 | Joseph Ray - Algebra - 1848 - 250 pages
...(a+l)2=a2+2a+l, is the square of the greater. (a)2=a2 is the square of the less. Their difference is 2a+l. Hence, the difference of the squares of two consecutive numbers, is equal to twice the less number, increased by unity. Consequently, when the remainder is less than 'twice the... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...square of the greater, and (a)'=aa, " " " " " less. Their difference is 2o-fl . From which we Bee, that the difference of the squares of two consecutive •numbers, is equal to twice the less number, increased by unity. EXAMPLES, In extracting the square root of whole numbers.... | |
 | Joseph Ray - Algebra - 1848 - 250 pages
...(a+l)2=a2+2a+1, is the square of the greater. (a)2=a2 is the square of the less. Their difference is 2a+l. Hence, the difference of the squares of two consecutive numbers, is equal to twice the less number, increased by unity. Consequently, when the remainder is less than twice the... | |
 | William Scott - Arithmetic - 1854 - 232 pages
...figures. Their squares are a2 and a2 + 2a + l, and the difference of their squares is 2a+l ; that is, the difference of the squares of two consecutive numbers is equal to twice the less number plus 1. Consequently, when any remainder is equal to or greater than twice the... | |
 | Philip Kelland - 1860 - 308 pages
...two parts the difference of their squares is equal to twice the difference of the parts. 57. Prove that the difference of the squares of two consecutive numbers is equal to the sum of the numbers. CHAPTER III. INVOLUTION, LAW OF INDICES, INDUCTION, AND EVOLUTION. 55. INVOLUTION is the continual... | |
 | Charles Alfred Jones - 1865 - 196 pages
...gave, and thus covers his rent and has £,2 over. How many acres were there? EXERCISE XXXVI. 1 . Shew that the difference of the squares of two consecutive numbers is equal to the sum of the numbers. 2. Find the LCM of (i) 10жа-30ж + 20, 15ж2 and (ii) a4 + a262 + 64, a8-68, a?+b2, and a2 -V. 3.... | |
 | Joseph Ray - Algebra - 1866 - 250 pages
...189. Extract the square root, of 529, and show the reason for each step, by referring to the formula. The difference of the squares of two consecutive numbers is equal to twice the less number increased by unity. Hence, When the remainder is less than twice the part of... | |
 | Charles Alfred Jones, Charles Hartwell Horne Cheyne - Algebra - 1867 - 176 pages
...gave, and thus covers his rent and has £2 over. How many acres were there ? EXERCISE XXXVI. 1. Shew that the difference of the squares of two consecutive numbers is equal to the sum of the numbers. 2. Find the ь.о.м. of (i) 10я»-30ж + 20, 15^-75*4-90, and6;e*-24;E+18, (ii) a'+a'V+b*, a3-b\... | |
 | Robert Wallace - 1870 - 164 pages
...greater than the divisor. But to show that the integer part of the root is thus obtained, we must prove that the 'difference of the squares of two consecutive numbers is equal to the sum of the numbers ; and that if the remainder in this process is less than the sum of the root and its next consecutive... | |
 | Joseph Ray - Algebra - 1866 - 420 pages
...(a+l)2=a2+2a+l, the square of the greater. And (a)2=a2, « " " less. Their difference is 2a-|-l. Hence, The difference of the squares of two consecutive numbers is equal to twice the less number, increased by unity. Therefore, when any remainder is less than twice the root... | |
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Consequently, when the remainder is less than 'twice the part of the root already found, plus unity, the last figure can not be increased. Extract the square root of the following numbers. 1. 4225 Ans. 
