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The rectangle contained by the sum and difference of two lines, is equivalent to the difference of the squares of those lines.
Elements of Geometry Upon the Inductive Method: To which is Added an ... - Page 62
by James Hayward - 1829 - 172 pages

## Elements of Geometry

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)....

## Elements of Geometry...: Translated from the French for the Use of the ...

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)....

## Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

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...

## Elements of Geometry and Trigonometry

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...

## Elements of Geometry

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)....

## Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

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...lines, is equivalent to the difference of the squares of those lines. Scholium. This proposition is equivalent to the algebraical formula, (a+b) x (a—...

## Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...formula, (a— 6)2=aa— 2ab+ b\ PROPOSITION III. 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 CBK On AB and AC, describe the squares ABIF. ACDE...

## Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...expressed algebraically thus: (a—by=a'—2ab+b\ Cor. (a+by—(a—V)'=<lab. PROPOSITION X. THEOREM. The rectangle contained by the sum and difference...lines, is equivalent to the difference of the squares of those lines. Let AB, BC be any two lines ; the rectangle contained by the sum and difference of...