## 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

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 128

When four magnitudes are continual proportionals , the first is said to have to the

When four magnitudes are continual proportionals , the first is said to have to the

**fourth**the triplicate ratio of that which it has to the second , and so on , quadruplicate , & c . increasing the denomination still by unity , in any ... Page 129

This 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

This 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**; or that the first is to the third as the second to the**fourth**: as is shown in ... Page 130

Convertendo , by conversion ; when there are four proportionals , and it is inferred , that the first is to its excess above the second , as the third to its excess above the

Convertendo , by conversion ; when there are four proportionals , and it is inferred , that the first is to its excess above the second , as the third to its excess above the

**fourth**. Prop . E. Book 5 . XVIII . Page 131

first rank , so is the last but two to the last but one of the second rank ; and as the third is to the

first rank , so is the last but two to the last 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 ...### 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