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

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Page 101

... the less can be multiplied so as to exceed the other . 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

... the less can be multiplied so as to exceed the other . 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. Page 102

when any

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

I.

I.

**EQUIMULTIPLES**of the same , or of equal magnitudes , , are equal to one another . II . Those magnitudes , of which the same or equal magnitudes are**equimultiples**, are equal to one another . III . A multiple of a greater magnitude is ... Page 106

Therefore , if any magnitudes , how many soever , be

Therefore , if any magnitudes , how many soever , be

**equimultiples**of as many , each of each ; whatsoever multiple any one of them is of its part , the same multiple shall all the first magnitudes be of all the others : For 6 the same ... Page 107

... and if of the first and third there be taken

... and if of the first and third there be taken

**equimultiples**; these shall be**equimultiples**, the one of the second ... that C the third is of D the fourth ; and of A , C let**equimultiples**EF , GH be taken : then EF shall be the same ...### 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