## The Elements of Euclid |

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Page 119

II . greater magnitude is said to be a

II . 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 120

Book V. 4 that of the fourth ; or , if the

Book V. 4 that of the fourth ; or , if the

**multiple**of the first be greated “ than that of the second , the**multiple**of the third is also greater than that of the fourth . VI . Magnitudes which have the same ratio are called ... Page 123

A

A

**multiple**of a greater magnitude is greater than the same**multiple**of a less . IV . That magnitude of which a**multiple**is greater than the same**multiple**of another , is greater than that other magnitude . 54 PROP . I. THEOR . Page 124

IF the first magnitude be the same

IF the first magnitude be the same

**multiple**of the second that the third is of the fourth , and the fifth the same**multiple**of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same ... Page 125

If the first be the same

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