The Elements of Algebra |
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Page 165
... 1 . ( 17 ) √13 +2 √10 + 4 √3 + 2 √30 = √2 + √5 + √6 . ( 18 ) √16 + 6 √2 + 4 √3 + 2 √6 +2 10 + 2 / 15 + 2√30 N = √2 + √3 + √5 + √ồ . CHAPTER V. RATIO , PROPORTION , AND VARIATION . RATIO SURDS AND IMAGINARY QUANTITIES . 165.
... 1 . ( 17 ) √13 +2 √10 + 4 √3 + 2 √30 = √2 + √5 + √6 . ( 18 ) √16 + 6 √2 + 4 √3 + 2 √6 +2 10 + 2 / 15 + 2√30 N = √2 + √3 + √5 + √ồ . CHAPTER V. RATIO , PROPORTION , AND VARIATION . RATIO SURDS AND IMAGINARY QUANTITIES . 165.
Page 166
Thomas Grainger Hall. CHAPTER V. RATIO , PROPORTION , AND VARIATION . RATIO . 116. RATIO is the relation which quantities bear to each other with regard to magnitude . Thus if one magnitude be two - thirds of another magni- tude , they ...
Thomas Grainger Hall. CHAPTER V. RATIO , PROPORTION , AND VARIATION . RATIO . 116. RATIO is the relation which quantities bear to each other with regard to magnitude . Thus if one magnitude be two - thirds of another magni- tude , they ...
Page 178
... VARIATION . When one quantity depends in any manner what- ever upon the change in magnitude of another , the former is said to vary as the latter . CC Then , if YaX and a be constant , Y is said to ... variation we 178 PROPORTION . Variation.
... VARIATION . When one quantity depends in any manner what- ever upon the change in magnitude of another , the former is said to vary as the latter . CC Then , if YaX and a be constant , Y is said to ... variation we 178 PROPORTION . Variation.
Page 179
Thomas Grainger Hall. As instances of the two preceding cases of variation we may take the following : We know that the quantity of work done ( W ) increases as the number of workmen ( A ) is increased , or technically W ... VARIATION . 179.
Thomas Grainger Hall. As instances of the two preceding cases of variation we may take the following : We know that the quantity of work done ( W ) increases as the number of workmen ( A ) is increased , or technically W ... VARIATION . 179.
Page 180
... agents in the same time T ; and V and w are done by the same num- ber of persons , in different times , then W : Ꮴ :: Ꭺ : a , and Vw T : t ; W : w A.T : a.t , or W∞ AT . Ex . If 252 men can dig a trench 210 180 VARIATION .
... agents in the same time T ; and V and w are done by the same num- ber of persons , in different times , then W : Ꮴ :: Ꭺ : a , and Vw T : t ; W : w A.T : a.t , or W∞ AT . Ex . If 252 men can dig a trench 210 180 VARIATION .
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Common terms and phrases
2ab+b² a²+2ab+b² a²x² a³b ab² ab³ algebraical quantities arithmetic mean arithmetic series arithmetical progression ax² binomial coefficient common difference compound cube root decimal denominator digits divided dividend division divisor equal examples expressed Extract the square factor Find the greatest find the numbers Find the sum fraction geometrical progression greatest common divisor greatest common measure Hence last term least common multiple less letters logarithm multiplied negative number of terms numbers in arithmetical P₁ permutations QUADRATIC EQUATIONS quotient ratio remainder result rule shew square root subtract surd third unity unknown quantity whence write written xy³
Popular passages
Page 38 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 199 - 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 22 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 173 - 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.