 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
....sv/,.')//«ii This proposition answers to the algebraic formula (a — b)3 = a3 + 6" — Zab. THEOREM. 184. The rectangle contained by the sum and difference of two lines is equal to the difference of their squares : that is (AB + BC) x (AB — BC) = AlT— EC (fig. 108).... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...proposition answers to the algebraic formula (a — 6)2 =a 2 + b2 — 2 a 6. . \ / "* ; THEOREM. / V-- 184. The rectangle contained by the sum and difference of two lines is equal to the difference of their squares ; thai is, (AB + BC) x (AB — BC) = A~B — BC*(%. 108).... | |
 | Adrien Marie Legendre - Geometry - 1828 - 346 pages
...E D THEOREM. f Q 184. The rectangle contained by the sum and the difference of two lines, is equal to the difference of the squares of those lines. Let AB, BC, be the lines ; then, will (AB+BC) . (AB— BC)=AB=— BC2. On AB and AC, construct the squares ABIF, ACDE... | |
 | James Hayward - Geometry - 1829 - 228 pages
...and the square described upon b } which gives the equation (a -j- b) X (a — b) •=. a 2 — 6 2 . The rectangle contained by the sum and difference...lines, is equivalent to the difference of the squares described upon the two lines. Fig. 97. v 177 - The two rectangles CEGD, DBFG, (fig. 97) of the same... | |
 | John Playfair - Geometry - 1829 - 210 pages
...two equal parts, the square of the whole line is equal to lour titties the square of half the line. The rectangle contained by the sum and difference of two lines is equal to the difference of their squares. The square of the difference of any two lines is less than... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...2ab + b*. PSOPOSITION X. THEOREM. The rectangle contained by the sum and the difference of twolines, is- equivalent to the difference of the squares of those lines. Let AB, BC, be two lines ; then, will (AB+BC) x (AB— BC) =AB2— BC* On AB and AC, describe the squares ABIF, ACDE... | |
 | Adrien Marie Legendre - Geometry - 1837 - 376 pages
...algebraical formula, (a— 6)2=a2 E PROPOSITION X. THEOREM. The rectangle contained by the sum and the difference of two lines, is equivalent to the difference of the squares of thost lines. Let AB, BC, be two lines ; then, will (AB +BC) x (AB— BC) = AB2— BC». On AB and AC,... | |
 | Adrien Marie Legendre - Geometry - 1838 - 372 pages
...(a— 6)2=a2— 2a6+62. B GI E D PROPOSITION X. THEOREM. « The rectangle contained by the sum and the difference of two lines, is equivalent to the difference of the squares of those lines. Let AB, BC, be two lines ; then, will (AB+BC) x (AB— BC)=AB2— BC8. On AB and AC, describe the squares ABIF, ACDE... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...Scholium. This proposition answers to the algebraic formula (a — 6)2 = aa + 6a — 2 a b. THEOREM. 184. The rectangle contained by the sum and difference of two lines is equal to the difference of their squares ; that is, ( AB + BC) X ( AB — BC) = AB — EC (fig. 108).... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...square DHIG, which latter is the square described on BC : therefore (AB + BC) x(AB-BC) = AB2-BC2. Hence, The rectangle contained by the sum and difference...equivalent to the difference of the squares of those lines. Scholium. This proposition is equivalent to the algebraical formula, (a+b) x (a— 4)=a2— b\ (Art.... | |
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THEOREM. The rectangle contained by the sum and difference of two lines, is equivalent to the difference of the squares of those lines. 
