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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 ...

Euclides - 1841 - 378 pages
...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 bases 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: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...ABC may fee 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...triangles on each side of it are similar to the whole triangle, and to one another. , Let ABC be aright angled triangle, having the right angle BAC ; and...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 320 pages
...to the triangle DEF. Wherefore, if the two triangles, &c. QED PROP. VIII. THEOR. 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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Report to the Trustees of the Dick Bequest for the Benefit of the ..., Volume 2

Church schools - 1844
...the segments of the other : and demonstrate this also by the properties of similar triangles. 3. That in a right angled triangle if a perpendicular be drawn from the right angle to the hypothenuse, the two triangles on each side of the perpendicular are each similar to the original triangle....
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...the triangle DEF. Wherefore, if two triangles, &c. QED PROPOSITION VIII. THEOR. — 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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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 pages
...the triangle DEF. Wherefore, if two triangles, &c. QED PROPOSITION VIII. THEOREM. In a right-angled triangle, if a perpendicular be drawn from the right...the triangles on each side of it are similar to the itholt triangle, and to one another. Let ABC be a right-angled triangle, having the right angle BAG;...
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley, William Henry Johnstone - Mathematics - 1845 - 222 pages
...of the sides of a regular hexagon and a decagon inscribed in the same circle. 173. In a right-angled triangle, if a perpendicular be drawn from the right angle to the hypothenuse, then the areas of the two circles inscribed in the triangles on each side of this perpendicular...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...that is, it is equal to it : wherefore, if two triangles, &c.f PROP. VIII. THEOR.— 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 Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1846 - 332 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...triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be aright angled triangle, having the right angle BAC ; and from...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...at C to the angle at F. Wherefore, If two triangles %c. UK o. PROP. VIII. THEOR. 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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