| 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).... | |
| 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 - 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... | |
| 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...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—... | |
| 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... | |
| 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... | |
| Charles Davies - Trigonometry - 1849 - 372 pages
...formula, (a—6) 2 =a 2 —2ab+b*. 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)=AB 2 —BC 2 . On AB and AC,... | |
| 582 pages
...join equal and parallel straight lines towards the same parts, are themselves equal and parallel. 3. **The rectangle contained by the sum and difference of two lines, is** equal to the difference of their squarea. SECTION II. 1. Angles in the same segment of a circle are... | |
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