## The Elements of Euclid |

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Page 10

... When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle : and the straight line which stands on the other is called a

... When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle : and the straight line which stands on the other is called a

**perpendicular**to it . Page 23

D B с A TO draw a straight line

D B с A TO draw a straight line

**perpendicular**to a given straight line of an unlimited length , from a given point without it . ai Let AB be the given straight line , which may be produced to any length both ways , and let C be a point ... Page 63

IN obtuse angled triangles , if a

IN obtuse angled triangles , if a

**perpendicular**be drawn from any of the acute angles to the opposite side produced , the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse ... Page 64

... the sides containing that angle , by twice the rectangle contained by either of these sides , and the straight line intereepted between the

... the sides containing that angle , by twice the rectangle contained by either of these sides , and the straight line intereepted between the

**perpendicular**let fall upon it from the opposite angle , and the acute angle . a 12.1 . 67. Page 65

А Lastly , Let the side AC be

А Lastly , Let the side AC be

**perpendicular**to BC ; then is BC the straight line between the**perpendicular**and the acute angle at B ; and it is manifest that the square of AB , BC are equal s to the square of AC and twice the square of ...### 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