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Teokset Teokset 71 - 80 / 88 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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Bulletin, Numerot 1–11

1911
...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...

College Entrance Examination Papers in Plane Geometry

1911 - 178 sivua
...1. Two and only two equal oblique lines can be drawn from a given point to a given straight line. 2. The perpendiculars from the vertices of a triangle to the opposite sides meet at a common point. 4. Define equal figures; equivalent figures; similar figures. Any two polygons are...

The Encyclopedia Britannica: A Dictionary of Arts, Sciences ..., Nide 27

Hugh Chisholm - 1911
...circumference to the sides arc collinear, the line being called Simson's line. We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent; their meet is called the orthocentre, and the triangle obtained by joining the feet...

Plane and Solid Geometry

George Wentworth, George Albert Wentworth, David Eugene Smith - 1913 - 470 sivua
...lie with respect to the 0. bisector PP' ? This point O is called the circumcenter of the triangle. 4. The perpendiculars from the vertices of a triangle to the opposite sides are concurrent. Let the Ji be AQ, BR, and CP. Through A, B, C suppose B'C', C'A', and A'B' drawn II...

Robbin's New Plane Geometry

Edward Rutledge Robbins - 1915 - 264 sivua
...= 00° (104). .-. MB = BC (115). .-. AB, or 2 x J/fi, = 2 x CB (Ax. 6). PROPOSITION L. THEOREM 142. The perpendiculars from the vertices of a triangle to, the opposite sides meet in a point. .£s Given: A ABC, ^IX-Lto BC, Br-Lto AC, and CZ -Lto AB. To Prove : These three J§ meet in a point....

Plane Geometry

John Wesley Young, Albert John Schwartz - 1915 - 223 sivua
...point of contact into segments which subtend equal angles at the point of contact of the circles. D 17. The perpendiculars from the vertices of a triangle to the opposite sides bisect the angles of the triangle formed by joining the feet. Describe circles on the three sides as...

Robbin's New Plane Geometry

Edward Rutledge Robbins - 1915 - 264 sivua
...for all positions of point P. [Draw BC. Prove tBCD, the ext ^ of £\PBC, ".. a constant. Etc.] 41. 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....

Junior High School Mathematics, Kirja 3

George Wentworth, David Eugene Smith, Joseph Clifton Brown - 1918
...about this joining line? \Vhere does 0 lie with respect to the J- bisector of the third side ? 15. The perpendiculars from the vertices of a triangle to the opposite sides are concurrent. , Given theJs-lQ, BR, and CP. Through \ R/ A, B, C draw B'C", C'A', and A'B' parallel...

Information Relative to the Appointment and Admission of Cadets to the ...

Military Academy, West Point
...Theorem: The bisectors of the citerior angles of a rhombus inclose a rectangle. No. 2.— Theorem: The perpendiculars from the vertices of a triangle to the opposite sides meet in a point. (Wt. 10.) No. 3. —Problem: To find the locus of the intersection of the diagonals of the parallelogram...

An Introduction to Analytical Geometry

...and AC, BD. Hence also AB, CD is also a rectangular hyperbola, ie AB is at right angles to CD. Thus: The perpendiculars from the vertices of a triangle to the opposite sides meet in a point (the orthocentre). Also Every conic through the vertices of a triangle and the orthocentre is a rectangular...
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