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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: 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...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 BAG ; and from...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 513 pages
...triPROP. VIII. THKOR. Sec N. In a right angled triangle, if a perpendicular k drawn from the riyltt angle to the base, the triangles on each side of it are similar to the ichole triangle and to one another. Let ABC be a right angled triangle, having: the right angle BAC...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...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 Element of Geometry

John Playfair - Geometry - 1836 - 114 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...triangles on each side of it are similar to the whole triangle, and to one another. i Let ABC be a right angled triangle, having the right angle BAG ; and...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 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...triangles on each side of it are similar to the whole triangle, and to one another. Сок. From this it is manifest, that the perpendicular drawn, from...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 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...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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 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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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...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 B AC ; and...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED PROP. VIII. THEOR, lie a right angled triangle, if a perpendicular be drawn...angle to the base, the triangles on each side of it *re similar to the whole triangle, and to one another.* ' See Note. Let ABC be a right angled triangle,...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...have those angles equal about which the sides are proportional. PROP. VIII. THEOR. 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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