 | 1864 - 96 páginas
...the points a, ß, y, a.', ß', y are iя the circumference of, the same circle. 12. Let 2) q, r be the feet of the perpendiculars from A, B, C, on BC, CA, AB; then since the triangle o'pais right•angled, and а 'а passes through M, which is its middle point,... | |
 | W. J. C. Miller - 1865 - 124 páginas
...The common radical axis of the system represented by (A) is given by the equation a cos A + 0 cos B + 7 cos C = 0. It is evident that this line is the polar...DEF, where D, E, F are the feet of the perpendiculars froni'A, B, C on BC, CA, AB. 6. The equations of the radical axes of (S', SJ ; ( S', S2) (S', S3) are... | |
 | 1865 - 128 páginas
...be put in the form (af-0 + 7)-i-(— a cos A + 0cos B + 7 cosC) = 0; hence we see that, if Rb R2, R3 are the feet of the perpendiculars from A, B, C on BC, CA, AB, respectively, the intersections of R2Rs with E3F2, of R3Ri with FiD3, and of R^ij with D2Ei, lie on... | |
 | 1865 - 132 páginas
...put in the form (a + /3 + >) + (— a cos A + /3cosB + 7cosC) = 0; hence we see that, if R^ R2, R3 are the feet of the perpendiculars from A, B, C on BC, CA, AB, respectively, the intersections of R2R3 with E3FB of R3Ri with FiDs, and of R,K2 with D^, lie on the... | |
 | Sir George Greenhill - 1876 - 318 páginas
...of the path on a transverse section ABC perpendicular to the axis of the prism must be the triangle DEF, where D, E, F are the feet of the perpendiculars from A, B, C on BC, 04, AB. The projection of the ball will describe the perimeter of DEF twice while the ball moves once... | |
 | John Bascombe Lock - 1882 - 378 páginas
...727173=|--f. (iii) The area of W.(iy) The radius of the circle circumscribing 717273=2,ff. (19) If D, E, F are the feet of the perpendiculars from A, B, C on the opposite sides, the triangle DEF is called the ' pedal triangle' of the triangle ABC*; prove that... | |
 | John Bascombe Lock - 1885 - 368 páginas
...angle (iii) T , AB sm- sin -sin(iv) The radius of the circle circumscribing 7^/3 = 2^. (19) If 7), E, F are the feet of the perpendiculars from A, B, C on the opposite sides, the triangle DEF is called the 'pedal triangle' of the triangle ABC*; prove that... | |
 | London Mathematical Society - 1889 - 464 páginas
...the first triangle ABO, and i, e, £ new coordinates referred to the sides d, e, f, ie, EF, FD, DE, where D, E, F are the feet of the perpendiculars from A, B, C on the opposite sides.] If the equation /3y sin A + ya sin D + a/3 sin C — (Za + m/3 + ny)(asin.<H-/36in.B-rysin... | |
 | Ernest William Hobson - 1891 - 380 páginas
...sin A cos (BC). 52. Shew that the radius of the circle which touches the three circles DCE, EAF, FBD, where D, E, F, are the feet of the perpendiculars from A, B,C, on the opposite sides, is 2Ä sin A sin В sin С cos A cos B cos С (sin A + sin B -f sin С)... | |
 | John Bascombe Lock - 1892 - 354 páginas
...- C) + b sin (0 - A) + e sin (A - S) = 0, (ii) c(cos^+cos/i) = 2(a + b)sin24C'. 109. Prove that if D, E, F are the feet of the perpendiculars from A, B, C upon the opposite sides of the triangle AEG the diameters of the circumscribing circles of the triangles... | |
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D, E, F are the feet of the perpendiculars from A, B, C, on the opposite sides: shew that OA, OB, OC are respectively perpendicular to EF, FD, DE. 
