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Teokset Teokset 61 - 70 / 109 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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PLANE AND SOLID GEOMETRY

FLETCHER DURELL. PH.D. - 1911
...of the A ABC meet in the point 0. Q,. ED PROPOSITION XLV. THEOREM 186* The perpendiculars from tlie vertices of a triangle to the opposite sides meet in a point (called the ortho-center),, B Given AD, BF, and CE the perpendiculars from the vertices A, B, and C...

Plane Geometry

Edward Rutledge Robbins - 1906 - 254 sivua
...length for all positions of point P. [Draw BC. Prove Z BCD, the e'xt. Z of APBC, = a constant. Etc.] 67. The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of these perpendiculars....

Plane and Solid Geometry

Edward Rutledge Robbins - 1907 - 412 sivua
...length for all positions of point P. [Draw EC. Prove Z BCD, the ext. Z of APfiC, = a constant. Etc.] 67. The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of these perpendiculars....

Plane and Solid Geometry

Elmer Adelbert Lyman - 1908 - 340 sivua
...Join O, the point of intersection, with the third vertex C. Prove that OC bisects Z C. 3. Prove that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point. SUGGESTIONS. Through the vertices of the triangle draw lines parallel respectively to the opposite...

New Plane and Solid Geometry

Webster Wells - 1908 - 298 sivua
...and C, by § 54 ; and also from A and (7.) 136. It follows from § 135 that PROP. XL VI. THEOREM 137. The perpendiculars from the vertices of a triangle to the opposite sides intersect at a common point. A Draw any A ABC. From A, B, and C draw lines AD (a), BE (6), and CF (c)...

New Plane Geometry

Webster Wells - 1908 - 174 sivua
...from A and C.) 136. It follows from § 135 that PLANE GEOMETRY — BOOK I PROP. XL VI. THEOREM 137. The perpendiculars from the vertices of a triangle to the opposite sides intersect at a common point. ,H Draw .any A ABC. From A, B, and C draw lines AD (a), BE (6), and CF...

Coordinate Geometry

Henry Burchard Fine, Henry Dallas Thompson - 1909 - 300 sivua
...AB at Я and DC at A". Prove that the lines AC, JÍG, and FK meet in a common point. 47. Prove that the perpendiculars from the vertices of a triangle to the opposite sides meet in a common point, taking one of the sides and the perpendicular to it as axes of reference. 48. Prove that...

Coordinate Geometry

Henry Burchard Fine, Henry Dallas Thompson - 1909 - 300 sivua
...been proved, when (4) is satisfied, the lines (1), (2), (3) meet in a common point. Example. Show that the perpendiculars from the vertices of a triangle to the opposite sides meet in a common point. Let the vertices be (x\, 2/1), (X2, 2/2), (x3, 2/3). The equation of the line joining...

Wentworth's Plane Geometry

David Eugene Smith - 1910 - 287 sivua
...with respect to the _L bisector Pi" ? This point 0 is called the circumcenter of the triangle. -APB 4. The perpendiculars from the vertices of a triangle to the opposite sides are concurrent. Let the Js be AQ, BR, and CP. Through A, B, C suppose B'C', and A'B' drawn II to CB,...

Bibliography of Science Teaching, Numerot 1–11

1911 - 27 sivua
...the tangent is a mean proportional between the whole secant and its external segment. 4. Prove that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point. 5. The lengths of the circumferences of two concentric circles differ by 6 inches. Compute the width...




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