## The Elements of Euclid |

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Page vi

by which the doctrine of compound ratios is rendered plain and easy . Besides , among the definitions of the 11th book , , there is this , which is the 10th , viz . “ Equal and

by which the doctrine of compound ratios is rendered plain and easy . Besides , among the definitions of the 11th book , , there is this , which is the 10th , viz . “ Equal and

**similar**solid figures are those which are contained by ... Page vii

18th of the 12th book , depend upon the 9th definition of the 11th book , which is not a right definition , because there may be solids contained by the same number of simiIdr plane figures , which are not

18th of the 12th book , depend upon the 9th definition of the 11th book , which is not a right definition , because there may be solids contained by the same number of simiIdr plane figures , which are not

**similar**to one another ... Page 68

**Similar**segments of a circle , are those in which the angles are cqual , or which contain equal angles . A 392 PROP . I. PROB . See Notes TO find the centre of a given circle . Let ABC be the given circle ; it is required to find its ... Page 87

UPON the same straight line , and upon the same See Note : side of it , there cannot be two

UPON the same straight line , and upon the same See Note : side of it , there cannot be two

**similar**segments of circles , not coinciding with one another . If it be possible , let the two**similar**segments of circles , viz . Page 88

Wherefore ,

Wherefore ,

**similar**segments , & c . Q. E. D. " 410 PROP . XXV . PROB , A SEGMENT of a circle being given , to describe . a . the circle of which it is the segment . 3 See Note . ' * 10 , 1 . b 11. 1 . C 6.1 .### 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