## A Complete Course in AlgebraLeach, Shewell, and Sanborn, 1885 |

### From inside the book

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**PROPORTION**255 • Properties of**Proportions**256 XXVII . ARITHMETICAL PROGRESSION 264 XXVIII . GEOMETRICAL PROGRESSION . 273 XXIX . BINOMIAL THEOREM 282 Proof of the Theorem for a Positive Integral Exponent 282 · XXX . LOGARITHMS 287 ... Page 255

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**Proportion**is an equality of ratios . Thus , if the ratio of a to b is equal to the ratio of c to d , they form a**proportion**, which may be written in either of the forms : a : b = c : d , or ...**PROPORTION**. 255 RATIO AND**PROPORTION**• Page 257

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**proportion**the terms are in**proportion**by Alternation ; that is , the first term is to the third , as the sec- ond term is to the fourth . Let Then , by Art . 293 ...**proportion**the terms are in**proportion**by RATIO AND**PROPORTION**. 257. Page 259

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**proportion**. Let and Then , a : b = c : d , e : f = g : h . Multiplying these equals , - and -2 e ae X X or cg bf d h bf dh Whence , ae : bfcg : dh . 304. In any**proportion**, like powers or like roots of the terms are in**proportion**... Page 260

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**proportion**, if the first and third terms be multiplied by any quantity , as also the second and fourth terms , the resulting quantities will be in**proportion**. Let Then , a : b = c : d . α с = b d Therefore , Whence , ma mc nb nd ma ...### Other editions - View all

### Common terms and phrases

a²-b² a²+2ab+b² a²b a²b² ab² ab³ Adding Algebra arithmetical means arithmetical progression ax² binomial cents change the sign coefficient cologarithm Completing the square cube root decimal derive the formula digits dividend divisor EXAMPLES exponent expression Extracting the square Find the H.C.F. Find the value Find two numbers following equations following rule geometrical progression Hence highest common factor last term less logarithm lowest common multiple mantissa minuend monomial Note number of terms parenthesis perfect square polynomial positive proportion QUADRATIC EQUATIONS quotient radical sign Reduce the following remainder Required the number result rods rule of Art second term simplest form Solve the equation Solve the following square root subtract third Transposing trial-divisor twice unknown quantity Whence x²y xy² α² α³ ах у² ху

### Popular passages

Page 166 - Arts. 200 and 201 we derive the following rule : Extract the required root of the numerical coefficient, and divide the exponent of each letter by the index of the root.

Page 213 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...

Page 44 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.

Page 49 - The exponent of b in the second term is 1, and increases by 1 in each succeeding term.

Page 255 - The first and fourth terms of a proportion are called the extremes; and the second and third terms the means. Thus, in the proportion a : b = с : d, a and d are the extremes, and b and с the means.

Page 258 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: b = c: d = e:f.

Page 5 - If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be changed.

Page 44 - 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.

Page 107 - Any term may be transposed from one side of an equation to the other by changing its sign. For, consider the equation x + a = b.

Page 227 - A' courier proceeds from P to Q in 14 hours. A second courier starts at the same time from a place 10 miles behind P, and arrives at Q at the same time as the first courier. The second courier finds that he takes half an hour less than the first to accomplish 20 miles. Find the distance from P to Q.