## A Treatise on Algebra: Arithmetical algebra |

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added addition Algebra application arithmetical assigned assume becomes called chance coefficient combinations common complete connected consequently considered continued converging corresponding cube decimal definition denominator denoted determined digits divided dividend division divisor effect equal equation equivalent event examples exists expressed factors final follows formation four fourth fractions geometrical given gives greater greatest identical immediately important inasmuch involve known less magnitudes manner means measure merely multiple necessary obtained operation ordinary original period positive possible preceding present primary unit prime principles problem proportion proposition quantities question quotient ratio reason recurring reduced reference relation remainder replace represent respectively result rule scale severally sides similar simple solution square root subtract successive suppose surds symbols taken theory third tion unknown symbols whole number

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Página 266 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...

Página 272 - A and B can do a piece of work in 6 days ; A and C can do it in 9 days, and A, B, C can do 8 times the same work in 45 days.

Página 177 - 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 166 - 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 256 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?

Página 34 - The product of the sum and difference of two numbers is equal to the difference of their squares.

Página 34 - The square of the sum of two numbers is equal to the square of the first, plus twice the product of the first and the second, plus the square of the second.

Página 269 - In wh.it time could each do it separately? Ans. A in 24, B in 48 days. 19. A and B drink from a cask of beer for 2 hours, after which A falls asleep, and B drinks the remainder in 2 hours and 48 minutes; but if B had fallen asleep and A had continued to drink. it would have taken him 4 hours and 40 minutes to finish the cask. In what time could each singly drink the whole? Ans. A in 10 hrs., B in 6 hrs.

Página 173 - If the first has to the second the same ratio which the third has to the fourth...

Página 167 - When four quantities are proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth, to their difference.