 | 1799 - 616 pages
...proportionality was something independent of definition. Others again, deiining numbers to be proportional, when the quotient of the first divided by the second is...to the quotient of the third divided by the fourth, have endeavoured to obviate the necessity for Euclid's, by extending this their definition to all magnitudes... | |
 | Ralph Griffiths, George Edward Griffiths - 1799 - 648 pages
...propornonality was something independent of definition. Others agnin, defining numbers to be proportional, when the quotient of the first divided by the second is equal to the quotient of the third diiidcd by the fourth, have endeavoured to 'obviate the necessity for Euclid's, by extending thii their... | |
 | Jeremiah Day - Measurement - 1815 - 388 pages
...Ex. 1. Required the square of 9. Extend the compasses from 1 to 9. Twice this extent will reach to 8i the square. 2. Required the cube of 4. The extent...quotient of the third divided by the fourth. (Alg. 364.) acab Thus if a: b::c:d, theny =-7,and — =-i- (Alg. 3SO.) But in logarithms, subtraction takes the... | |
 | Jeremiah Day - Logarithms - 1815 - 172 pages
...proposed root. Ex. 1 . Required the square root of 49. Half th* extent from 1 to 49, will reach from' 1 te 7 the root. 2. Required the cube root of 27. One third...quotient of the third divided by the fourth. (Alg. 364.) aca 6 Thus if a:b::c:d, then -IT=-T, and— =-r (Alg. 3S0.) But in logarithms, subtraction takes the... | |
 | Bewick Bridge - Algebra - 1818 - 254 pages
..., and that of the ratio u с : d by the fraction — , it follows thatT = —, or, "that when dud " four quantities are proportional, the quotient of...the quotient of the third " divided by the fourth ;" and vice versa, if " there be four " quantities a, b, c, d, such, that — = — , then those four... | |
 | John Davidson, Robert Scott (writing master) - Arithmetic - 1818 - 190 pages
...of it, as often as the third contains the fourth, or the like part of it. In either of these cases, the quotient of the first divided by the second, is equal to that of the third divided by the fourth'. Proportionals are written thus, 6 : 2 : ; 9 : 3 ; and read... | |
 | Bewick Bridge - Algebra - 1821 - 284 pages
...the fraction -, and that of the ratio с : d by the fraction ~ it follows that ?=?, or, " that when " four quantities are proportional, the quotient of...the quotient of the third " divided by the fourth ;" and vice versa, if " there be four " quantities a, b, c, d, such, that |=í , then those four quan"... | |
 | Jeremiah Day - Geometry - 1824 - 440 pages
...in logarithms, by adding the two middle terms, and from the sum, subtracting the first term. (~'/rt. 52.) But it is more convenient in practice to begin...third divided by the fourth. (Alg. 364.) Thus if a : b::c ', d, then ^=^, and" =^' (Alg. 380.) But in logarithms, subtraction takes the place of division... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...fraction r, and that of the ratio С fl f с : d by the fraction n, it follows that f= -5» that is, when four quantities are proportional, the quotient of...to the quotient of the third divided by the fourth; and rice versa, if there be four quantities o, b, c, d, such, that fl С -= -, then those four quantities... | |
 | Bézout - Arithmetic - 1825 - 258 pages
...to sav, ^ = '5' ; therefore, the four numbers 12, 3, 16, 4, are in geometrical proportion, because the quotient of the first divided by the second is equal to the quotient of the third by the fourth. The reasoning would be the same for any other numbers. "Four numbers are not in geometrical... | |
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... term. (Art. 52.) But it is more convenient in practice to begin by subtracting the first term from one of the others. If four quantities are proportional, the quotient of the first divided by the second, is equal to the quotient of the third divided... 
