 | Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...squares of AB and BC, together with twice the rectangle contained by these lines. PROP. XXII. THEOR. The square described on the difference of two straight lines, is equivalent to the squares of those lines, diminished by twice their rectangle. Let AC be the difference of two straight... | |
 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...E JJ 57 PROPOSITION XI. THEOREM. The square described on the hypotenuse of a right-angled triangle is equivalent to the sum of the squares described on the two sides. Let the triangle ABC be rightangled at A. Having formed squares on the three sides, let fall... | |
 | Adrien Marie Legendre - Geometry - 1830 - 344 pages
...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 be the two lines,... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...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 = b ; therefore,... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...; 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, AC their difference... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...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 ; therefore, by... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...<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 ; therefore, by... | |
 | Nathan Scholfield - 1845 - 894 pages
...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, AC their difference... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...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 ; therefore, by... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...that product. THEOREM XI. If a line be divided into two parts, the square described on the whole line is equivalent to the sum of the squares described on the two parts, together with twice the rectangle contained by the parts. Let the line AB be divided into two... | |
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The squa/re described on the difference of two straight lines is equivalent to the sum of the squares described on the two lines, diminished by twice the rectangle contained by the lines. 
