## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |

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Page 126

A greater magnitude is said to be a

A greater magnitude is said to be a

**multiple**of a less , when the greater is measured by the less , that is , ' when the greater contains the « less a certain number of times exactly . ' III . “ Ratio is a mutual relation of two ... Page 127

When of the equimultiples of four magnitudes ( taken as in the fifth definition ) , the

When of the equimultiples of four magnitudes ( taken as in the fifth definition ) , the

**multiple**of the first is greater than that of the second , but the**multiple**of the third is not greater than the ... Page 131

A

A

**multiple**of a greater magnitude is greater than the same**multiple**of a less . ... If any number of magnitudes be equimultiples of as many , each of each ; what**multiple**soever any one of them is of its part , the same**multiple**shall ... Page 132

L Because AB is the same

L Because AB is the same

**multiple**of E that CD is of F , as many magnitudes as there are in AB equal to E , so many are there in А. CD equal to F. Divide AB into magnitudes equal to E , viz . AG , GB ; and G E CD into CH , HD , equal ... Page 133

second , that EH the sixth is of D F the fourth : then shall AG , the A first together with the fifth , be E the same

second , that EH the sixth is of D F the fourth : then shall AG , the A first together with the fifth , be E the same

**multiple**of C the se- B fond , that DH , the third together with the sixth , is of F the Gc II c ! fourth .### What people are saying - Write a review

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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |

### Common terms and phrases

altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equimultiples fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid Q. E. D. PROP ratio reason rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole