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, Τόμος 1University at Cambridge, 1801 - 426 σελίδες |
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Σελίδα 14
... proof , is founded on the known axiom , " the whole is equal to the sum of all its parts . " All that requires explaining is the method of placing the num- bers , 2. Add up the figures in the row of units ARITHMETIC . Simple Addition.
... proof , is founded on the known axiom , " the whole is equal to the sum of all its parts . " All that requires explaining is the method of placing the num- bers , 2. Add up the figures in the row of units ARITHMETIC . Simple Addition.
Σελίδα 15
... viz . that any num- ber , divided by 9 , will leave the same remainder as the sum of its figures or digits divided by 9 ; which may be thus demonstrated . DEMON . Method of PROOF . 1. Draw a line below the SIMPLE ADDITION . 15.
... viz . that any num- ber , divided by 9 , will leave the same remainder as the sum of its figures or digits divided by 9 ; which may be thus demonstrated . DEMON . Method of PROOF . 1. Draw a line below the SIMPLE ADDITION . 15.
Σελίδα 16
... PROOF . 1. Draw a line below the uppermost number , and sup- pose it cut off . 2. Add all the rest together , and set their sum under the number to be proved . 3. Add DEMON . Let there be any number , as 3467 ; this separated into its ...
... PROOF . 1. Draw a line below the uppermost number , and sup- pose it cut off . 2. Add all the rest together , and set their sum under the number to be proved . 3. Add DEMON . Let there be any number , as 3467 ; this separated into its ...
Σελίδα 17
... Proof . 99755 Proof . 39087 Proof . 4. Add 8635 , 2194 , 7421 , 5063 , 2196 , and 1245 to- gether . Ans . 26754- 5. Add the sum of the former excesses , it is plain this last excess must be equal to the excess of nines contained in the ...
... Proof . 99755 Proof . 39087 Proof . 4. Add 8635 , 2194 , 7421 , 5063 , 2196 , and 1245 to- gether . Ans . 26754- 5. Add the sum of the former excesses , it is plain this last excess must be equal to the excess of nines contained in the ...
Σελίδα 19
... Proof 3287625 Proof 5327467 Froof 1234567 4. From 2. When any figure of the greater number is less than its cor- respondent figure in the less , the ten , which is added by the rule , is the value of an unit in the next higher place ...
... Proof 3287625 Proof 5327467 Froof 1234567 4. From 2. When any figure of the greater number is less than its cor- respondent figure in the less , the ten , which is added by the rule , is the value of an unit in the next higher place ...
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Άλλες εκδόσεις - Προβολή όλων
Mathematics: Compiled from the Best Authors, and Intended to be the ..., Τόμος 1 Πλήρης προβολή - 1808 |
Mathematics: Compiled from the Best Authors, and Intended to be the ..., Τόμος 1 Πλήρης προβολή - 1808 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 168 - Divide the difference of the extremes by the number of terms, less 1, and the quotient will be the common difference.