## 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, Volume 1 |

### From inside the book

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**cypher**, and the rest , or rather all of them , are called figures or digits . The names and signification of these characters , and the origin or generation of the numbers they stand for , are as follow : o nothing ; I one , or a ... Page 12

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**cypher**, though it signifies nothing of itself , yet it occupies a place , and , when set on the right hand of other figures , in- creases their value in the same ten - fold proportion ; thus , 5 sig- nifies only five , but 50 is five ... Page 13

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**cyphers**, which are omitted in the question . EXAMPLES . 5. For the more easily reading of large numbers , they are di- vided into periods , and half periods , each half period consisting of three figures ; the name of the first period ... Page 16

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**cyphers**as a , the highest digit , is places from unity . Then Na with n , o's + b with n - 1 , o's + c with n - 2 , o's , & c . by the nature of notation ; = aXn - 1 , 9's + a + bxn − 2 , 9's + b + c × n — 3 , 9's + c , & c . = aXn ... Page 24

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**cyphers**to the right hand of one or both the numbers to be multiplied . RULE . Proceed as before , neglecting the**cyphers**, and to the right hand of the product place as many**cyphers**as are in both the numbers . EXAMPLES . 1. Multiply ...### Contents

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### Common terms and phrases

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 combinations 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

### Popular passages

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.

Page 168 - Divide the difference of the extremes by the number of terms, less 1, and the quotient will be the common difference.