 | William Chauvenet - Geometry - 1871 - 380 pages
...with the opposite vertices of the tri angle meet in a point ; that the three perpendiculars from the vertices of a triangle to the opposite sides meet in a point ; and that the three medial lines, of a triangle meet in a point. ANHARMONIC RATIO. 8. Definition.... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...(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 the perpendiculars... | |
 | Dublin city, univ - 1876 - 420 pages
...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 of the... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...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 opposite... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...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 sides.... | |
 | Edward Albert Bowser - Geometry, Analytic - 1880 - 334 pages
...has mastered all the examples in any one article.] 1. Prove that the perpendiculars drawn from the vertices of a triangle to the opposite sides meet in a point. Let ABC be the triangle ; AF, BE, CD the perpendiculars. Assume AX and AY as the rectanguE « Fig.... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...at the middle oftliat line). QED PROPOSITION XXXVII. THEOREM. 121. The three perpendiculars from the vertices of a triangle to the opposite sides meet in a point. A' In the triangle ABC, let BP, AН, С К, be the perpendiculars from the vertices to the opposite... | |
 | Samuel Constable - Geometry - 1882 - 222 pages
...D must pass through 0. Hence the three lines meet in a point. PROP. 21. The perpendiculars from the vertices of a triangle to the opposite sides meet in a point: and if a triangle be formed by joining their feet, its sides will be equally inclined to those of the... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...parallelogram bisect the angles, it is a rhombus. THEOREM XXXIII. 226. The three perpendiculars from the vertices of a triangle to the opposite sides meet in a point. HYPOTHESIS. Let DU, EE', FF', be the three perpendiculars from the vertices D, E, F, to the opposite... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...parallelogram bisect the angles, it is a rhombus. THEOREM XXXIII. 226. The three perpendiculars from the vertices of a triangle to the opposite sides meet in a point. HYPOTHESIS. Let DLf, EEf, FF', be the three perpendiculars from the vertices D, E, F, to the opposite... | |
| |
The perpendiculars from the vertices of a triangle to the opposite sides meet in a point. 
