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Teokset Teokset 21 - 30 / 111 haulle The perpendiculars from the vertices of a triangle to the opposite sides meet in....
" 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 ... - Sivu 106
tekijä(t) Edwin Bidwell Wilson, Josiah Willard Gibbs - 1901 - 436 sivua
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THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...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...

The Elements of Geometry

George Bruce Halsted - 1886 - 366 sivua
...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...

The Elements of Geometry

Webster Wells - 1886 - 371 sivua
...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...

CHAUVENETS TREATISE ON ELEMENTARY GEOMETRY

W. E. BYERLY - 1887
...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...

A Text-book of Geometry

George Albert Wentworth - 1888 - 386 sivua
...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....

The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II ...

Association for the Improvement of Geometrical Teaching - 1888
...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...

Examinations Papers

1888
...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...

The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - 1890 - 393 sivua
...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...

Plane and Solid Geometry

Seth Thayer Stewart - 1891 - 406 sivua
...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....

Elementary Geometry

William Chauvenet - 1893
...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...




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