## The Elements of Euclid |

### From inside the book

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Page vi

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**magnitude**. " Now this proposition is a theorem , not a definition ; because the equality of figures of any kind must be demonstrated , and not assumed ; and , therefore , though this were a true proposition , it ought to have been ... Page vii

plane angles of the same number and

plane angles of the same number and

**magnitude**, placed in the same order ; but neither is this universally true , except in the case in which the solid angles are contained by no more than three plane angles ; nor of this case is there ... Page 119

I. A LESS

I. A LESS

**magnitude**is said to be a part of a greater**magnitude**, when the less measures the greater , that is , when the less is contained a certăin number of times exactly in the greater . ' II . greater**magnitude**is said to be a ... Page 120

N. B. " When four

N. B. " When four

**magnitudes**are proportionals , it is usually expressed by saying , the first is to the se• cond , as the ... then the first is said to.have to the second a greāter ratio than the third .**magnitude**has to the fourth ... Page 121

Geometers make use of the following technical words to sig . nify certain ways of changing either the order or

Geometers make use of the following technical words to sig . nify certain ways of changing either the order or

**magnitude**of proportionals , so as that they continue still to ...### 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