...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...

...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,...

...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...

...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...

...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,...

...? 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...

...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...

...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...

...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...

...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...