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" From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines. "
Elements of Plane Geometry: For the Use of Schools - Page 61
by Nicholas Tillinghast - 1844 - 96 pages
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 208 pages
...The square of a line is equivalent to four times the square of half the line. , ' ^ . PROPOSITION VI. THEOREM. The square described on the difference of two lines is equivalent to the squares on the two lines diminished by twice their rectangle. The square upon AB, the difference of...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...demonstrated in algebra, in obtaining the square of a binomial ; which is expressed thus : IF THEOREM. 1 82. The square described on the difference of two lines, is equivalent to the sum of thc squares described on the lines respectively, minus twice the rectangle contained by the lines....
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1830 - 344 pages
...demonstrated in algebra, in obtaining the square of a binomial ; which is expressed thus : THEOREM. 182. The square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines. Let AB and BC...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 316 pages
...adding <? to each member of this equality, we shall have, COR. From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines. For a — c...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...demonstrated in algebra, in obtaining the square of a binominal ; which is expressed thus : PROPOSITION IX, THEOREM. The square described on the difference, of...two lines, is equivalent to the sum of the squares described on the lines, minus twice the rectangle contained by the lines. Let AB and BC be two lines,...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1837 - 332 pages
...equality, we shall have, COR. From this proposition it is evident, that the square described on Hie difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines. For a — c=4...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...member of this equality, we shall have, or <z2+c2=2ac+R Coa. From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines. For a — c=b...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...taking these two rectangles from each member of the equation we have AC2= AB2+BC'— 2(AB x BC). Hence, The square described on the difference of two lines, is equivalent to the sum of the sqt,ares described on each of the linesi minus twice the rectangle contained by those lines. BOOK IV....
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...into which a line may be divided. This is equivalent to the algebraical expression PROPOSITION XI. THEOREM. The square described on the difference of...two lines is equivalent to the sum, of the squares described on the lines, minus twice the rectangle contained by the lines. Let AB and BC be two lines,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1846 - 332 pages
....-.a2+c2=62+2c(6+c), or a2+c2=2ac+62. COR. From this proposition it is evident, that the square described on tJte difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines. For a — c=b...
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