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

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Page 127

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 and ... Page 131

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 132

... CD together equal to E and F together : therefore , whatsoever multiple AB is of E , the same multiple is AB and CD together of E and F together . Therefore , if any magnitudes , how many soever , be

... CD together equal to E and F together : therefore , whatsoever multiple AB is of E , the same multiple is AB and CD together of E and F together . Therefore , if any magnitudes , how many soever , be

**equimultiples**of as many ... Page 133

If the first be the sume 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 sume 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 . Page 134

If the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any

If the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any

**equimultiples**whatever of the first and third shall have the same ratio to any**equimultiples**of the second and fourth , vis .### 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

altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole