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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. "
A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the ... - Page 278
by Thomas Malton - 1774 - 440 pages
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 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 angle to the base, the triangles on each side of it are similar to the whole triangle and to one another. B 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...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 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...
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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 angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC...
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The Quadrature of the Circle: The Square Root of Two, and the Right-angled ...

William Alexander Myers - Circle-squaring - 1874 - 207 pages
...straight lines AB, J5(7, a mean proportional DB is found. PROPOSITION 5. THEOREM. 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 each other. See Plate...
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Examination Christmas,1875

Education Department,London - 1876 - 1010 pages
...alternate segments of the sides will be equal to the continued product of the other three segments. 3. 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. Write...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...and have those angles equal about which the sides are proportionals. . . . . . . . . . . . . 215 8. 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. .. .....
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...have the same ratio which the other sides of the triangle have to one another. 4. 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. 5. If...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878 - 100 pages
...straight line &c. QED Cor. The angle in a semicircle is a right angle. PROP. xxv. THEOREM. (E. 6. 8). In a right angled triangle if a perpendicular be drawn from the right angle to the opposite side, the triangles on each side of the perpendicular are similar to the whole triangle, and...
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Civil Service of India: Open Competition for the Regulations, Examinations ...

Civil service - 1878 - 228 pages
...and the base produced is equal to the perpendicular altitude of the triangle. 6. 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. Prove...
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