 | Elias Loomis - Conic sections - 1849 - 252 pages
...squares. Scholium. This proposition is expressed algebraically thus: (a+b)'=a'+2ab+V. PROPOSITION IX. THEOREM. The square described on the difference of...lines, is equivalent to the sum of the squares of the lines, diminished by twice the rectangle contained by the lines. squares on AB and CB, diminished... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...algebra, in obtaining the square of a binomial ; which is expressed thus : D II PROPOSITION IX. THEOEEM. The square described on the difference of two lines, is equivalent to the sum of the squares descr1bed on the lines, diminished by twice the rectangle contained by the lines. Let AB, BC, be two... | |
 | Euclid, John Playfair - Geometry - 1853 - 336 pages
...<z2-f-c2=42--2c(4+c), or a2+c2=2ac-f-42. COR. From this proposition it is evident, that the square aescribod 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. For a — c=b... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...the square of a binomial ; which is expressed thus : PROPOSITION IX. THEOREM. The square descr1bed on the difference of two lines, •is equivalent to the sum of the squares described on the lines, dim1nished by twice the rectangle contained by the lines. Let AB, BC} be two... | |
 | George Roberts Perkins - Geometry - 1856 - 460 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... | |
 | John Playfair - Euclid's Elements - 1856 - 346 pages
...a2+c2=S2+2c(J+c), or a2+c2=2ac+42. COR. From this proposition it is evident, that the square described on tfie 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. For a — c=b... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...become equal squares. Scholium. This proposition is expressed algebraically thus : PROPOSITION IX. THEOREM. The square described on the difference of...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, and... | |
 | 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 is equivalent to the sum of the squares described on the two lines diminished by twice the rectangle contained by the lines. Let AB represent... | |
 | 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... | |
 | 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 is equivalent to the sum of the squares described on the lines, diminished by twice the rectangle contained by the lines. And give the..algebraic... | |
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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. 
