 | John Playfair - Circle-squaring - 1819 - 350 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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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 