 | Charles Davies - 1860 - 412 σελίδες
...both members, N* = a? + 2ab '+ 62 : Hence, the square of a number is equal to the square of the lens, plus twice the product of the tens by the units, plus the square of the units. For example, 78 = 70 + 8, hence, (78)2 = (70)2 + 2 x 70 x 8 + (8)2 = 4900 + 1120 + 64 = 6084. 95* Let... | |
 | Charles Hutton - 1860 - 1020 σελίδες
...second period 41, and annexing them on the right of 4, the result is 441, a number which contains tnice the product of the tens by the units, plus the square of the units. We may further prove, as in the last case, that if we point off the last figure 1, and divide the preceding... | |
 | Charles Davies - 1861 - 322 σελίδες
...Which proves that the square of a number composed of tens and units, equals the square of the lens plus twice the product of the tens by the units, plus the square of the units. 94. If now, we make the units 1, 2, 3, 4, &c., tens, or units of the second order, by annexing to each... | |
 | 1861 - 552 σελίδες
...period must be the square of the tens. After taking out this square of the tens, we have left the double product of the tens by the units plus the square of the units. By dividing the double product by double the tens, we find the units. BY inspection, we may often determine... | |
 | Thomas Sherwin - 1862 - 252 σελίδες
...+ 9 = 529. Hence, When a number contains units and tens, its second power contains the second power of the tens, plus twice the product of the tens by the units, plus the second power of the units. Let us now, by a reverse operation, deduce the root from the power. Operation.... | |
 | Benjamin Greenleaf - 1863 - 338 σελίδες
...figures in the square root. 2141 The square of any number, consisting of more than one place of figures, is equal to the square of the tens, plus twice the...the tens by the units, plus the square of the units. For, if the tens of a number bo denoted by a, and the units by Ь, the number will be denoted by a... | |
 | Charles Davies - 1863 - 346 σελίδες
...the sum is, 33+ 2 (3 x 0) + 63: that is, 3 + 6 3 + 6 3x6 3' + 3 x 6 2(3x6) + 6 The square of a number is equal to the square of the tens plus twice the product of the tens by the units, plus th» square of the units. The same may be shown by the figure : Let the line AB represent the 3 tens... | |
 | Charles William Hackley - 1864 - 532 σελίδες
...tens, plus two units.) ' Now the square of the root sought, that is, the proposed number, contains the square of the tens, plus twice the product of the tens by the units, pins the square of the units. But the square of the tens must give at least hundreds; hence the last... | |
 | Elias Loomis - 1864 - 386 σελίδες
...the number of tens, whose square is 400; and if we subtract this from 529, the remainder 129 contains twice the product of the tens by the units, plus the square of the units. If, then, we divide this remainder by twice the tens, we shall obtain the units, or possibly a number... | |
 | Charles Davies - 1865 - 468 σελίδες
...period, and subtract; this 85^42 5 takes away the square of the tens, and leaves 42 5 425, which is twice the product of the tens by the units plus the square of the units. If, now, we double the tens, and then divide the remainder, exclusive of the right-hand figure (since... | |
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Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units. 
