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

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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 9

Which was to be

Which was to be

**demonstrated**. 1 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 10

And , since it has been

And , since it has been

**demonstrated**, that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; therefore the remaining angle ABC is equal + to the remaining angle ACB , which are ... Page 14

... be

... be

**demonstrated**, that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B drawt BE at right angles to AB ... Page 15

... have been

... have been

**demonstrated**to be equal to the same three angles ; and things D B -C D * 10 Def . * 1 Ax . that are equal to the same BOOK I. PROP . XII . XIII . 15.### What people are saying - Write a review

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

### Common terms and phrases

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