| 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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