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" IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another. "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 92
by Dennis M'Curdy - 1846 - 138 pages
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...to the triangle DEF. Wherefore, if two triangles &c. QED PROPOSITION 8. THEOREM. In a right-angled triangle, if a perpendicular be drawn from the right...triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right-angled triangle, having the right angle BAC; and from...
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Manual of Euclid: Books IV, V, VI.

Euclid - 1868 - 138 pages
...aiv кQfто ^0jr т irpb тy кaQтф Tpiofid laT Tif тf o\if Kai In a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of the perpendicular are similar to the whole and to Statement. — Let ABC be a right-angled triangle,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pages
...THEOREM. In a right-angled triangle, if a perpendicular be draion from the rightangle to the bate ; the triangles on each side of it are similar to the whole triangle, and to one another, Let ABC be a right angled-triangle, having the right angle BA C; and...
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Annual Report of the Normal, Model, Grammar, and Common Schools in Ontario ...

Ontario Chief Superintendent of Education - Education - 1869
...line. 11. Inscribe an equiangular and equilateral pentagon in a given circle. 12. In a right-angled triangle if a perpendicular be drawn from the right...triangles on each side of it are similar to the whole triangle, and to each other. No. 15. NATURAL PHILOSOPHY— BOTH DIVISIONS. 1. Describe briefly the...
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The Geometry of the Circle and Mathematics as Applied to Geometry by ...

James Smith - Circle-squaring - 1869 - 459 pages
...circle X, and, (OH2 — H T2) = area of a regular inscribed dodecagon to the circle X. In a right-angled triangle, if a perpendicular be drawn from the right angle to the opposite side, the triangles on each side of it, are similar to the whole triangle and to each other....
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The geometry of the circle and mathematics as applied to geometry by ...

James Smith - 1869 - 470 pages
...whole triangle AC D. Now, by Euclid: Prop 8 : Book 6 : it is made to appear that: In a right-angled triangle, if a perpendicular be drawn from the right angle to the opposite side, the triangles on each side of it are similar to the whole triangle and to each other,...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...fourth proportional to the lines BD, DH, AB. PROPOSITION XII. THEOREM. (Eucl. vi. 8.) In a right.angled triangle, if a perpendicular be drawn from the right...triangles on each side of it are similar to the whole triangle and to one another. B a Let ABC be a right.angled A , having L BAC a rt. i , and from A let...
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The Quadrature of the Circle: The Square Root of Two, and the Right-angled ...

William Alexander Myers - Circle-squaring - 1873 - 238 pages
...therefrom, the square root of the remaining || can be extracted exactly. THEOREM 3. In any right-angle triangle if a perpendicular be drawn from the right angle to the base the triangles on each side are similar to the whole triangle and to one another, and the perpendicular is a mean proportional...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...the triangle DEF. Wherefore, if two triangles, &c. QED PROPOSITION 8.— Theorem. In a right-angled triangle, if a perpendicular be drawn from the right...triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right-angled triangle, having the right angle BA C, and...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 349 pages
...corresponding angles equal and the sides about the equal angles proportional. PROPOSITION VI. In a right-angled triangle, if a perpendicular be drawn from the right...angle to the base; the triangles on each side of it shall be similar to the whole triangle and to one another. n Let ACB be a right-angled A having the...
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