Difference between revisions of ".Mzcw.NzE5Ng"
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(19) | (19) | ||
that of the diagonal of a square to its side, | that of the diagonal of a square to its side, | ||
| − | which | + | which cannot be expressed [[unclear]], and |
| + | therefore [[unclear]] cannot be said to | ||
| + | have either [[unclear]] numerator or denominator, tho | ||
| + | these may be [[unclear]] to any degree required of | ||
| + | of exactness. | ||
| + | |||
| + | 79. The doctrine of ratios being well | ||
| + | understood throws great light on some | ||
| + | parts of the theory of fractions that seem | ||
| + | obscure to beginners. Thus the multiplycation | ||
| + | & division of fractions generally prelexes. | ||
| + | but the dificulty vanishes when it is considered, | ||
| + | that in every multiplication [[unclear]] | ||
| + | is to the multipliers as the multiplicand | ||
| + | is to the product. Therefore if the multiplier | ||
| + | be less than unity, the product must also | ||
| + | be less than the multiplicand. For instance, | ||
| + | let 1/2 be multiplied by 1/2, the product according | ||
| + | to the rule is 1/4. And this is very evident; | ||
Latest revision as of 18:51, 11 August 2018
(19) that of the diagonal of a square to its side, which cannot be expressed unclear, and therefore unclear cannot be said to have either unclear numerator or denominator, tho these may be unclear to any degree required of of exactness.
79. The doctrine of ratios being well understood throws great light on some parts of the theory of fractions that seem obscure to beginners. Thus the multiplycation & division of fractions generally prelexes. but the dificulty vanishes when it is considered, that in every multiplication unclear is to the multipliers as the multiplicand is to the product. Therefore if the multiplier be less than unity, the product must also be less than the multiplicand. For instance, let 1/2 be multiplied by 1/2, the product according to the rule is 1/4. And this is very evident;
