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" The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. "
Elements of Geometry - Page 54
by Adrien Marie Legendre - 1825 - 224 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...members and observing that BE=DE, we have JB + ID + DC + BC- 4AE + 4DE. But 4.4JU is the square of <2JLE or of AC; and 4DE is the square of BD ; therefore...sides of a parallelogram is equal to the sum of the squares of the diagonals. THEORKM. Fig. 114. 1 96. The line DE (fig. 1 1 4), drawn parallel to the...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...members and observing that BE=DE, we have AB + AD + DC + BC = 4AE + IDE. But 4AE is the square of 2AE or of AC; and 4DE is the square of BD ; therefore...sides of a parallelogram is equal to the sum of the squares of the diagonals. THEOREM. Fig. 114. 196. The line DE (fig. 114), drawn parallel to the base...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 pages
...IDE. 2 2 • But 4AE is the square of 2.4 or of AC; and 4DE is the square of BD ; therefore the su;n of the squares of the sides of a parallelogram is equal to the sum of the squares- f the diagonals. THEOREM. Fig. 114. 1 96. Tlie line DE (fig. 1 1 4), drawn parallel to the...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...squares of BF and DF is equal to twice that of EF and D E. Hence the proposition is manifest. (301) The sum of the squares of the sides of a parallelogram is equal to that of the diagonals. For in that case the line EF vanishes, since the diagonals bisect each other...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 183 pages
...with twice the square of BC ; because CP and BC are equal. Fig: 7. Schol. Hence it is evident that the sum of the squares of the sides of a parallelogram is equal to the (i)Prcp.29. sum of the squares of the diagonals. B- 1- Because the angles DEC and BDA, ACB and CAD...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 235 pages
...that BE = DE, we have JB + AD + DC + BC = 4AE + 4DE. But 4AE is the square of 2AE or ofAC; and 4DEis the square of BD ; therefore the sum of the squares...sides of a parallelogram is equal to the sum of the squares of the diagonals. THEOREM. Fig 114. 196. The line DE (fig. 114), drawn parallel to the lose...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...is equal to the square on AB, together with twice the square on BC. 147. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 148. The base of a triangle is given and is bisected by the centre of a given...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...is equal to the square on AB, together with twice the square on BC. 147. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 148. The base of a triangle is given and is bisected by the centre of a given...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1871 - 492 pages
...equal to AC', and 4.DE2 to BD' (P. Vin., C.) : hence, AB2 + BC2 + CD2 + DA2 = AC2 + BD'. That is, the sum of the squares of the sides of a parallelogram, is equal to the sum of the squares of its diagonals. / ^ PROPOSITION XV. THEOREM. In any triangle, a line drawn parallel to the...
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 285 pages
...sum of the squares of AP and BP is equal to the sum of the squares of AQ and BQ. 9. Prove that the sum of the squares of the sides of a parallelogram is equal to that of the squares of its two diagonals. 10. Prove that if any point within a parallelogram be joined...
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