| William Chauvenet - 1871 - 380 σελίδες
...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 sidw meet in a point ; it is required to determine its reciprocal theorem by the method of reciprocal... | |
| William Chauvenet - 1872 - 382 σελίδες
...meet is equally distant from the three vertices of the triangle. ' PROPOSITION XLII.— THEOREM. 132. The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point. Let AD, BE, CF, be the perpendiculars from the vertices of the triangle ABC to the opposite sides,... | |
| William Chauvenet - 1872 - 382 σελίδες
...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 σελίδες
...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... | |
| 1876 - 646 σελίδες
...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 σελίδες
...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 σελίδες
...? 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... | |
| George Albert Wentworth - 1877 - 416 σελίδες
...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 σελίδες
...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... | |
| George Albert Wentworth - 1877 - 436 σελίδες
...line is the JL erected at the middle ofthat line). GEOMETRY. BOOK I. PROPOSITION XXXVII. THEOREM. 121. The three perpendiculars from the vertices of a triangle to the opposite aides meet in a point. In the triangle ABC, let B Р, AН, С K, be the perpendiculars from the vertices... | |
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