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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 the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...triangle ABC may be proved to be equiangular to the triangle DEF, as in the first case. PROP. VIII. THEOR. 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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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...divide the triangle into two triangles which are similar to the whole triangle, and also to each other. In a right angled triangle if a perpendicular be drawn from the right angle to the hypothenuse, it will be a mean proportional between the segments of the hypothenuse ; and each of the...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...1.), and therefore similar (31. Cor. 1.). Therefore, SEC. ' PROP. 34. (Eue. vi. 8.) In a right-angled triangle, if a perpendicular be drawn from the right angle to the hypotenuse, the triangles upon either side of it shall be similar to the whole triangle, and to one...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...equiangular to the triangle DEF. " at'yles," &c. QED Wherefore, " if two triPROP. VIII. THEOR. See N. 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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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...1.), and therefore similar (31. Cor. 1.). Therefore, &c. PROP. 34. (Eue. vi. 8.) In a right-angled triangle, if a perpendicular be drawn from the right angle to the hypotenuse, the triangles upon either side of it shall be similar to the whole triangle, and to one...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...triangles, shall be equiangular, and have those angles, equal about which the sides are proportionals. VIII. 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. Сок....
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The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...triangle ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED \ PROP. VIII. THEOR. 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. i Let...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...the enunciation is also altered, with a view to render it more simple and plain. IN a right-angled triangle, if a perpendicular be drawn from the right angle to the hypotenuse, the triangles on each side of it are similar to the whole triangle, and to one another....
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...equiangular to the triangle DEF, aa in the first case. PROPOSITION VIII. 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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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...equiangular to the triangle DEF, as in the first case. Wherefore if two triangles, &c. QED PROP. VIII. THEOR. 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...
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