## The Elements of Euclid |

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Page 16

Ax . therefore the remainder AL is equal to the remainder f BG : but it has been

Ax . therefore the remainder AL is equal to the remainder f BG : but it has been

**shown**, that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ... Page 29

... DB ; but it has been

... DB ; but it has been

**shown**that BA , AC are greater than BE , EC ; much more then are BA , AC B с greater than BD , DC . Again , because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior ... Page 36

Again , A -B because the straight line GK cuts the parallel straight lines EF , CD , the angle GHF is equal to a the E angle GKD ; and it was

Again , A -B because the straight line GK cuts the parallel straight lines EF , CD , the angle GHF is equal to a the E angle GKD ; and it was

**shown**that K the angle AGK is equal to the an- C D gle GHF ; therefore also AGK is equal to ... Page 39

... and because the Book I. straight line BC meets the two straight lines AC , BD , and makes the alternate angles ACB , CBD equal to one another , AC is parallels to BD ; and it was

... and because the Book I. straight line BC meets the two straight lines AC , BD , and makes the alternate angles ACB , CBD equal to one another , AC is parallels to BD ; and it was

**shown**to be equal to it . c 27. 1 . Page 69

... the greater to the less , which is impossible : therefore G is not the centre of the circle ABC : in the same manner.it can be

... the greater to the less , which is impossible : therefore G is not the centre of the circle ABC : in the same manner.it can be

**shown**, that no other point but F is the centre ; that is , F is the centre of the circle ABC .### 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