = - — ............ (2). f* A Now the conic section is an ellipse, parabola, or hyperbola according as e is less than, equal to, or greater than unity. Hence, from equation (1), the orbit described is an ellipse, parabola, or hyperbola about the focus according... | |
 | Matthew O'Brien - Geometry, Analytic - 1844 - 210 pages
...this rectangle, and therefore, by (1), we have мрг _ QHH'M = (e* - 1) x\ Hence it is evident that, according as e is less than, equal to, or greater than unity, the square of the ordinate falls short of, is equal to, or exceeds the rectangle under the abscissa... | |
 | Archibald Sandeman - Dynamics - 1850 - 222 pages
...the equation of a conic section referred to a focus as pole ; the curve is an ellipse, parabola, or hyperbola, according as e is less than, equal to, or greater than unity ; that is, according as — r - w'8 is positive, zero, or ne2 gative. The latus rectum is equal to-v'V2sinsi.... | |
 | George Holmes Howison - Geometry, Analytic - 1869 - 622 pages
...\ve may write, as the equation to the Conic, p = ed: which will denote an ellipse, a parabola, or an hyperbola, according as e is less than, equal to, or greater than unity. 636. It follows from the property mentioned above, that the Conic may be defined as the locus of a... | |
 | George Shoobridge Carr - Mathematics - 1880
...either directrix XM, X'M' , by the law just proved. 1153 The conic is an Ellipse, a Parabola, or an Hyperbola, according as e is less than, equal to, or greater than unity. That is, according as the cutting plane emerges on both sides of the lower cone, or is parallel to... | |
 | Edward Albert Bowser - Mechanics, Analytic - 1884 - 538 pages
...V*R - 2u) RV* sin2 0 + 1 ; . (10) 0 = 0 - c'. (11) Now the conic section is an ellipse, parabola, or hyperbola, according as e is less than,, equal to, or greater than unity; and from (10) e is less than, equal to, or greater than, unity according as V*R — 2/» is negative,... | |
 | George Shoobridge Carr - Mathematics - 1886 - 1036 pages
...either directrix XM, X'M', by the law just proved. 1153 The conic is an Ellipse, a Parabola, or an Hyperbola, according as e is less than, equal to, or greater than unity. That is, according as the cutting plane emerges on both sides of the lower cone, or is parallel to... | |
 | Edwin Henry Barton - Mechanics, Analytic - 1911 - 568 pages
...the orbit is a conic, b being the constant of integration. It is clear from (13) that this conic is an ellipse, a parabola, or a hyperbola according as e is less than, equal to, or greater than unity; or, by (n), according as O is within the circle, on the circumference, or outside it; that is to say,... | |
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Hyperbola, according as e is less than, equal to, or greater than unity. 
