## The Elements of Euclid |

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Page 121

Dividendo , by division ; when there are four proportionals , and it is inferred , that the

Dividendo , by division ; when there are four proportionals , and it is inferred , that the

**excess**of the first above second , is to the second , as the**excess**of the third above the fourth , is 10 the fourth . 17th . prop . book 5 . Page 122

Book V. second , as the third to its

Book V. second , as the third to its

**excess**above the fourth . Prop . E , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance ; when there is any number of magnitudes more than two , and as many others ... Page 144

IF four magnitudes be proportionals , they are also proportionals by conversion , that is , the first is to its

IF four magnitudes be proportionals , they are also proportionals by conversion , that is , the first is to its

**excess**above the second , as the third to its**excess**above the fourth . 1 à 17. Page 149

If the same hypothesis be made as in the proposition , the

If the same hypothesis be made as in the proposition , the

**excess**of the first and fifth shall be to the sccond , as . பேதியாக்கம் Book v . the**excess**of the third and sixth OF EUCLID . Page 150

Book v . the

Book v . the

**excess**of the third and sixth to the fourth . The demon stration of this is the same with that of the proposition , if division be used instead of composition . CoR . 2. The proposition holds true of two ranks of magnitudes ...### What people are saying - Write a review

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### Other editions - View all

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid No preview available - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prisms produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole