 | Adrien Marie Legendre, John Farrar - 1825 - 294 σελίδες
...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... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 σελίδες
...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... | |
 | Adrien Marie Legendre - 1825 - 276 σελίδες
...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... | |
 | Euclid, Dionysius Lardner - 1828 - 542 σελίδες
...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... | |
 | Euclid - 1833 - 216 σελίδες
...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... | |
 | Adrien Marie Legendre - 1841 - 288 σελίδες
...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... | |
 | Euclid, Isaac Todhunter - 1867 - 424 σελίδες
...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... | |
 | Euclid, Isaac Todhunter - 1867 - 426 σελίδες
...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... | |
 | Adrien Marie Legendre - 1871 - 490 σελίδες
...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... | |
 | Henry William Watson - 1871 - 320 σελίδες
...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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The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 
