## A Course of Mathematics: In Two Volumes. For the Use of the Royal Military Academy, Volume 1 |

### From inside the book

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Page 36

The Rule of Three enables us to find a fourth

The Rule of Three enables us to find a fourth

**proportional**to three numbers given : for which reason it is sometimes called the Rule of Proportion . It is called the Rule of Three , because three terms or numbers are given ... Page 75

To denote numbers as being geometrically

To denote numbers as being geometrically

**proportional**, a colon is set between the terms of each couplet , to denote their ratio ; and a double colon , or else a mark of equality ... Page 76

... term it ) of

... term it ) of

**proportionality**, can be readily subjected to Euclid's test : but the proposition is not convertible . ... all the properties of**proportional**quantities as expressed by numbers , to whatever branch of pure or applied ... Page 78

To find an arithmetical mean

To find an arithmetical mean

**proportional**between two given terms . Add the two given extremes or terms together , and take half their sum for the arithmetical mean required . EXAMPLE . To find an arithmetical mean between the two ... Page 79

If the two means are equal , as in the terms 3 , 6 , 6 , 12 , their product becomes a square . Hence . THEOREM 111. The mean

If the two means are equal , as in the terms 3 , 6 , 6 , 12 , their product becomes a square . Hence . THEOREM 111. The mean

**proportional**between two numbers is the square root of their product . We may without destroying the accuracy ...### What people are saying - Write a review

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A Course of Mathematics: Composed for the Use of the Royal Military Academy Charles Hutton No preview available - 2015 |

### Common terms and phrases

added algebraic angle answer applied arithmetical base called centre circle coefficients common compound contained continued cube decimal denominator denote describe diameter difference distance divided division divisor double draw drawn equal equation EXAMPLES expression extremes factors figure former four fraction functions give given greater half hence interest intersection join latter length less manner means measure meeting method Multiply obtained operation opposite parallel parallelogram perpendicular plane position principal PROBLEM proportional quantity question quotient radius ratio rectangle Reduce remainder respectively result right angles root rule sides signs simple solution square subtract successive supposing taken THEOREM third triangle Whence whole yards