 | George Roberts Perkins - Geometry - 1856 - 460 pages
...and for altitudes BE = IK = IF. GEOMETRY. THEOREM XXXI. The rectangle constructed on the sum and the difference of two lines, is equivalent to the difference of the squares constructed on these two lines. Let AB be the greater line, BE = BE' the less, so that AE will represent... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...proposition is expressed algebraically thus : Cor. (a+by— (a— b)'=4ab. PROPOSITION X. THEOREM. Hie rectangle contained by the sum and difference of two...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 AB... | |
 | 1857 - 408 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 squares. SECT. II. — I. Angles in the same segment ofa circle are... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...expressed algebraically thus : (a—by=a'—2ab+b\ Cor. (a+by—(a—b)'=4ab. PROPOSITION X. THEOREM. Fhe rectangle contained by the sum and difference of two...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 AB... | |
 | Elias Loomis - Conic sections - 1860 - 246 pages
...expressed algebraically thus: (a—by=a t —2ab+b\ Cor. (a+by—(a—by=4ab. PROPOSITION X. THEOREM. fhe rectangle contained by the sum and difference of two lines, is equivalent to the difference of tlte squares of those lines Let AB, BC be any two lines ; the rectangle contained by the sum and difference... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...rectangle AB xBE. * . -1 r- OO GEOMETRY. THEOREM XXXI. The rectangle constructed on the sum and the difference of two lines, is equivalent to the difference of the squares constructed on these two lines. Let AB be the greater line, BE = BE' the less, so that AE will represent... | |
 | Edward Olney - Geometry - 1872 - 96 pages
...the sum of the squares on the lines, minus twice the rectangle of the lines. 66 Y. The rectangle of the sum and difference of two lines is equivalent to the difference of the squares described on the lines. Sen.— The three preceding propositions are but geometrical conceptions and demonstrations... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...the sum of the squares on the lines, minus twice the rectangle of the lines. 667. The rectangle of the sum and difference of two lines is equivalent to the difference of the squares described on the lines. OJ Fio. 370. oS Fio. 871. Fio. 873. VARIOUS DEMONSTRATIONS OF THE PYTHAGOREAN PROPOSITION.... | |
 | Edward Olney - Geometry - 1872 - 102 pages
...the sum of the squares on the lines, minus twice the rectangle of the lines. 667. The rectangle of the sum and difference of two lines is equivalent to the difference of the squares described on the lines. FIG. 370. VARIOUS DEMONSTRATIONS OF THE PYTHAGOREAN PROPOSITION. 668. The square described... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...the square of AC : hence, AC* = AB* + BC* - 1AB x BC ; was to be proved. PROPOSITION X. THEOREM. CB The rectangle contained by the sum and difference of two lines, is equal to the difference of their squares. Let AB and BC be two lines, of which AB is th* greater :... | |
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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. 
