## The Elements of Euclid |

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Page 13

Parallel straight lines , are such as are in the same plane , and which being

Parallel straight lines , are such as are in the same plane , and which being

**produced**ever so far both ways , do not meet . POSTULATES . I : Let it be granted that a straight line may be drawn from any one point to any other point . Page 14

“ If a straight line meet two straight lines , so as to make the “ two interior angles on the same side of it taken together less " than two right angles , these straight lines being continually “

“ If a straight line meet two straight lines , so as to make the “ two interior angles on the same side of it taken together less " than two right angles , these straight lines being continually “

**produced**, shall at length meet upon ... Page 15

Di From the point A to B draw a the straight line AB ; and upon it describe the equilateral triangle DAB , and

Di From the point A to B draw a the straight line AB ; and upon it describe the equilateral triangle DAB , and

**produce**c the straight lines DA , DB , to E and F ; from the centre B , at the distance BC , described the circle CGH ... Page 17

The angles at the base of an isosceles triangle are equal to one another ; and , if the equal sides be

The angles at the base of an isosceles triangle are equal to one another ; and , if the equal sides be

**produced**, the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side AB is с b ... Page 18

b Book I. equal to AC , and let the straight lines AB , AC be

b Book I. equal to AC , and let the straight lines AB , AC be

**produced**to SD and E , the angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut off a 3.### 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