## 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

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

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 103

... the last of them the ratio compounded of the ratio which the first nas to , the second , and of the ratio which the second has to the third , and of the ratio which the third has to the

... the last of them the ratio compounded of the ratio which the first nas to , the second , and of the ratio which the second has to the third , and of the ratio which the third has to the

**fourth**, and so on unto the last magnitude . Page 104

**fourth**: as is shewn in the 16th Prop . of this fifth Book . XIV . Invertendo , by inversion ; when there are four proportionals , and it is inferred , that the second is to the first as the**fourth**to the third . Prop . B. Book 5 . XV . Page 105

... but one of the second rank ; and as the third is to the

... but one of the second rank ; and as the third is to the

**fourth**of the first rank , so is the third from the last to the last but two of the second rank ; and so on in a cross order : and the inference is as in the 18th definition .### 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