 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...geometrically the algebraic formula, 174 AREAS OF POLYGONS PROPOSITION IX. THEOREM 357. The square constructed on the difference of two lines is equivalent to the sum of the two squares constructed on these lines, diminished by twice the rectangle of these lines. HINT. —... | |
 | Alan Sanders - Geometry - 1903 - 392 pages
...lines is equivalent to the sum of the squares of the lines increased by twice their rectangle. 18. The square described on the difference of two lines is equivalent to the sum of the squares of the lines diminished by twice their rectangle. 19. The rectangle having for its sides the sum and the... | |
 | Alan Sanders - Geometry - 1903 - 396 pages
...diagonals of a trapezoid dividing it into two equivalent trapezoids. 17. The square described on the sum of two lines is equivalent to the sum of the squares of the lines increased by twice their rectangle. 18. The square described on the difference of two lines... | |
 | James McMahon - Geometry, Plane - 1903 - 380 pages
...[AE, EB] + sq. EB, ^[AB, EB] + sq. AE + [AB, EB], [40 (a) Square on difference. 46. Cor. The square on the difference of two lines is equivalent to the sum of their squares diminished by twice their rectangle. Square on sum of whole and part. 47. THEOREM 14.... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...AB and BC. This theorem is expressed algebraically, thus : (a + 6)2 = a2 + 2 ab + 62. 816 The square on the difference of two lines is equivalent to the sum of the squares on the lines diminished by twice the rectangle of the lines. Let AB and BC be two lines, and AC their... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...AB and BC. This theorem is expressed algebraically, thus : (o + 6)2 = a2 + 2 ab + 62. 816 The square on the difference of two lines is equivalent to the sum of the squares on the lines diminished by twice the rectangle of the lines. Let AB and BC be two lines, and AC their... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...the rectangle of these lines. To Prove : Square AE =*ro2 + n2 + 2 mn. 39. The square described upon the difference of two lines is equivalent to the sum of the squares described upon the two lines minus twice the rectangle of these lines. To Prove : Square AD = m2 +... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...the rectangle of these lines. To Prove : Square AE «=m2 + n2 + 2 mn. 39. The square described upon the difference of two lines is equivalent to the sum of the squares described upon the two lines minus twice the rectangle of these lines. To Prove : Square AD = m2 +... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...rectangle of two lines is their product.) SUGGESTION. Let AB and BC be the given lines. 14. The square on the difference of two lines is equivalent to the sum of the squares on the two lines minus twice their rectangle. 15. The difference of the squares on two lines is equivalent... | |
 | Grace Lawrence Edgett - Geometry - 1909 - 104 pages
...constructed upon these lines increased by twice the rectangle of these lines. 35. The square constructed upon the difference of two lines is equivalent to the sum of the squares constructed upon these lines diminished by twice the rectangle of these lines. 36. The difference between... | |
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From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines. 
