 | John Casey - 1882 - 186 lapas
...in harmonical progression. Prop. 4.—Any line cutting a circle, and passing through a fixed point, is cut harmonically by the circle, the point, and the polar of the point. Let D be the point, EF its polar, DGH a line cutting the Q in the points G and H, and the polar of... | |
 | John Casey - 1888 - 279 lapas
...harmonical progression. Prop. 4. — Any line cutting a circle, and passing through a fixed point, is cut harmonically by the circle^ the point •, and the polar of the point. Let D be the point, EE its polar, DGH a line cutting the O in the points G and H, and the polar of... | |
 | William John McClelland, Thomas Preston - 1893 - 402 lapas
...opposite vertex is said to be Self-Reciprocal or Self -Conjugate with respect to the small circle. 153. Theorem. — Any secant drawn through a fixed...of O in R. Denote the perpendiculars from M on OT, OT', TT' by j?,, pt,p, respectively, and the corresponding perpendiculars from N by wi, OTZ, OT. Then... | |
 | Andrew Wheeler Phillips, Irving Fisher - 1896 - 570 lapas
...pencil (0. A BCD') and therefore harmonic. 56. A line cutting a circle and passing through a fixed point is cut harmonically by the circle, the point, and the polar of the point. Hint. — Let P be the fixed point, LC its polar, and PM the line cutting the circle. Since PO.PC=PA.PB... | |
 | Andrew Wheeler Phillips, Irving Fisher - 1896 - 574 lapas
...pencil (O.ABCD) and therefore harmonic. 56. A line cutting a circle and passing through a fixed point is cut harmonically by the circle, the point, and the polar of the point. Hint. — Let P be the fixed point, LC its polar, and PM the line cutting the circle. Since PO.PC—PA.PB... | |
 | Charles Godfrey, Arthur Warry Siddons - 1912 - 190 lapas
...Chapter vn. Th. 31. If a straight line is drawn through any point to cut a circle, the line is divided harmonically by the circle, the point, and the polar of the point with respect to the circle. Th. 32. If the polar of a point P with respect to a circle passes through a point Q, then the polar... | |
 | Ray C. Jurgensen, Alfred J. Donnelly, Mary P. Dolciani - 1963 - 198 lapas
...harmonically. THEOREM 31. If a strajght line is drawn through any point to cut a circle, the line is divided harmonically by the circle, the point and the polar of the point with respect to the circle. fig. 86. Let T be the point, TRHS the line cutting the circle at R, S and the polar of T at H ; let... | |
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A line cutting a circle and passing through a fixed point is cut harmonically by the circle, the point, and the polar of the point. 