 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...of their difference is less than the sum of their squares, by twice their rectangle, it follows that the square of the sum of two lines, is equal to the square of their difference, together with four times their rectangle. PROP. VIII. THEOR. IF a straight line be... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...For (4) B (A — B)=AB — B • B, or (A — B) B = AB — B2. t Si c > FK PROPOSITION VII. THEOREM. The square of the sum of two lines is equal to the sum of the rectangles under that sum and each of the lines. Let A, B, be two lines, then (A + B)2 =... | |
 | Bourdon (M., Louis Pierre Marie) - Algebra - 1839 - 368 pages
...binomial, (a-\-b). We have, from known principles, That is, the square ofthe sum of two quantities is equal to the square of the first, plus twice the product of tl>e first by the second, plus the square of the second. Thus, to form the square of 5a2+8a26, we have,... | |
 | Charles Davies - Algebra - 1840 - 264 pages
...the binomial (a+6). We have, from known principles, That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the frst by the second, plus the square of the second. 1. Form the square of 2a+3J. We have from the rule... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...of their difference is less than the sum of their squares, by twice their rectangle, it follows that the square of the sum of two lines, is equal to the square of their difference, together with four tunes their rectangle. PROP. VIII. THEOR. — If a straight line... | |
 | Elias Loomis - Algebra - 1846 - 376 pages
...that they should be carefully committed to memory. THEOREM I. The square of the sum of two quantities is equal to the square of the first, plus twice the product j)f the first by the second, plus the square of the second. Thus if we multiply a + b By a + b a2 -\-... | |
 | Algebra - 1848 - 394 pages
...the following theorems. THEOREM I. The square of the sum of two quantities is equal to the squarg vf the first, plus twice the product of the first by the second, plut the square of the second. Let a denote one of the quantities and b the other : then a + Ъ = their... | |
 | Olinthus Gilbert Gregory - 1848 - 572 pages
...-f B C- — 2 AC x B C. Or A B3 -(- 8 AC x BC = A Ca + B C1. (Fig. 7.) [Euc. B. II. Prop. 7.] VIII. The square of the sum of two lines is equal to the sum of their squares, together with their rectangle. IX. The rectangle of the sum and difference of... | |
 | Rufus Putnam - Arithmetic - 1849 - 402 pages
...+ 3)*. From these examples and illustrations, wo see that the square of the sum of any two numbers is equal to the square of the first, plus twice the product of the first into the second, plus the square of the second. 5. Find by this method the square of4-f-3; 5-f-8; lf-4;... | |
 | Stephen Chase - Algebra - 1849 - 348 pages
...have (a+6) 2 = (a+J) (a+J) = a2+2ab+b2. That is, THEOREM I. The square of the sum of two numbers i> equal to the square of the first, plus twice the product of tlte Jirst by the second, plus the square of the second. Or, more briefly, The square of the sum of... | |
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The square of the sum of two numbers is equal to the square of the first, plus twice the product of the first and the second, plus the square of the second. 
