## A Treatise on Algebra |

### From inside the book

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**Proportion**, as used in Arithmetic and in Geometry in Arithmetic , there exists an absolute definition of ratio , which perfectly embodies the popular notions which are attached to the term , and the same definition may be assumed ... Page xxvi

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**proportion**. The general views and opinions which are proposed on the very various subjects which are embraced in the twelfth Chapter are so different from those which have commonly been admitted as well founded , that I feel it to be ... Page xxviii

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**proportion**of lines to each other which are not in the same direction , which involves the determination of the meaning of the product or quotient of the signs of affection of two or more lines : he subse- quently examines the ... Page xxxviii

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**Proportions**... 308 CHAP . XII . General Theory of Simple Roots , with the Principles of the Application of Algebra to Geometry CHAP . XIII . On Indeterminate Coefficients CHAP . XIV . On Logarithms and Logarithmic Tables and their ... Page 84

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**proportion**of the numbers 5 and 4 , and also represented by them : if we divide AB into 5 equal parts in the points a , b , c , d , and AC in 4 equal parts in the points a , B , y , each of those parts will be a line which is re ...### Other editions - View all

### Common terms and phrases

a+b+c a₁ affected arith Arithmetical Algebra arithmetical values assumed b₁ binomial binomial theorem c₁ chance coefficients common connection consequently considered contravalent corresponding cosines cube cubic equation decimal deduced definition denoted determined digit divided dividend divisor equa equal equation equivalent form examples expression factors follows formula fraction geometrical greater identical inasmuch interpretation inverse involve least common multiple likewise logarithms magnitudes means metical multiplied necessary negative number of terms numerator and denominator operations P₁ partial fractions plane position powers primitive equation primitive line principle problem proportion proposition quadratic equation quotient ratio rectangle reduced remainder represent respect result right angles shew shewn sides signs similar manner sines solution square root Subtraction symbols tion triangle unknown quantities whole number zero

### Popular passages

Page 104 - Whatever form is algebraically equivalent to another when expressed in general symbols, must continue to be equivalent whatever those symbols denote.

Page 669 - But if the digits be inverted, and then divided by a number greater by unity than the sum of the digits, the quotient is greater by 2 than the preceding quotient ? Required the number.

Page 27 - The product is a2+2a6-}-62; from which it appears, that 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 331 - ... of the second and 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 339 - If four quantities are in proportion, they will be in proportion by 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.

Page 332 - 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...

Page 340 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.

Page 674 - A person bought some sheep for £. 72 ; and found that if he had bought 6 more for the same money, he would have paid £. 1 less for each. How many did he buy...

Page 139 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.

Page 435 - If two triangles have two sides of one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second...