## The Elements of Euclid |

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Page 48

TO describe a

TO describe a

**square**upon a given straight line . 2 11. 1 . b 3.1 . e 31.1 . d 34. 1 . Let AB be the given straight line ; it is required to describe a**square**upon AB . From the point A draw a**AC**at right angles to AB ; and make b AD ... Page 49

AE . therefore the parallelogram BL is equal to the

AE . therefore the parallelogram BL is equal to the

**square**GB : and in the same manner , by joining AE , BK , it is ... and the**squares**GB , HC upon BA ,**AC**: wherefore the**square**upon the side BC is equal to the**squares**upon the ... Page 50

If the

If the

**square**described upon BC , one of the sides of the triangle ABC , be equal to the**squares**upon the other sides BA ,**AC**, the angle BAC is a right angle . From the point A draw . AD at right angles to**AC**, and make AD equal to BA ... Page 52

B В. Let the straight line AB be divided into A any two parts in the point C ; the rectangle contained by AB , BC , together with the rectangle * AB ,

B В. Let the straight line AB be divided into A any two parts in the point C ; the rectangle contained by AB , BC , together with the rectangle * AB ,

**AC**, shall be equal to the**square**of AB . Upon AB describe a the**square**ADEB ... Page 53

**AC**; for it is contained by DA ,**AC**, of which AD is equal to Bock II . ... 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 .### 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