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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... EQUATIONS , AND OF THE RESOLUTION OF THOSE EQUATIONS . CHAPTER I. Of the Solution of Problems in general . CHAPTER II . Of the Resolution of Simple Equations , or Equations of the first degree . CHAPTER III . Of the Solution of ...
... EQUATIONS , AND OF THE RESOLUTION OF THOSE EQUATIONS . CHAPTER I. Of the Solution of Problems in general . CHAPTER II . Of the Resolution of Simple Equations , or Equations of the first degree . CHAPTER III . Of the Solution of ...
Page 59
... equation b = - a 212. Now , as it frequently happens that the number c cannot be really divided by the number a , while the letter b must how- ever have a determinate value , another new kind of numbers presents itself ; these are ...
... equation b = - a 212. Now , as it frequently happens that the number c cannot be really divided by the number a , while the letter b must how- ever have a determinate value , another new kind of numbers presents itself ; these are ...
Page 60
... equation in which three letters a , b , c , are found . Now we have shewn in treating of powers , how to find the power itself , that is , the letter c , when a root a and its Suppose , for example , a = 5 , and b = 3 , so that c = 53 ...
... equation in which three letters a , b , c , are found . Now we have shewn in treating of powers , how to find the power itself , that is , the letter c , when a root a and its Suppose , for example , a = 5 , and b = 3 , so that c = 53 ...
Page 82
... equation 1 = 1 + 1 / 2 - ÷ ÷ = ÷ = 1 + − ¡ ¬¿ + ¿ ' s + tis — xix , & c . 6 64 12 Suppose a , we shall have the equation 1 1 ÷ = ÷ = 1 + ¿ —‚— ¿ ì + 7 } t , == 1 + } 27 & c . If we take the four leading terms of this series , we have ...
... equation 1 = 1 + 1 / 2 - ÷ ÷ = ÷ = 1 + − ¡ ¬¿ + ¿ ' s + tis — xix , & c . 6 64 12 Suppose a , we shall have the equation 1 1 ÷ = ÷ = 1 + ¿ —‚— ¿ ì + 7 } t , == 1 + } 27 & c . If we take the four leading terms of this series , we have ...
Page 84
... equations : : ( a + 1 ) 2 = aa + 2a + 1 ; ( a + 2 ) 2 = aa + 4 a + 4 ; ( a + 3 ) 2 = a a + 6a + 9 ; ( a + 4 ) 2 = a a + 8 a ... equation ( a · —b ) 2 = aa — 2ab + bb , we shall have ( a - 1 ) = aa — 2a + 1 . The square of a - 1 is found ...
... equations : : ( a + 1 ) 2 = aa + 2a + 1 ; ( a + 2 ) 2 = aa + 4 a + 4 ; ( a + 3 ) 2 = a a + 6a + 9 ; ( a + 4 ) 2 = a a + 8 a ... equation ( a · —b ) 2 = aa — 2ab + bb , we shall have ( a - 1 ) = aa — 2a + 1 . The square of a - 1 is found ...
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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
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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.