 | 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... | |
| |
The rectangle contained by the sum and difference of two lines, is equivalent to the difference of the squares of those lines. 
