An Elementary Treatise on Algebra, Theoretical and Practical: Adapted to the Instruction of Youth in Schools and Colleges |
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An Elementary Treatise on Algebra, Theoretical and Practical . . James Ryan No preview available - 2012 |
Common terms and phrases
aČ-bČ aČ+ab+bČ according added algebraic quantities becomes binomial changing the signs coefficients common denominator completing the square compound quantities consequently cube root denoted difference digits divided dividend division equa equal example exponent expression extracting the root factors find the values formula fraction required fractional quantity greater greatest common divisor greatest common measure Hence improper fraction least common multiple less letter lowest terms lues manner method miles mixed quantity multiplied number of terms numbers or quantities observed operation prefixed PROB problem proportion quadratic equations quadratic surds quan quotient radical quantities radical sign ratio Reduce remainder Required the cube Required the square required to find result RULE second equation shillings side simple equations simple quantity square root substituting subtracted surd third tion tities transposition unity unknown quantity values of x whence whole number
Popular passages
Page 41 - with the highest, and place the divisor at the right hand of the dividend ; then divide the first term of the dividend by the first term of the divisor, as in Case I., and place the result under the divisor. Multiply the whole divisor by this partial quotient, and subtract the product from the dividend,
Page 194 - Multiply the divisor, so increased, by the term of the root last placed in the quotient, and subtract the product from the dividend, and to the remainder bring down as many terms as are necessary for a dividend, and continue the operation as before.
Page 9 - aa Scholium. Articles (49), (50), (51), might have been deduced from Art. (48); but they are all easily admitted as axioms. 52. If the same quantity be added to and subtracted from another, the value of the latter will not be altered. Thus, if a~c, then
Page 134 - A hare, 50 of her leaps before a greyhound, takes 4 leaps to the greyhound's three ; but two of the greyhound's leaps are as much as three of the hare's. How many leaps must the greyhound take to catch the hare ? Let 3i= the number of leaps the
Page 323 - Three quantities are said to be 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. Thus, a, b, c, are harmonically proportional, when a : c
Page 249 - and 8 equal to the two parts required, the same as in Ex. 2., which is a particular case of this general problem. PROB. 10. What two numbers are those, whose sum is to the greater as 10 to 7 ; and whose sum, multiplied by the less, produces 270? Ans. ±21 and ±9. PROB.
Page 323 - Four quantities are in harmonical proportion, when the first is to the fourth, as the difference between the first and second is to the difference between the third and fourth. Thus, a, b, c, d, are in harmonical proportion, when a : d : : a — b : c — d, or
Page 248 - 8. A detachment from 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 five lines. Required the number of men. Let x= the number in front;