## The Elements of Euclid |

### From inside the book

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Page 48

... A B BED is a right angle ; wherefore the figure ADEB is

... A B BED is a right angle ; wherefore the figure ADEB is

**rectangular**, and it has been demonstrated that it ... the side subtending the right angle , is equal to the squares described upon the sides which**contain**the right angle . Page 51

If there be two straight lines , one of which is divided into any number of parts ; the

If there be two straight lines , one of which is divided into any number of parts ; the

**rectangle contained**by the two straight lines , is equal to the**rectangles contained**by the undivided line , and the several parts of the divided ... Page 52

Let A and BC be two straight lines , and let BC be divided pinto any parts in the points D , E , the

Let A and BC be two straight lines , and let BC be divided pinto any parts in the points D , E , the

**rectangle contained**by the straight lines A , BC is equal B D E C to the**rectangle contained**by A , BD , together with that contained ... Page 53

AC ; for it is contained by DA , AC , of which AD is equal to Bock II .. AB ; and CE is contained by AB , BC , for BE is equal to AB ; therefore the

AC ; for it is contained by DA , AC , of which AD is equal to Bock II .. AB ; and CE is contained by AB , BC , for BE is equal to AB ; therefore the

**rectangle contained**by AB , AC , together with the rectangle AB , BC , is equal to the ... Page 54

... G H K and CG to BK ; wherefore the figure CGKB is equilateral ; it is likewise rectangular ; for CG is parallel to ... CB ; and because the complement AG is equals to the complement GE , ảnd that AG is the

... G H K and CG to BK ; wherefore the figure CGKB is equilateral ; it is likewise rectangular ; for CG is parallel to ... CB ; and because the complement AG is equals to the complement GE , ảnd that AG is the

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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