| John Playfair - Circle-squaring - 1819 - 348 pages
...2.) ; and " therefore, 2BC3+2AC.BC=2AB.BC ; and " .therefore AB3+BC3=AC3+2AB.BC." H A " COR. Hence, **the sum of the squares of any two lines is equal " to twice the** rectangle contained by the lines together with the •' square of the difference of the lines." PROP.... | |
| John Playfair - 1819 - 354 pages
...therefore, 2BCaH-2AC.BC=2AB.BC ; and " therefore AB3-fBC3=ACa+2AB.BC." 1 >LCB / G H / K " Con.. Hence, **the sum of the squares of any two lines is equal " to** twioe the rectangle contained by the lines together with the " square of the difference of the lines."... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...BC as two independent lines, and AC as their difference, this proposition will be thus announced : ' **The sum of the squares of any two lines is equal to twice the** rectangle under them together with the square of their difference.' (256) COR. 2. — Hence and by... | |
| Mathematics - 1836 - 488 pages
...rectangle contained by the whole and that part, together with the square of the other part. Сон. Hence **the sum of the squares of any two lines is equal to twice the** rectangle contained by the lines together with the square of the difference of the lines. VIII. If... | |
| John Playfair - Euclid's Elements - 1837 - 332 pages
...AKF+HF=AE = AB2, AB2+CK=2AB.BC-fHF, that is, (since CK=CB2, and HF=AC2,) AB2+CB2=2AB.BC+AC2. " COR. Hence, **the sum of the squares of any two lines is equal to " twice the** rectangle contained by the lines together with the square of " the difference of the lines." SCHOLIUM.... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...HF=AE=AB2, AB2+CK=2AB.BC + HF, that is, (since CK=CB2, and HF=AC2,) AB2+CB2=2AB.BC+AC2. " COR. Hence, **the sum of the squares of any two lines is equal to " twice the** rectangle contained by the lines together with the square of " the difference of the lines." SCHOLIUM.... | |
| Dennis M'Curdy - Geometry - 1846 - 166 pages
...Wherefore, the two squares described, &c. QED Recite (a) p. 46 of b. 1 ; (4) p. 31 of b. 1. Cor. Hence **the sum of the squares of any two lines, is equal to twice the** rectangle of the two with the square of their difference 8 Th. If a straight line (AB), be divided... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...AKF+HF=AE=AB2, AB2+CK=2AB.BC+HF, that is, (since CK=CB2, and HF=AC2,) AB2+CB2=2AB.BC+AC2. " COR. Hence, **the sum of the squares of any two lines is equal to " twice the** rectangle contained by the lines together with the square of " the difference of the lines." SCHOLIUM.... | |
| Euclides - 1858 - 248 pages
...2mS AD2+DB2 = 2a2 + 2ni2 = 2AC2 + 2CD2 = 2a2 + 2m2 SCH. — 1. The Proposition may be expressed, " **the sum of the squares of any two lines is equal to twice the** square of half their sum together with twice the square of half their difference. " Because AD2 = (AC... | |
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