A Treatise on AlgebraJ. & J.J. Deighton, 1830 - 685 sider |
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Side xiii
... properties independently of such signs , that we are obliged to seek for an interpre- tation , when possible , of the meaning of such operations and of their results , which may be in strict accordance with the different assumptions ...
... properties independently of such signs , that we are obliged to seek for an interpre- tation , when possible , of the meaning of such operations and of their results , which may be in strict accordance with the different assumptions ...
Side xx
... properties for such purposes constitutes a great part of the substance of the investigations and artifices of Algebra , and it becomes a question of the greatest conse- quence , not merely to ascertain whether such forms exist by ...
... properties for such purposes constitutes a great part of the substance of the investigations and artifices of Algebra , and it becomes a question of the greatest conse- quence , not merely to ascertain whether such forms exist by ...
Side xxix
... values of 1 and ( -1 ) where m is a whole number , are precisely the same in number and in form with those of 1 " and ( − 1 ) ′′ . m 1 1 Having ascertained the symbolical properties of these signs of affection PREFACE . xxix.
... values of 1 and ( -1 ) where m is a whole number , are precisely the same in number and in form with those of 1 " and ( − 1 ) ′′ . m 1 1 Having ascertained the symbolical properties of these signs of affection PREFACE . xxix.
Side xxx
... properties ; we thus shew that if a represent a line in a given position , that the different symbolical values of ( 1 ) aa , when n is a whole number , will represent a series of equal lines making angles equal to each other and toth ...
... properties ; we thus shew that if a represent a line in a given position , that the different symbolical values of ( 1 ) aa , when n is a whole number , will represent a series of equal lines making angles equal to each other and toth ...
Side xxxi
... of suggestion , instead of Arithmetic : we begin , therefore , with the geometrical definition of the sine and cosine of an angle , and determine their fun- damental properties by means of it , and , subsequently PREFACE . xxxi.
... of suggestion , instead of Arithmetic : we begin , therefore , with the geometrical definition of the sine and cosine of an angle , and determine their fun- damental properties by means of it , and , subsequently PREFACE . xxxi.
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Vanlige uttrykk og setninger
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...