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" 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 of the perpendiculars is called the pedal triangle. "
A Text-book of Euclid's Elements for the Use of Schools - Strona 242
autor: Euclid - 1904 - Liczba stron: 456
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Mathematical Exercises ...

Samuel H. Winter - 1867
...equilibrium, prove that f '. QI Bi;sin QOR : sin ROF : sin POQ. Three forces are represented in direction by the perpendiculars drawn from the vertices of a triangle to the opposite sides, and are inversely proportional to those perpendiculars; prove that they are in equilibrium. 3. Find...
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An elementary treatise on statics

J W. Mulcaster - 1871
...OQ, through P, P v Q, is isosceles and right-angled. 29. Three forces are represented in direction by the perpendiculars drawn from the vertices of a triangle to the opposite sides, and are inversely proportional to those perpendiculars; prove that they are in equilibrium. 30. The...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...right angle, (I. Def. 8.) and OD is perpendicular to BC. QED Cor. — Hence it follows that the three perpendiculars drawn from the vertices of a triangle to the opposite sides, meet in the same point. Let AD, BE, CF bo the three perpendiculars from the angles A, B, C of the triangle...
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Dublin examination papers

Dublin city, univ - 1876
...his father gets $s. a day ? MR. BURNSIDE. 7. Show how to inscribe a square in any given triangle. 8. The perpendiculars drawn from the vertices of a triangle to the opposite sides meet in a point. 9. Prove that the sum of the squares on the diagonals of a parallelogram is equal...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1877 - Liczba stron: 443
...Therefore, Prop. IV., the three lines AD, BE, CF pass through the same point. PROPOSITION VI. 90. The three perpendiculars drawn from the vertices of a triangle to the opposite sides meet in a point. Let ABC be a triangle, and let AD, BE, CF be drawn from the vertices perpendicular...
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An Elementary Treatise on Analytic Geometry, Embracing Plane Geometry and an ...

Edward Albert Bowser - 1880 - Liczba stron: 287
...need not necessarily tarry till he has mastered all the examples in any one article.] 1. Prove that the perpendiculars drawn from the vertices of a triangle to the opposite sides meet in a point. Let ABC be the triangle ; AF, BE, CD the perpendiculars. Assume AX and AY as the rectanguE...
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Elements of Plane Geometry

Franklin Ibach - 1882 - Liczba stron: 196
...AED = A BED, and BD = AD=IAC. (63) (138). (45) (83) ELEMENTS OF PLANE GEOMETRY. THEOREM XLIX. 143. The perpendiculars drawn from the vertices of a triangle to the opposite sides meet in a common point. In the A ABC, let AD, BE, and CF be the _Ls from the vertices to the opposite...
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A Mathematical Solution Book Containing Systematic Solutions to Many of the ...

Benjamin Franklin Finkel - 1888 - Liczba stron: 481
...and escribed circles of the triangle. The Pedal Triangle is a triangle formed by joining the feet of the perpendiculars drawn from the vertices of a triangle to the opposite bides. The Orthocenter is the point of intersection of these perpendiculars. Medial Lines, or Medians,...
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The Laws of Motion: An Elementary Treatise on Dynamics

W. H. Laverty - 1889 - Liczba stron: 224
...one-twelfth of the weight, compare the acceleration with that of gravity. 21. Forces act for a moment along the perpendiculars drawn from the vertices of a triangle to the opposite sides. Find their relative magnitudes that for the moment there may be no acceleration. 22. Three equal perfectly...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - 1890 - Liczba stron: 393
...angles A and B, find the value of the angle AOB. D/C Proposition 43. Theorem. 170. The perpendiculars from the vertices of a triangle to the opposite sides are concurrent. Hyp. Let ABC be a A , and RX— AD,' BE, CF,the three J_s from \ , B< A, B, C to the opp. sides. \...
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