An Introduction to the Elements of Algebra: Designed for the Use of Those who are Acquainted Only with the First Principles of Arithmetic |
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Page 12
... gives , as is wanted , a result one less than would arise from the written figures . In the first of the following examples , after having taken 6 units from 14 , we count the next figure of the lower number 8 , as 9 , and so in the ...
... gives , as is wanted , a result one less than would arise from the written figures . In the first of the following examples , after having taken 6 units from 14 , we count the next figure of the lower number 8 , as 9 , and so in the ...
Page 14
... gives the greatest . Thus to ascertain the exactness of the following subtraction , 524 297 227 524 we add the remainder to the smallest number , and find the sum , in reality , equal to the greatest . MULTIPLICATION . 21. WHEN the ...
... gives the greatest . Thus to ascertain the exactness of the following subtraction , 524 297 227 524 we add the remainder to the smallest number , and find the sum , in reality , equal to the greatest . MULTIPLICATION . 21. WHEN the ...
Page 17
... gives a good illustration of the manner , in which the product of two numbers is formed . To make it more easily un ... give the same product . It is easy to extend this reasoning to any numbers , if we conceive each line to contain as ...
... gives a good illustration of the manner , in which the product of two numbers is formed . To make it more easily un ... give the same product . It is easy to extend this reasoning to any numbers , if we conceive each line to contain as ...
Page 19
... give the product its proper value , it is necessary to put , on the right of it , as many Os as there are in the multiplicand . As for the Os , which may occur between the figures of the mul- tiplicand , they give no product , and a 0 ...
... give the product its proper value , it is necessary to put , on the right of it , as many Os as there are in the multiplicand . As for the Os , which may occur between the figures of the mul- tiplicand , they give no product , and a 0 ...
Page 24
... gives 15 hundreds , and the dividend , 1656 , con- tains 16 hundreds ; the difference , 1 hundred , must have come then from the reserved number , arising from the multiplication of the other figures of the quotient by the divisor . If ...
... gives 15 hundreds , and the dividend , 1656 , con- tains 16 hundreds ; the difference , 1 hundred , must have come then from the reserved number , arising from the multiplication of the other figures of the quotient by the divisor . If ...
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An Introduction to the Elements of Algebra: Designed for the Use of Those ... Professor John Farrar,Leonhard Euler No preview available - 2016 |
Common terms and phrases
added algebra Arith arithmetical arithmetical progression called CHAPTER ciphers coefficient column comma compound numbers consequently consider contains crowns cube root decametre decimal figures decimal fraction denominator difference division dollars Dry Measures ducats equal equation evident Examples for practice exponent expression factors fourth frac gallons geometrical progression given number gives greater number greatest common divisor hundred hundredths instance integer last term lastly less letters manner measures metical multi multiplicand multiplied negative numbers number of days number of terms obtain operation partial dividend pence performed pound preceding prime numbers progression proportion proposed quantity question quotient ratio reduced remainder represented required to find result rule shews shillings square root subtract suppose tens tenth third thousandths tion units unity vulgar fraction whence whole numbers write yards
Popular passages
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 107 - A wall to be built to the height of 27 feet, was raised to the height of 9 feet by 12 men in 6 days : how many men must be employed to finish the wall in 4 days at the same ruts.- of working 1 31.
Page 132 - District Clerk's Office. BE IT REMEMBERED, That on the seventh day of May, AD 1828, in the fifty-second year of the Independence of the UNITED STATES OF AMERICA, SG Goodrich, of the said District, has deposited in this office the...
Page 73 - Divide the given denomination by that number which it takes of this denomination to make ONE of the next higher. Proceed in this manner with each successive denomination, till you come to the one required.
Page 34 - ... by the same number, the value of the fraction will not be altered ; for if, on the one hand, by dividing the numerator the fraction is made 2, 3, &c.
Page 119 - A man being asked how many sheep he had in his drove, said, if he had as many more, half as many more, and 7 sheep and a half, he should have 20; how many had he ? Ans. 5.
Page 123 - ... heavens, as that which surrounds an artificial globe, is divided into the same number of parts. The number 360 is entirely arbitrary, and any other number, had mathematicians chosen, might have been fixed upon : and hence the French, in their measures of the circle, divide it into 400 equal parts or degrees ; each degree into 100 minutes, and each minute into 100 seconds. The reason why the number 360 appears to have been selected is, that this number may be divided into halves, quarters, and...
Page 117 - Part 1200 acres of land among A, B, and C, so that B may have 100 more than A, and C 64 more than B.
Page 214 - A privateer running at the rate of 10 miles an hour discovers a ship 18 miles off making way at the rate of 8 miles an hour : how many miles can the ship run before being overtaken ? Ans.
Page 107 - If a footman travel 130 miles in 3 days, when the days are 12 hours long; in how many days, of 10 hours each, may he travel 360 miles ? Ans.