A Treatise on AlgebraJ. & J.J. Deighton, 1830 - 685 sider |
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Side xxi
... my views respecting the first principles of Algebra , in order to explain , and in some measure to justify , the course which I have followed in stating them : : I had imagined that it would be possible to PREFACE . xxi.
... my views respecting the first principles of Algebra , in order to explain , and in some measure to justify , the course which I have followed in stating them : : I had imagined that it would be possible to PREFACE . xxi.
Side xxiii
... measure of two numbers , and the highest common divisor of two alge- braical expressions , the necessity for whose separate and independent consideration we have had particular occasion to point out . The sixth Chapter is devoted to the ...
... measure of two numbers , and the highest common divisor of two alge- braical expressions , the necessity for whose separate and independent consideration we have had particular occasion to point out . The sixth Chapter is devoted to the ...
Side xxxii
... measured by the ratio of the arc of any circle , which subtends them at its centre , to its radius , and , consequently , circles are merely used or in- troduced into this science as furnishing measures of angles : we are thus enabled ...
... measured by the ratio of the arc of any circle , which subtends them at its centre , to its radius , and , consequently , circles are merely used or in- troduced into this science as furnishing measures of angles : we are thus enabled ...
Side 8
... measured sions . by the sum of the indices of the symbols involved : thus a is a quantity of one dimension : xy and a2 are quantities of two dimensions : xyz and a3 are quantities of three dimen- sions , and æ ” , în - 1y , xn − 2 y2 ...
... measured sions . by the sum of the indices of the symbols involved : thus a is a quantity of one dimension : xy and a2 are quantities of two dimensions : xyz and a3 are quantities of three dimen- sions , and æ ” , în - 1y , xn − 2 y2 ...
Side 43
... a2 : for a a1 ÷ a3 = = a ' : for ( 7 ) α ( 8 ) ( 9 ) 3 a3 - a = α χα = a2 . a απ α και - = = a1 . a3 a3 3 12bc 3bc -12abcde ÷÷ −8acd = - dividing 8 2 12 and 8 severally by their common measure 4 . Зас 5 abd Зас 6 18 ac ( 10 ) 43.
... a2 : for a a1 ÷ a3 = = a ' : for ( 7 ) α ( 8 ) ( 9 ) 3 a3 - a = α χα = a2 . a απ α και - = = a1 . a3 a3 3 12bc 3bc -12abcde ÷÷ −8acd = - dividing 8 2 12 and 8 severally by their common measure 4 . Зас 5 abd Зас 6 18 ac ( 10 ) 43.
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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
Populære avsnitt
Side 104 - Whatever form is algebraically equivalent to another when expressed in general symbols, must continue to be equivalent whatever those symbols denote.
Side 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.
Side 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.
Side 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...
Side 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.
Side 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...
Side 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.
Side 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...
Side 139 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Side 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...