## The Elements of Euclid |

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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

AB ; and CE is contained by AB , BC , for BE is equal to AB ; therefore the

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 square of AB . If therefore a straight line , & c . Q. E. D. PROP . III . Page 54

... and because the complement AG is equals to the complement GE , ảnd that AG is the

... and because the complement AG is equals to the complement GE , ảnd that AG is the

**rectangle**contained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the**rectangle**AC , CB ; wherefore AG , GE are equal to twice ... Page 55

Let the straight line AB be divided into two equal parts in the point C , and into two unequal parts at the point D ; the

Let the straight line AB be divided into two equal parts in the point C , and into two unequal parts at the point D ; the

**rectangle**AD , DB , together with the square of CD , is equal to the square of CB . Upon CB describe a the square ...### 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