 | Euclid - 1892 - عدد الصفحات: 460
...> DEB Hyp. i. 32. QED [For an Alternative Proof see page 10U.] DEFINITIONS. (i) The intersection of the perpendiculars drawn from the vertices of a triangle to the opposite sides is called its ortho. centre. (ii) The triangle formed by joining the feet of the perpendiculars is... | |
 | Robert Lachlan - 1893 - عدد الصفحات: 312
...A, B, C of a triangle to the middle points of the sides BC, CA, AB are concurrent. Ex. 2. Show that the perpendiculars drawn from the vertices of a triangle to the opposite sides are concurrent. Ex. 3. If a straight line be drawn parallel to BC, cutting the sides AC, AB in Y and Z, and if BY,... | |
 | Great Britain. Education Department. Department of Science and Art - 1894 - عدد الصفحات: 894
...shall pass through B, C, F, G, whose diameter is double that of the former circle. (40-) 46. Show that the perpendiculars drawn from the vertices of a triangle to the opposite sides are concurrent. If ABFG, ACKH are the squares described on the sides AB, AC of a triangle ABC, in which the angle A... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1895 - عدد الصفحات: 346
...The perpendicular bisectors of the sides of a triangle are concurrent. 533. Also, the perpendiculars from the vertices of a triangle to the opposite sides are concurrent. 534. If three circumferences intersect in pairs, the common chords are concurrent. Theorem 11. If three... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1895 - عدد الصفحات: 344
...The perpendicular bisectors of the sides of a triangle are concurrent. 533. Also, the perpendiculars from the vertices of a triangle to the opposite sides are concurrent. PLANE GEOMETRY. Theorem 11. If three lines, x, y, z, drawfl from the vertices of triangle ABC to meet... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1899 - عدد الصفحات: 272
....'. P1 lies on CT. Similarly for P , . Prop. XLII PROPOSITION XLV. 133. Theorem. The perpendiculars from the vertices of a triangle to the opposite sides are concurrent. Given the A ABC. To prove that the perpendiculars from A, B, C, to a, b, c, respectively, are concurrent.... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1899 - عدد الصفحات: 400
....'. P l lies on CT. Similarly for P 4 . Prop. XLII PROPOSITION XLV. 133. Theorem. The perpendiculars from the vertices of a triangle to the opposite sides are concurrent. \ V Given the A ABC. c To prove that the perpendiculars from A, B, C, to a, b, c, respectively, are... | |
 | Charles Austin Hobbs - 1899 - عدد الصفحات: 266
...CD ; if EF cuts AC at G and BD at H, prove that EG = FH. 61 Proposition 7O. Theorem. 82. The three perpendiculars drawn from the vertices of a triangle to the opposite sides intersect at a common point. Hypothesis. AD, BE, and CF are the Js drawn from the vertices of the A... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - 1900 - عدد الصفحات: 330
...meet at the point OQED [For an Alternative Proof see p. 114.] DEFINITIONS. (i) The intersection of the perpendiculars drawn from the vertices of a triangle to the opposite sides is called its orthocentre. (ii) The triangle formed by joining the feet of the perpendiculars ia called... | |
 | University of St. Andrews - 1902 - عدد الصفحات: 740
...4y. (6) r = acos 8. (7) r = asec fl. MATHEMATICS— (FIRST PAPER). 25TH MARCH 1902 — 9 TO 11 AM 1. The perpendiculars drawn from the vertices of a triangle to the opposite sides are concurrent. If the feet of the perpendiculars of a triangle be joined, the triangle thus formed will have its angles... | |
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We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent ; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle. 
