## The Elements of Euclid |

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Page vi

Now this proposition is a theorem , not a definition ; because the equality of figures of any kind must be

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**demonstrated**. Page vii

... which are not similar to one another , in the true sense of similarity received by all geometers ; and all these propositions have , for these reasons , been insufficiently

... which are not similar to one another , in the true sense of similarity received by all geometers ; and all these propositions have , for these reasons , been insufficiently

**demonstrated**since Theon's time hitherto . Page 17

Which was . to be

Which was . to be

**demonstrated**. PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and , if the equal sides be produced , the angles upon the other side of the base shall be equal . Page 18

... and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG : and , since it has been

... and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG : and , since it has been

**demonstrated**, that the whole angle ... Page 19

Again , because CB is equal to DB , the angle BDC is fequal a to the angle BCD ; but it has been

Again , because CB is equal to DB , the angle BDC is fequal a to the angle BCD ; but it has been

**demonstrated**to be a 5. I greater than it ; which is impossible . a Book L But if one of the vertices , OF EUCLID . 19.### 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