## The Elements of Euclid |

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Page 12

Of four sided figures , a

Of four sided figures , a

**square**is that which has all its sides equal , and all its angles right angles . 1 XXXI . An oblong , is that which has all its angles right angles , but has not all its sides equal . XXXII . 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 demonstrated that the parallelogram CL is equal to the**square**HC : therefore the whole**square**BDEC is equal to the two ... 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

IF a straight line be divided into any two parts , the rectangles contained by the whole and each of the parts are together equal to the

IF a straight line be divided into any two parts , the rectangles contained by the whole and each of the parts are together equal to the

**square**of the whole line , с . B В. Let the straight line AB be divided into A any two parts in the ...### 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