 The perpendiculars from the vertices of a triangle to the opposite sides meet in a point. Let the Js be AH, BP, and CK. Through A, B, C suppose B'C', A'C', A'B', drawn II to BC, AC, AB, respectively. Then AH is _L to B'C'. (Why ?) Now ABCB' and A CBC'...  Vector Analysis: A Text-book for the Use of Students of Mathematics ... - الصفحة 106بواسطة Edwin Bidwell Wilson, Josiah Willard Gibbs - 1901 - عدد الصفحات: 436عرض كامل - لمحة عن هذا الكتاب
 | George Bruce Halsted - 1885 - عدد الصفحات: 389
...the diagonals of a 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 - 1886 - عدد الصفحات: 394
...the diagonals of a 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... | |
 | Webster Wells - 1886 - عدد الصفحات: 392
...of a triangle is equally distant from the vertices of the triangle. PROPOSITION XLIII. THEOREM. 129. The perpendiculars from the vertices of a triangle to the opposite sides meet in a common point. Let AD, BE, and CF be the perpendiculars from the vertices of the triangle ABC to the... | |
 | William Chauvenet, William Elwood Byerly - 1887 - عدد الصفحات: 331
...to the diagonals, they will form a parallelogram twice as large as the quadrilateral. 27. The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point. Suggestion. Draw through the three vertices lines parallel to the opposite sides of... | |
 | George Albert Wentworth - 1888 - عدد الصفحات: 264
...A and .5. Hence O is equidistant from B and C, and therefore is in the _L bisector FF'. (Why ?) 32. The perpendiculars from the vertices of a triangle to the opposite sides meet in a point. HINT. Let the _k be AH, BP, and Through A, B, C suppose B'C', A'C', A'B' drawn II to BC, AC, AB, respectively.... | |
 | Association for the Improvement of Geometrical Teaching - 1888 - عدد الصفحات: 208
...vertices of a triangle on the opposite sides are equal to one another. *i69. If three straight lines drawn from the vertices of a triangle to the opposite sides meet in a point and are divided at that point into segments containing equal rectangles, shew that the point must be... | |
 | 1888 - عدد الصفحات: 666
...the third booi 1 Is it completely treated ? Give fully -the reasons for your answer. 2. Prove that the perpendiculars from the vertices of a triangle to the opposite sides pass through a point, and that the circle which passes through . • the feet of these perpendiculars... | |
 | Edward Albert Bowser - 1890 - عدد الصفحات: 414
...pt., being the _L bisectors oflhe three sides oftfie A PQR (168). QED 171. DsF. The intersection of the perpendiculars from the vertices of a triangle to the opposite sides is called its arthocentrc, --" Proposition 44. Theorem. 172. The three medial lines of a triangle are... | |
 | Seth Thayer Stewart - 1891 - عدد الصفحات: 422
...chord produced to meet a line drawn from the given point through the extremity of the first arc. 7. The perpendiculars from the vertices of a triangle to the opposite sides are the bisectrices of the angles of the triangle formed by joining the feet of the perpendiculars.... | |
 | 1913 - عدد الصفحات: 730
...Amer Math. Sac., IV (1903), pl— 12) Morley has found for я lines analogues of the theorems that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point, and that four such points, or orthocenters, of the four triangles of a four- line are on a line. For... | |
| |
