 | Elias Loomis - Conic sections - 1858 - 256 pages
...figures AI, CG, FH, ID become equal squares. Scholium. This proposition is expressed algebraically thus : PROPOSITION IX. THEOREM. The square described on the...two lines, is equivalent to the sum of the squares of the lines, diminished by twice the rectangle contained by the lines. Let AB, BC be any two lines,... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...square described on any line is four times the square described on one half of it. THEOREM XXXVII. The square described on the difference of two lines...equivalent to the sum of the squares described on the two lines diminished by twice the rectangle contained by the lines. Let AB represent the greater of... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...regard to areas, with which we will close this Book. THEOREM XXX. The square constructed on the sum or on the difference of two lines, is equivalent to the sum of the squares constructed respectively on these lines, plus or minus twice their rectangle. The simple inspection... | |
 | Elias Loomis - Conic sections - 1860 - 246 pages
...ID become equal squares. Scholium. This proposition is expressed algebraically thus: (a+by=a2+2ab+b\ PROPOSITION IX. THEOREM. The square described on the difference of two lines, is equiv alent to the sum of the squares of the lines, diminished by twice the rectangle contained by... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...formula, LF G K H PROPOSITION IX.— THEOREM. 233. The squa/re described on the difference of two straight lines is equivalent to the sum of the squares described on the two lines, diminished by twice the rectangle contained by the lines. Let AB and BC be two lines, and... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...Zab + b1. . PROPOSITION IX. — THEOREM. 233. The square described on, the difference of two straight lines is equivalent to the sum of the squares described on the two lines, diminished by twice the rectangle contained by the lines. Let AB and BC be two lines, and... | |
 | Cincinnati (Ohio). Board of Education, Cincinnati Public Schools - Cincinnati (Ohio) - 1863 - 152 pages
...are the different modes of computing logarithms? Which is the most convenient, and why ? 8. Show that the square described on the difference of two lines...described on the lines, diminished by twice the rectangle contained by the lines. And give the..algebraic expression of this proposition. 9. Show that like powers,... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...hence, the square described on a line is equal to four times the square described on half the line. PROPOSITION IX. THEOREM. The square described on the difference of two lines is equal to the sum of the squares described on the lines, diminished by twice the rectangle of the lines.... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...«2+ 2 LF GI PROPOSITION IX. — THEOREM. 233. The square described on the difference of two straight lines is equivalent to the sum of the squares described on the two fines, diminished by twice the rectangle contained by the lines. Let AB and BC be two lines, and... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...formula, therefore, includes the following geometrical 403. Theorem. — The square described upon the sum of two lines is equivalent to the sum of the squares described on the two lines, increased by twice the rectangle contained by these two lines. Since the truths of algebra... | |
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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. 
