Mathematics: Compiled from the Best Authors and Intended to be the Text-book of the Course of Private Lectures on These Sciences in the University at Cambridge, Volumen1University at Cambridge, 1801 - 426 páginas |
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Página 17
... true sum will always appear to be true by this proof ; and to make a false one appear true , there must be at least two errors , and these op- posite to each other ; and if there be more than two errors , they must balance among ...
... true sum will always appear to be true by this proof ; and to make a false one appear true , there must be at least two errors , and these op- posite to each other ; and if there be more than two errors , they must balance among ...
Página 18
... true difference sought ; because as the sum of the parts is equal to the whole , so must the sum of the differences of all the similar parts be equal to the difference of the whole . 2. When 2. Begin at the right hand , and take each 18 ...
... true difference sought ; because as the sum of the parts is equal to the whole , so must the sum of the differences of all the similar parts be equal to the difference of the whole . 2. When 2. Begin at the right hand , and take each 18 ...
Página 22
... true of any number of factors whatever . The following examples are subjoined to make the reason of the rale appear as plain as possible . ( 1 ) 37565 ( 2 ) 5 1375435 4567 25 = 5 × 5 9628045 [ tiplicand . 7 times the mul 30 = 60 × 5 ...
... true of any number of factors whatever . The following examples are subjoined to make the reason of the rale appear as plain as possible . ( 1 ) 37565 ( 2 ) 5 1375435 4567 25 = 5 × 5 9628045 [ tiplicand . 7 times the mul 30 = 60 × 5 ...
Página 23
... true . Q. E. D. This method is liable to the same inconvenience with that in addition . Multiplication may also , very naturally , be proved by division for the product being divided by either of the factors , will evi- dently give the ...
... true . Q. E. D. This method is liable to the same inconvenience with that in addition . Multiplication may also , very naturally , be proved by division for the product being divided by either of the factors , will evi- dently give the ...
Página 26
... true quotient of the whole dividend by the divisor ; which may be thus demonstrated : DEMON . The complete value of the first part of the dividend , is , by the nature of notation , 10 , 100 , or 1000 , & c . times the 2. Find how many ...
... true quotient of the whole dividend by the divisor ; which may be thus demonstrated : DEMON . The complete value of the first part of the dividend , is , by the nature of notation , 10 , 100 , or 1000 , & c . times the 2. Find how many ...
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Términos y frases comunes
2qrs angle annuity annum arithmetical bushel called carats cent centre circle circumference coefficient common denominator completing the square compound interest cube root cyphers decimal denoted discount Divide dividend division divisor draw equal equation EXAMPLES exponent farthings figures find the value fourth gallons geometrical progression geometrical series give given Line given number greater greatest common measure improper fraction integers least common multiple less number logarithm manner multiplicand Multiply negative NOTE number of terms number of things payment perpendicular pound present worth PROBLEM PROBLEM proportion quotient radius ratio Reduce remainder repetend required to find shews shillings sides simple interest square root subtract Suppose surd taken tare third triangle TROY WEIGHT unknown quantity vulgar fraction Whence whole number yards ΙΟ
Pasajes populares
Página 352 - 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.
Página 54 - In the same manner multiply all the multiplicand by the inches, or second denomination, in the multiplier) and set the result of each term one place removed to the right 'hand of those in the multiplicand.
Página 136 - As the sum of the several products, Is to the whole gain or loss : So is each man's particular product, To his particular share of the gain or low. EXAMPLES. 1. A, B and C hold a pasture in common, for which they pay 197.
Página 379 - A point is a dimensionless figure ; or an indivisible part of space. A line is a point continued, and a figure of one capacity, namely, length. A superficies is a figure of two dimensions, namely, length and breadth. A solid is a figure of three dimensions, namely, length, breadth, and thickness.
Página 166 - The first term, the last term, and the number of terms given, to find the sum of all the terms. RULE.* — Multiply the sum of the extremes by the number of terms, and half the product will be the answer.
Página 127 - ... have to their consequents, the proportion between the first antecedent and the last consequent is discovered, as well as the proportion between the others in their several respects.
Página 350 - B's, and B's is triple of C's, and the sum of all their ages is 140. What is the age of each ? Ans. A's =84, B's =42, and C's =14.
Página 388 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees; and each degree into 60 minutes, each minute into 60 seconds, and so on.
Página 244 - Briggs' logarithm of the number N ; so that the common logarithm of any number 10" or N is n, the index of that power of 10 which is equal to the said number. Thus, 100, being the second power of 10, will have 2 for its logarithm ; and 1000, being the third power of 10, will have 3 for its logarithm. Hence, also, if 50 = 101-00*7, then is 1.69897 the common logarithm of 50.
Página 168 - Divide the difference of the extremes by the number of terms, less 1, and the quotient will be the common difference.