## The Practical Analyst: Or, A Treatise on Algebra, Containing the Most Useful Parts of that Science, Illustrated by a Copious Collection of Examples, Designed for the Use of Schools |

### From inside the book

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Page ix

... and impossible roots , was left to exercise the ingenuity of succeeding inquirers . Vieta employed the large letters of the alphabet , and indicated their powers by initials placed over them , as

... and impossible roots , was left to exercise the ingenuity of succeeding inquirers . Vieta employed the large letters of the alphabet , and indicated their powers by initials placed over them , as

**exponents**PREFACE . ix. Page x

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**exponents**are now used : Harriott substituted small letters , and denoted their powers by repetitions of the letter ; thus instead of A , Ac , & c . he wrote aa , aaa , & c . , a small change indeed , but still an obvious improvement in ... Page 14

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**exponent**; thus , 1 × 5 × 5 × 5 × 5 = 625 ; and , 1 × a × a × a × a × a , or aaaaa , are the 4th and 5th powers of 5 and a respectively , and are usually expressed by the root with the index of the power set over it ; as 54 , a5 ; hence ... Page 23

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**exponents**; when the**exponents**are not the same , sub- tract the**exponent**of the divisor from that of the dividend , and use the remainder as the index of the letter in the quotient ; write in the quotient the letters which have not ... Page 28

... - efficient of the second term is the index of the given power ; and if a co - efficient , already found , be mul- tiplied by the

... - efficient of the second term is the index of the given power ; and if a co - efficient , already found , be mul- tiplied by the

**exponent**of the leading quantity , or first term of the root , contained in the same term 28 INVOLUTION .### Other editions - View all

A Treatise on Algebra, Containing the Most Useful Parts of That Science ... Enoch Lewis No preview available - 2016 |

The Practical Analyst, Or a Treatise on Algebra: Containing the Most Useful ... Enoch Lewis No preview available - 2017 |

### Common terms and phrases

3d power 4th power 4th root absolute number added Alexandrian school algebra arithmetical progression Assume bers binomial cents co-efficient compound quantity containing continued product cube root cubic equation denote diff digits Diophantus Divide divisor dollars equa equal EXAMPLES exponents expressed Extract the root find the value find x former four numbers fraction gallons geometrical progression given equation Hence impossible roots improper fraction indicated involution letters logarithm lues moidore Multiply number of terms numbers in geometrical obtained proportionals quadratic surd quan Quere the number quotient radical sign ratio compounded Reduce remainder Required the 4th required the numbers Required the square Required the sum Required the values Required to find Result root figure solution square root third three numbers tion tity transposition unknown quantity values of x vulgar fraction Whence whole number whole positive numbers

### Popular passages

Page ii - An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies during the times therein mentioned." And also to the act, entitled " An Act supplementary to an Act, entitled, " An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies during the time therein mentioned," and extending the benefits thereof to the arts of designing, engraving, and...

Page ii - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...

Page 93 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.

Page 70 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from home, it lasted the woman 30 days ; how many days would the man alone be in drinking it ? Ans.

Page 84 - A laborer dug two trenches, one of which was 6 yards longer than the other, for 17 pounds, 16 shillings, and the digging of each of them cost as many shillings per yard as there were yards in its length. What was the length of each ? Ans. 10 and 16 yards.

Page 70 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.

Page 32 - Arrange the terms according to the powers of some letter. Extract the square root of the first term, write the result as the first term of the root, and subtract its square from the polynomial.

Page 85 - What number is that, which, being divided by the product of its digits, the quotient is 3 ; and if 18 be added to it, the digits will be inverted ? Ans.

Page 91 - There are three numbers, the difference of whose differences is 5; their sum is 44, and continued product 1950; find the numbers.

Page 89 - Ans. 15 and 9. 11. What two numbers are those, whose difference, sum, and product, are as the numbers 2, 3, and 5, respectively ? Ans. 10 and 2.