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" If from the middle point of one of the sides of a right-angled triangle, a perpendicular be drawn to the hypotenuse, the difference of the squares on the segments into which it is divided, is equal to the square on the other side. "
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Page 24
by Euclides - 1860
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 pages
...is equal to the difference of the squares of the segments of the base. 74. If from the middle point of one of the sides of a right-angled triangle a perpendicular be drawn to the hypothenuse, the difference of the squares of the segments into which it is divided, is equal to the...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...the hypothenuse by three times the square upon half the line bisected. 2. If from the middle point of one of the sides of a right-angled triangle a perpendicular be drawn to the hypothenuse, the difference of the squares of the segments so formed is equal to the square of the...
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The Elements of Euclid: With Many Additional Propositions ..., Part 1

Euclid - Geometry - 1853 - 176 pages
...equal to the square on the third side ; and if one of the given sides subtends the right angle, then the square on the third side is equal to the difference of the squares on the two given sides. This application of the 47th proposition to the purposes of finding the parts of right-angled...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...is equal to the difference of the squares on the segments of the base. 150. If from the middle point of one of the sides of a right-angled triangle, a perpendicular be drawn to the hypotenuse, the difference of the squares on the segments into which it is divided, is equal to tht, square on the...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 pages
...is equal to the difference of the squares on the segments of the base. 150. If from the middle point of one of the sides of a right-angled triangle, a perpendicular be drawn to the hypotenuse, the difference of the squares on the segments into which it is divided, is equal to the square on the other...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...is equal to the difference of the squares on the segments of the base. 169. If from the middle point of one of the sides of a right-angled triangle, a perpendicular be drawn to the hypotenuse, the difference of the squares on the segments into which it is divided, is equal to the square on the other...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...is equal to the difference of the squares on the segments of the base. 150. If from the middle point of one of the sides of a right-angled triangle, a perpendicular be drawn to the hypotenuse, the difference of the squares on the segments into which it is divided, is equal to the square on the other...
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First book of mathematics

Hugo Reid - Mathematics - 1872 - 142 pages
...joined, AEC would be a triangle, right-angled at E (72). Whence it appears that if from the right angle of a right-angled triangle a perpendicular be drawn to the hypotenuse, the perpendicular is a mean proportional between the segments of the hypotenuse. Farther, such perpendicular...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...four equal portions by lines drawn from any point in one of its sides. 62. If from the middle point of one of the sides of a right-angled triangle, a perpendicular be drawn to the hypotenuse, the difference of the squares on the segments into which it is divided is equal to the square on the other...
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Exercises Contained in Wentworth's Geometry: With Key, Followed by a ...

George Albert Wentworth - 1879 - 196 pages
...and BD the line; then BC* = BA* + AC* = BA* + 4 AD* = BD* + 3 AD*. Ex. 15. If from the middle point of one of the sides of a right.angled triangle a perpendicular be drawn to the hypotenuse, the difference of the squares on the segments so formed is equal to the square on the other side. Given...
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