| James Wallace MacDonald - Geometry - 1894 - 76 pages
...contained by the lines. SCHOLIUM. Compare (a — b)* = a" — 2 ab + b*. Proposition X. A Theorem. 245. **The rectangle contained by the sum and difference of two lines is** equal to the difference of their squares. SCHOLIUM. Compare (a + b) (a — b) = a1 — 63. Proposition... | |
| George Irving Hopkins - 1891 - 210 pages
...upon the L'-vo lines, minus twice the rectangle formed by the two lines. 425. The rectangle formed **by the sum and difference of two lines is equivalent to the difference of the squares** upon the two lines. 426. The square described upon the hypothenuse of a right triangle is equivalent... | |
| Education - 1891 - 740 pages
...circumference can be drawn through three points not in the same straight line. Demonstrate. 6. Show that **the rectangle contained by the sum and difference of two lines is** equal to the difference of their squares. 7. Find the area of a square inscribed in a circle whose... | |
| Queensland. Department of Public Instruction - Education - 1892 - 508 pages
...(i. Enunciata and prove either of the propositions of the second book bv which it ean lie shewn that **the rectangle contained by the sum and difference of two lines is** equal to the difference of the squares described upon them, and shew how the ali.ive result follows... | |
| W. J. Johnston - Geometry, Analytic - 1893 - 448 pages
...the product of the lengths of its sides, and (2) (a + b) (a - b) = a2 - b2, we deduce the theorem : **The rectangle contained by the sum and difference of two lines is** equal to the difference of the squares on those lines. As another example let us solve this problem... | |
| John Macnie - Geometry - 1895 - 386 pages
...SCHOLIUM. This result may be expressed algebraically thus : (rt ± b) 2= a2 ± 2 ab + b2. 337. COR. **2. The rectangle contained by the sum and difference...lines is equivalent to the difference of the squares** of the lines. Let A and B be the lines. Then (A + B) . (A — B)=s= A (A — B) + B(A — B), =c= A2... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...BC be the given lines. 434. The rectangle whose sides are the sum and the difference of two straight **lines is equivalent to the difference of the squares described upon the two lines.** ABC Hint. — Let AB and SCbe the given lines. Question. — To what three formulas of algebra* do... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...BC be the given lines. 434. The rectangle whose sides are the sum and the difference of two straight **lines is equivalent to the difference of the squares described upon the two lines.** ABC Hint.— Let AB and £Cbe the given lines. Question. — To what three formulas of algebra* do... | |
| George Washington Hull - Geometry - 1897 - 408 pages
...the sum of the squares described on the lines, diminished by twice the rectangle of the lines. 595. **The rectangle contained by the sum and difference of two lines is equivalent to the difference of** their squares. 596. If two fixed parallel tangents are cut by a variable tangent, the rectangle of... | |
| Henry W. Keigwin - Geometry - 1897 - 254 pages
...on the lines minus twice the rectangle on the lines. 313. THEOREM. The rectangle on the sum and the **difference of two lines is equivalent to the difference of the squares** on the lines. PROPOSITION III. THEOREM. 314. The square on the hypotenuse of a right triangle is equivalent... | |
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