## An Easy Introduction to the Mathematics: In which the Theory and Practice are Laid Down and Familiarly Explained ... A Complete and Easy System of Elementary Instruction in the Leading Branches of the Mathematics; ... Adapted to the Use of Schools, Junior Students at the Universities, and Private Learners, Especially Those who Study Without a Tutor. In Two Volumes, Volume 1 |

### From inside the book

Results 1-5 of 25

Page 27

3 from 8, and 5 remain to put down; then 2 from - 3, and 1 remains ; 1 from 7, and

6 remain; 2 from 4, Diff. 2615 and 2 remain; the whole remainder then is 2615.

**Earplanation**. 4738 Having placed the less number under the greater, I 2123 take3 from 8, and 5 remain to put down; then 2 from - 3, and 1 remains ; 1 from 7, and

6 remain; 2 from 4, Diff. 2615 and 2 remain; the whole remainder then is 2615.

Page 32

multiply all the figures of the multi- plicand by six, exactly as was done in the last

Product 484592580 rule. - 28. 29. 3O. 31. Multiply 142736 238957 3689.15

490.192 ...

**Earplanation**. * I first write down the 0 for the right hand fi807 o, gure; then Imultiply all the figures of the multi- plicand by six, exactly as was done in the last

Product 484592580 rule. - 28. 29. 3O. 31. Multiply 142736 238957 3689.15

490.192 ...

Page 45

last figure 4 from the dividend, I divide th. Quotient 78561; remaining figures in

the latter by 2. Having divided TETO. T the 3, I have 1 remaining, which is placed

...

**Earplanation**. Here having cut off the cipher from the divisor 20157,284 and thelast figure 4 from the dividend, I divide th. Quotient 78561; remaining figures in

the latter by 2. Having divided TETO. T the 3, I have 1 remaining, which is placed

...

Page 57

10 11 7 2 19 12

12, 8 and take in the 11 for ounces; these I multiply - by 8, and take in the 7 for

drams; the drams I 1055 drams. multiply by 3, and take in the 2 for scruples; ...

10 11 7 2 19 12

**Earplanation**. 131 ounces. Beginning at the pounds, I multiply by12, 8 and take in the 11 for ounces; these I multiply - by 8, and take in the 7 for

drams; the drams I 1055 drams. multiply by 3, and take in the 2 for scruples; ...

Page 62

mile,) and the 3 furlongs are added to the product, this gives furlongs; these are

multiplied by 40, (because 40 poles make a furlong,) and the 4 taken in, this

gives ...

**Earplanation**. The miles are here multiplied by 8, (because 8 furlongs make amile,) and the 3 furlongs are added to the product, this gives furlongs; these are

multiplied by 40, (because 40 poles make a furlong,) and the 4 taken in, this

gives ...

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### Contents

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### Other editions - View all

### Common terms and phrases

added Algebra aliquot answer Arithmetic called carry ciphers coefficient common denominator compound contained cube root cubic decimal denotes Diff Diophantus Divide dividend division divisor Earplanation equal equation Euclid's Elements example farthings former fourth gallons geometrical progression Geometry given number greater greatest common measure greatest term hundred improper fraction improvements inches latter learning least common multiple least term left hand less likewise logarithm lowest terms Mathematics method mixed number multiplicand Multiply namely number of terms operation ounces pence pounds Prod Proof proper Quot quotient ratio Reduce remainder repetend right hand figure rule second term shewn shews shillings simple square root subjoin subtract surd tens third thousand tion transposition units unknown quantity vinculum vulgar fraction whence wherefore whole number yards

### Popular passages

Page xxiv - Just so it is in the mind ; would you have a man reason well, you must use him to it betimes, exercise his mind in observing the connection of ideas and following them in train. Nothing does this better than mathematics, which therefore I think should be taught all those who have the time and opportunity, not so much to' make them mathematicians as to make them reasonable creatures...

Page 64 - LIQUID MEASURE 4 gills (gi.) = 1 pint (pt.) 2 pints = 1 quart (qt...

Page 114 - Then multiply the second and third terms together, and divide the product by the first term: the quotient will be the fourth term, or answer.

Page 466 - What number is that, which, being divided by the product of its digits, the quotient is 3 ; and if 18 be added to it, the digits will be inverted ? Ans.

Page 62 - Square Measure 144 square inches = 1 square, foot 9 square feet = 1...

Page 122 - State and reduce the terms as in the Rule of Three Direct. 2. Multiply the first and second terms together, and divide the product by the third ; the quotient will be the answer in the same denomination as the middle term was reduced into.

Page 252 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...

Page 450 - A hare is 50 leaps before a greyhound, and takes 4 leaps to- the greyhound's 3, but 2 of the greyhound's leaps are as much as 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Ans. 300.

Page 307 - Multiply the whole number by the numerator of the fraction, and divide the product by the denominator ; or divide the whole number by the denominator of the fraction, and multiply the quotient by the numerator.

Page 238 - ... 2. Multiply each term in the multiplicand, beginning at the lowest, by the feet in the multiplier, and write...