 | William Chauvenet - 1872 - 382 pagina’s
...pencils have equal anharmonic ratios (13). PROPOSITION XVII.—PROBLEM. 63. It is a known theorem that the three perpendiculars from the vertices of a triangle to the opposite sides meet in a point; it is required to determine its reciprocal theorem by the method of reciprocal polars, Let... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 pagina’s
...8.) and OD is perpendicular to BC. QED Cor. — Hence it follows that the three perpendiculars drawn from the vertices of a triangle to the opposite sides, meet in the same point. Let AD, BE, CF bo the three perpendiculars from the angles A, B, C of the triangle ABC; it is required to prove that... | |
 | William Chauvenet - 1875 - 390 pagina’s
...from A and C; therefore it is equally distant from A and B, and must lie in the perpendicular FK (89). That is, the perpendicular FK passes through O, and...perpendiculars from the vertices of a triangle to tho opposite sides meet in the same point. Let AD, BE, CF, be the perpen- ?' * *' diculars from the... | |
 | 1876 - 646 pagina’s
...triangle with respect to a point lying within and with respect to an axis cutting the triangle. 2. The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point. 3. To construct a polygon similar to a given polygon, the ratio of similitude of the two polygons being... | |
 | Aaron Schuyler - 1876 - 384 pagina’s
...triangle, at tlieir middle points, to the tliree vertices are equal. (?) 112. Proposition LI.— Theorem. The three perpendiculars from the vertices of a triangle to the opposite sides meet in tlie same point. Let ABC be a triangle, AD, y__ BE, CF, perpendiculars from \ the vertices, A, B, C,... | |
 | Dublin city, univ - 1876 - 420 pagina’s
...? MR. BURNSIDE. 7. Show how to inscribe a square in any given triangle. 8. The perpendiculars drawn from the vertices of a triangle to the opposite sides meet in a point. 9. Prove that the sum of the squares on the diagonals of a parallelogram is equal to the sum... | |
 | William Chauvenet - 1877 - 396 pagina’s
...angles of a triangle meet is equally distant from the three sides of the triangle. PROPOSITION XLL— THEOREM. 130. The three perpendiculars erected at...sides meet in the same point. Let AD, BE, CF, be the perpen- £'. * .•»' diculars from the vertices of the tri- \ / angle ABC to the opposite sides,... | |
 | George Albert Wentworth - 1877 - 416 pagina’s
...of a straight line is the J. erected at the middle of that line). PROPOSITION XXXVII. THEOREM. 121. The three perpendiculars from the vertices of a triangle to the opposite sides meet in a point. Bi In the triangle A£C, let BP, AH, CK, be the perpendiculars from the vertices to the opposite... | |
 | William Frothingham Bradbury - 1877 - 262 pagina’s
...vertices of the equilateral triangles to the opposite angles of the given triangle are equal. 143. The three perpendiculars from the vertices of a triangle to the opposite sides intersect at the same point. Through the vertices draw lines parallel to the opposite sides forming... | |
 | Elias Loomis - 1877 - 458 pagina’s
...three lines AD, BE, CF pass through the same point. PROPOSITION VI. 90. The three perpendiculars drawn from the vertices of a triangle to the opposite sides meet in a point. Let ABC be a triangle, and let AD, BE, CF be drawn from the vertices perpendicular to the... | |
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The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point. 
