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admit affected algebraical quantities application arith Arithmetical Algebra arithmetical series arithmetical values assigned assumed binomial binomial theorem chance circumstances coefficients coincide common connection consequently considered contravalent conversely corresponding cosine cube cube root cubic equation decimal deduced definition determined digit divided dividend division divisor equa equivalent form examples existence expression factors follows forces formula fraction geometrical given greater identical inasmuch interpretation inverse involve least common multiple less likewise logarithms magnitudes means metical multiplied necessary negative number of terms numerator and denominator partial fractions plane plane of reference position preceding primitive equation primitive line principle problem proportion proposition quadratic equation quotient ratio rectangle reduced remainder represent respect result right angles shew shewn sides signs similar manner sines solution square root Subtraction successive suppose symbols tion triangle unknown quantities whole number
Página 104 - Whatever form is algebraically equivalent to another when expressed in general symbols, must continue to be equivalent whatever those symbols denote.
Página 27 - The product is a2+2a6-}-62; from which it appears, that the square of the sum of two quantities, is equal to the square of the first plus twice the product of the first by the second, plus the square of the second.
Página 331 - ... of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Página 339 - If four quantities are in proportion, they will be in proportion by COMPOSITION ; that is, the sum of the first and second, will be to the second, as the sum of the third and fourth, is to the fourth.
Página 332 - When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third...
Página 340 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Página 674 - A person bought some sheep for £. 72 ; and found that if he had bought 6 more for the same money, he would have paid £. 1 less for each. How many did he buy...
Página 139 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.