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

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Page 76

When four quantities are in arithmetical proportion , the sum of the two

When four quantities are in arithmetical proportion , the sum of the two

**extremes**is equal to the sum of the two means . Thus , with regard to the four , 2 , 4 , 6 , 8 , we have 2 + 8 = 4 + 6 = 10 . THEOREM 2. Page 77

The difference between the

The difference between the

**extreme**terms of an arithmetical progression , is equal to the common difference of the ... The sum of all the terms of any arithmetical progression , is equal to the sum of the two**extremes**multiplied by the ... Page 78

If the

If the

**extremes**be 10 and 70 , and the number of terms 21 ; what is the common difference , and the sum of the series ? Ans . , the common difference is 3 , and the sum is 840 . 3. A certain debt can be discharged in one year ... Page 79

To find any number of arithmetical means between two given terms or

To find any number of arithmetical means between two given terms or

**extremes**. SUBTRACT the less**extreme**from the greater , and divide the difference by 1 more than the number of means required to be found , which will give the common ... Page 80

3 = 3 a - 3 3 Thus , with respect to the proportion 6 : 3 :: 14 : 7 , which gives 6 x7 = 3 x 14 , we may displace the

3 = 3 a - 3 3 Thus , with respect to the proportion 6 : 3 :: 14 : 7 , which gives 6 x7 = 3 x 14 , we may displace the

**extremes**, or the means , an operation which is denoted by the word Alternando . This will give 6 : 14 :: 3 : 7 or 7 ...### 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