## The Elements of Euclid |

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Page 119

... which the third . has to the

... 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 and**fourth**; if the multiple of the first be less than that of the second ... Page 120

Book V. 4 that of 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 121

Permutando , or alternando , by permutation , or alternately ; this See Note : word is used when there are four proportionals , and it is inferred , that the first has the same ratio to the third , which the second has to the

Permutando , or alternando , by permutation , or alternately ; this See Note : word is used when there are four proportionals , and it is inferred , that the first has the same ratio to the third , which the second has to the

**fourth**... Page 122

Book V. second , as the third to its excess above the

Book V. second , as the third to its excess above the

**fourth**. Prop . E , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance ; when there is any number of magnitudes more than two , and as many others ... Page 124

IF the first magnitude be the same multiple of the second that the third is of the

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 ...### 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