## The Elements of Euclid |

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Page 119

V. The first of four magnitudes is said to have the same ratio to the second , which the third . has to the fourth , when any

V. The first of four magnitudes is said to have the same ratio to the second , which the third . has to the fourth , when any

**equimultiples**whatsoever of the first and third being taken , and any**equimultiples**whatsoever of the second ... Page 120

When of the

When of the

**equimultiples**of four magnitudes ( taken as in the fifth definition , the multiple of the first is greater then that of the - second , but the multiple of the third is not greater than the multiple of the fourth ; then the ... Page 122

I.

I.

**EQUIMULTIPLES**of the same , or of equal magnitudes , are equal to one another . * 4. Prop . lib . 2. Archimedis de spliæra et cylindro . Bool : V. II . Those magnitudes of which the 122 THE ELEMENTS. Page 123

Those magnitudes of which the same , or equal magnitudes are

Those magnitudes of which the same , or equal magnitudes are

**equimultiples**, are equal to one another . III . A multiple of a greater magnitude is greater than the same multiple of a less . IV . That magnitude of which a multiple is ... Page 125

If the first be the same multiple of the second , which the third is of the fourth ; and if of the first and third there be taken

If the first be the same multiple of the second , which the third is of the fourth ; and if of the first and third there be taken

**equimultiples**, these shall be**equimultiples**, the one of the second , and the other of the fourth .### What people are saying - Write a review

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### Other editions - View all

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid No preview available - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |

### Common terms and phrases

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