 | Benjamin Theophilus Moore - 1863 - 320 sider
...ratio BC : AC, and their sums are ultimately the areas of the semi-ellipse and the semicircle. 76. To find the area of a segment of a parabola cut off by any straight line. Let CAC' be a segment of a parabola cut off by the straight line CO'. Bisect CC'... | |
 | Elias Loomis - 1877 - 458 sider
...through the focus parallel to the tangent at A in C, prove thatAC=AG. (See fig., Pr. 14.) 13. Required the area of a segment of a parabola cut off by a chord 15 inches in length, perpendicular to the axis, the corresponding abscissa of the axis being... | |
 | William Elwood Byerly - 1879 - 300 sider
...as the angle F'PT ; and .-. F'PT=FPP', and the tangent makes equal angles with the focal radii. QED EXAMPLE. Prove that a tangent to an hyperbola bisects...of the circumscribing rectangle. We can regard the first as made up of the infinitesimal rectangles of which PMUS is a type, and the second of the corresponding... | |
 | Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 sider
...given in Question 10, must be a circle. 12. Integrate (1.) va2 dx (3.) (log sin x-\- x cot x) dx. 13. Find the area of a segment of a parabola cut off by the latus rectum. STATICS. 1 1. Mention any fundamental principles by means of which the science of... | |
 | George Bruce Halsted - 1881 - 266 sider
...distance of its ''C'from its midcross-section. a\ B2 — B^) 8 . —- """512. Find the PC of a portion of a parabola cut off by a line perpendicular to the axis at a distance h from the vertex. \h. Ans. 513. Find the PC of the segment of a globe at a distance... | |
 | William Elwood Byerly - 1890 - 294 sider
...FPP'=F'P'P; but the lines F'P' and F'P coincide, so that the angle F'P'P is the same as the angle F'PT; and EXAMPLE. Prove that a tangent to an hyperbola bisects...the second of the corresponding rectangles of which QNPlt is one. Draw the directrix. PF= SD and DO = OF, by the definition of the parabola; but PF= FT... | |
 | John Greaves - 1894 - 240 sider
...the nature of the equilibrium, when (1) the cross section is a circle, (2) an ellipse, (3) a portion of a parabola cut off by a line perpendicular to the axis, the curved portion only being immersed. Ans. The curves of floatation and buoyancy are (1) circles,... | |
 | William Elwood Byerly - 1895 - 324 sider
...as the angle F'PT ; and .-. F'PT=FPP', and the tangent makes equal angles with the focal radii. QED EXAMPLE. Prove that a tangent to an hyperbola bisects...the circumscribing rectangle. We can regard the P' FS first as made up of the infinitesimal rectangles of which PMUS is a type, and the second of the... | |
 | William Elwood Byerly - 1895 - 298 sider
...FPP'=F'P'P; but the lines F'P' and F'P coincide, so that the angle F'P'P is the same as the angle F'PT ; and EXAMPLE. Prove that a tangent to an hyperbola bisects...of the circumscribing rectangle. We can regard the N f S first as made up of the infinitesimal rectangles of which PMUS is a type, and the second of the... | |
 | William Elwood Byerly - 1898 - 296 sider
...as the angle F'PT ; and .-. F'PT=FPP', and the tangent makes equal angles with the focal radii. QED DIFFERENTIAL CALCULUS. [ART. 168. EXAMPLE. Prove that...of the circumscribing rectangle. We can regard the Tl F 8 first as made up of the infinitesimal rectangles of which PMUS is a type, and the second of... | |
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EXAMPLE. Prove that a tangent to an hyperbola bisects the angle between the focal radii drawn to the point of contact. 168. To find the area of a segment of a parabola cut off by a line perpendicular to the axis. Compare the required area with the area... 
