A Practical System of Algebra: Designed for the Use of Schools and Private StudentsBaldwin and Cradock, 1831 - 309 σελίδες |
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Σελίδα 169
... observing in the general arithmetical progression a , atd , a + 2d , a + 3d , a + 4d , & c . that there are as many times d in any term as the terms are in number , minus one ; therefore in a series consisting of n terms , the last term ...
... observing in the general arithmetical progression a , atd , a + 2d , a + 3d , a + 4d , & c . that there are as many times d in any term as the terms are in number , minus one ; therefore in a series consisting of n terms , the last term ...
Σελίδα 193
... observing , however , that if Q be the coefficient of the first term of the original equation , we must substitute A for Q2 - 1 ; and if Q be the last term but one , or of the same number , as the degree of the equation , we must ...
... observing , however , that if Q be the coefficient of the first term of the original equation , we must substitute A for Q2 - 1 ; and if Q be the last term but one , or of the same number , as the degree of the equation , we must ...
Σελίδα 206
... observing , however , that the absolute number of the transformed equation must have the same sign as the original , otherwise the process must be renewed with a less number . 3. Repeat this last process as often as it will be found ...
... observing , however , that the absolute number of the transformed equation must have the same sign as the original , otherwise the process must be renewed with a less number . 3. Repeat this last process as often as it will be found ...
Σελίδα 207
... observing that , 4 is the first decimal figure , the next transformation is 7,0 11,00 -6,000 ( 4 7,4 2,96 1,396 7,8 8,2 3,12 17,08 5,584 - , 416 Obs . The nature of decimals evidently direct to annex one cipher to the first , two to the ...
... observing that , 4 is the first decimal figure , the next transformation is 7,0 11,00 -6,000 ( 4 7,4 2,96 1,396 7,8 8,2 3,12 17,08 5,584 - , 416 Obs . The nature of decimals evidently direct to annex one cipher to the first , two to the ...
Σελίδα 233
... observing , however , that the subtrahend must always be less than the dividend . EXAMPLE . Find the cube root of 40489652369 . * The triple roots may be continued , without actually multiplying the roots by 3 , by adding double the ...
... observing , however , that the subtrahend must always be less than the dividend . EXAMPLE . Find the cube root of 40489652369 . * The triple roots may be continued , without actually multiplying the roots by 3 , by adding double the ...
Συχνά εμφανιζόμενοι όροι και φράσεις
1st eq 2nd eq absolute number added Algebra arithmetical progression binomial biquadratic change of signs coefficient common denominator common difference compound quantity cube root cubic equation Divide the number dividend divisor equa equal quantities EXAMPLES FOR PRACTICE expressed Extg Extracting the roots Find a number Find the sum find the value Find two numbers find x geometrical progression Given the common greatest common measure hence highest power improper fraction infinite series last term 41 less method Multg Multiply nth root number of terms operation original equation proposed equation quadratic equation ques Reduce remainder Required the cube Required the numbers RULE second term side simple equations square root substituting subtract successive sums surd terms 20 third term trans transformed equation unknown quantity Whence whole number
Δημοφιλή αποσπάσματα
Σελίδα 154 - What two numbers are those, whose difference is to the greater as 2 to 9, and the difference of whose squares is 128 1 Prob.
Σελίδα 68 - ... the square of the two terms of the root already obtained, the remainder will be equal to twice the first two terms of the root multiplied by the third plus the square of the third. Dividing this remainder, therefore, by twice the terms of the root already found, or which is the same thing, dividing the first term of the remainder by twice the first term of the root, we shall obtain the third term sought. Subtracting from the first remainder twice the product of the first two terms of the root...
Σελίδα 302 - J of the first, \ of the second, and \ of the third, may be all equal to each other. Ans. 8, 12, and 16.
Σελίδα 120 - Two persons, A and B, lay out equal sums of money in trade ; A gains $126, and B loses $87, and A's money is now double of B's : what did each lay out ? Ans. $300.
Σελίδα 53 - 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 305 - The sum of the first and second of four numbers in geometrical progression is 15, and the sum of the third and fourth is 60. Required the numbers.
Σελίδα 33 - 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 308 - One hundred stones being placed on the ground, in a straight line, at the distance of a yard from each other, how far will a person travel who shall bring them one by one to a basket, which is placed one yard from the first Stone ? Ans.
Σελίδα 307 - Find four numbers in arithmetical progression such that the sum of the first and third shall be 22, and the sum of the second and fourth 36.