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according added addition algebraical amount Arithmetic called cent changed ciphers common denominator complete compound consisting contain continued corresponding cube decimal difference digits Divide dividend divisible divisor equal equation equivalent EXAMPLES FOR PRACTICE expression extracting feet figures former four fourth fraction geometrical given gives greater greatest common factor Hence highest increased indices integers interest involved latter least common multiple less logarithms lowest terms means method Multiply negative obtained operation positive pound progression proportion proposed quantities quotient ratio Reduce remainder represent Required the sum respectively result root Rule sides simple square square root substituting subtraction suppose symbol taken taking things third Transform unit unknown quantities variations vulgar fractions whence whole written
Page 157 - ... 8 days. But on the evening of the sixth day, 100 men were killed in a sally, and afterwards the mortality increased to 10 daily. Supposing the stock of provisions unconsumed at the end of the sixth day to support 6 men for 61 days ; it is required to find how long it would support the garrison, and the number of men alive when the provisions were exhausted.
Page 141 - A detachment of an army was marching in regular column, with 5 men more in depth than in front ; but upon the enemy coming in sight, the front was increased by 845 men ; and by this movement the detachment was drawn up in 5 lines. Required the number of men.
Page 5 - RULE.* Divide the numerator by the denominator, and the quotient will be the whole or mixed number required.
Page 149 - ... 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...
Page 168 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 96 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Page 146 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.
Page 52 - From and after the passing of this act, all articles sold by weight shall be sold by avoirdupois weight, except gold, silver, platina, diamonds, or other precious stones, which may be sold by troy weight ; and drugs, which, when sold by retail, may be sola by apothecaries 's weight.