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The perpendiculars from the vertices of a triangle on the opposite sides are concurrent.
Proceedings of the Edinburgh Mathematical Society - Page 13
by Edinburgh Mathematical Society - 1894

## Geometry for schools, comprising books i. and ii. of Euclid, with some ...

Euclides - 1883 - 96 pages
...trisection of each of them. 217. To construct a triangle having given the three medians. 218. The three perpendiculars from the vertices of a triangle on the opposite sides are concurrent. 219. The lines perpendicular to the sides of a triangle through their middle points are concurrent....

## The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1885
...position between AD and AF ; AE lies in magnitude between AD and AF. I. 19, Cor. 20. Since the sum of the perpendiculars from the vertices of a triangle on the opposite sides is greater than the semiperimeter, by the fifteenth deduction ; and since, by the preceding deduction,...

## Mathematical Questions with Their Solutions: From the ..., Volumes 40-42

1884 - 430 pages
...(Professor Malet, FR8.)— If A = I—**2, prove that * loc1 A -^7332. (The Editor.) — If plt p,, p, be the perpendiculars from the vertices of a triangle on the opposite sides ; rf,, dj, rfa the distances from the vertices to the points of contact of the escribed circles with...

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

...from B or C on the opposite side of the triangle meet AD at O ; shew that OD is equal to DP. *i66. The perpendiculars from the vertices of a triangle on the opposite sides meet in a point (called the orthocentre of the triangle). *i67. If O is the orthocentre of the triangle...

## The Directional Calculus: Based Upon the Methods of Hermann Grassmann

Edward Wyllys Hyde - Ausdehnungslehre - 1890 - 247 pages
...the mean point of eu e2, e3, and trisects the distance from el to p^ (2) To find the common point of the perpendiculars from the vertices of a triangle on the opposite sides. Let l, m, n be the ratios of the sides of the triangle to the cosines of the opposite angles ; ie T>f*...

## Elementary Trigonometry

John Maximilian Dyer - Plane trigonometry - 1891 - 306 pages
...= -. (3) If л/o2 — x¡i cos ß + o sin a = x sin /3, find a. (4) If Z, m, и, be the lengths of the perpendiculars from the vertices of a triangle on the opposite sides, prove that the area of the triangle is - Z' »»' и* (cosec A cosec В cosec C)*. ¿ * (5) An object...

## An Elementary Treatise on Modern Pure Geometry

Robert Lachlan - Geometry - 1893 - 312 pages
...PQR divides the line joining the median points of the triangles ABC, A'B'C' in the ratio m : n. 115. The perpendiculars from the vertices of a triangle on the opposite sides meet in a point (§ 9G, Ex. 2), which is called the orthocentre of the triangle. If ABC be the triangle,...

## The Educational Times, and Journal of the College of Preceptors, Volume 68

Education - 1915 - 412 pages
...Find the condition that the vectors x — a, b—c may be perpendicular, and hence show that the three perpendiculars from the vertices of a triangle on the opposite sides are concurrent. 18119. (VV SATYANARAYAN.) — The ratio compounded of the ratios in which any two i»ogonal conjugates...