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

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Page 101

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 6 of times exactly . III . « Ratio is a mutual relation of two magnitudes ... Page 102

when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and fourth ; if the

when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and fourth ; if the

**multiple**of the first be less than that of the second , the**multiple**of the third is also less ... Page 105

That magnitude , of which a

That magnitude , of which a

**multiple**is greater than the same**multiple**of another , is greater than that other ... If any number of magnitudes be equimultiples of as many , each of each ; what**multiple**soever any one of them is of its ... Page 106

tiples of as many others E , F , each of each : whatsoever

tiples of as many others E , F , each of each : whatsoever

**multiple**AB is of E , the same**multiple**shall AB and CD together be of E and F together . Because AB is the same**multiple**of Ethat CD is of F , as many magnitudes as there are ... Page 107

From this it is plain , that if any number of magnitudes AB , BG , GH , be

From this it is plain , that if any number of magnitudes AB , BG , GH , be

**multiples**of another C ; and as many DE , EK , KL , be the same**multiples**of F , each of each : then the whole of the first , viz . AH , is the same**multiple**of ...### 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

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid sphere square square of AC taken THEOR third triangle ABC wherefore whole