An Introduction to Algebra: With Notes and Observations : Designed for the Use of Schools and Places of Public Education : to which is Added an Appendix on the Application of Algebra to GeometryEvert Duyckinck, Daniel D. Smith and George Long, 1818 - 260 σελίδες |
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Σελίδα 11
... taking their sums or differences , as in the foregoing cases , and set down those that are unlike , one after another , with their proper signs . EXAMPLES . 5xy 4ax 2xy - 2x2 3x2 + xy 2ax - 30 3x2 - 2αx -xy 4αx x2 + xy 4x2 - 3xy 5x2 ...
... taking their sums or differences , as in the foregoing cases , and set down those that are unlike , one after another , with their proper signs . EXAMPLES . 5xy 4ax 2xy - 2x2 3x2 + xy 2ax - 30 3x2 - 2αx -xy 4αx x2 + xy 4x2 - 3xy 5x2 ...
Σελίδα 12
... taking of one quantity from ano- ther ; or the method of finding the difference between any two quantities of the same kind ; which is perform- ed as follows ( b ) : RULE . Change all the signs ( + and - ) of the lower line , or ...
... taking of one quantity from ano- ther ; or the method of finding the difference between any two quantities of the same kind ; which is perform- ed as follows ( b ) : RULE . Change all the signs ( + and - ) of the lower line , or ...
Σελίδα 34
... taking only the fractional parts , We shall have { 3x2 Xc = 3cx 2ux Xb = 20bx } the numerators . And bXc bc the common denominator . Whence a 3cx2 bc . + b + 2abx bc 2abx - 3cx2 = a + b + the bc sum . 2x 5x 4. It is required to find the ...
... taking only the fractional parts , We shall have { 3x2 Xc = 3cx 2ux Xb = 20bx } the numerators . And bXc bc the common denominator . Whence a 3cx2 bc . + b + 2abx bc 2abx - 3cx2 = a + b + the bc sum . 2x 5x 4. It is required to find the ...
Σελίδα 34
... taking only the fractional parts , 20x C We shall have { 3x2 Xc = 3cx 2ax xb = 20bx } the numerators . And bXc = bc the common denominator . Whence a 3cx2 bc +6+ 2abx bc 2abx -- 3cx2 = a + b + the bc sum . 2x 4. It is required to find ...
... taking only the fractional parts , 20x C We shall have { 3x2 Xc = 3cx 2ax xb = 20bx } the numerators . And bXc = bc the common denominator . Whence a 3cx2 bc +6+ 2abx bc 2abx -- 3cx2 = a + b + the bc sum . 2x 4. It is required to find ...
Σελίδα 44
... taking the root both of its numerator and denominator . Note . The square root , the fourth root , or any other even root , of an affirmative quantity , may be either + or Thus , Va = + a or - a , and / b4 + b or − b , & c . But the ...
... taking the root both of its numerator and denominator . Note . The square root , the fourth root , or any other even root , of an affirmative quantity , may be either + or Thus , Va = + a or - a , and / b4 + b or − b , & c . But the ...
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An Introduction to Algebra; With Notes and Observations: Designed for the ... John Bonnycastle Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
Algebra arithmetical arithmetical mean arithmetical series bers coefficient common denominator compound quantity consequently cube root cubic equation decimal denoted Diophantus dividend divisor equal EXAMPLES FOR PRACTICE find the difference find the least find the product find the square find the sum find the value find two numbers fraction required geometrical geometrical progression geometrical series give given number greatest common measure Hence improper frac improper fraction infinite series last term letters loga logarithms mixed quantity multiplied negative nth root number of terms number required PROBLEM proportion quadratic equation question quotient rational reduce the fraction remainder Required the difference Required the sum required to convert required to divide required to find required to reduce result rithm rule second term side simple form square number square root square sought substituted subtracted sum required surd tion triangle unknown quantity Whence α α
Δημοφιλή αποσπάσματα
Σελίδα 10 - 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.
Σελίδα 20 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Σελίδα 27 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Σελίδα 173 - Ios- y" &cFrom which it is evident, that the logarithm of the product of any number of factors is equal to the sum of the logarithms of those factors. Hence...
Σελίδα 77 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Σελίδα 93 - It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Ans. 10 and 14.
Σελίδα 93 - It is required to divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5.
Σελίδα 94 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the less, is equal to 12 ? Ans.
Σελίδα 30 - Multiply the index of the quantity by the index of the power to which it is to be raised, and the result will be the power required.