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

### From inside the book

Page 130

Exæquali ( sc . distantiâ ) , or ex æquo , from equality of distance : when there is any number of magnitudes more than two , and as many others , such that they are proportionals when

Exæquali ( sc . distantiâ ) , or ex æquo , from equality of distance : when there is any number of magnitudes more than two , and as many others , such that they are proportionals when

**taken**two and two of each rank , and it is inferred ... 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

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

... which the equimultiple of the third has to that of the fourthi ' Let A the first have to B the second the same ratio which the third C has to the fourth D ; and * 3.5 of A and C let there be

... which the equimultiple of the third has to that of the fourthi ' Let A the first have to B the second the same ratio which the third C has to the fourth D ; and * 3.5 of A and C let there be

**taken**134 EUCLID'S ELEMENTS . Page 135

3.5 of A and C let there be

3.5 of A and C let there be

**taken**any equimultiples whatever E , F ; and of B and D any equimultiples whatever G , H : then E shall have the same ratio to G , which F has to H. Take of E and F any equimultiples whatever K , L , and of G ... Page 136

K - is the same multiple of A , that L is of C : and because t A is to B , as C is to D , and of A and C certain equimultiples have been

K - is the same multiple of A , that L is of C : and because t A is to B , as C is to D , and of A and C certain equimultiples have been

**taken**, viz . K and L ; and of B and D certain equimultiples G , H ; therefore , if K be greater ...### What people are saying - Write a review

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### Other editions - View all

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2013 |

### 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