## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |

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Page 5

**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 24

1 + Hyp . +1 Ax . * 16. 1 . + Hyp . + Hyp . † 4. 1 . Q. E , D. PROP . XXVII . THEOR . If a straight line falling upon two other straight lines make the alternate angles equal to one another , these two straight lines shall be

1 + Hyp . +1 Ax . * 16. 1 . + Hyp . + Hyp . † 4. 1 . Q. E , D. PROP . XXVII . THEOR . If a straight line falling upon two other straight lines make the alternate angles equal to one another , these two straight lines shall be

**parallel**. Page 25

... C : but those straight lines which meet neither way , though produced ever so far , are

... C : but those straight lines which meet neither way , though produced ever so far , are

**parallel*** to one an- * 35 Def . other : therefore AB is**parallel**to CD . Wherefore , if a straight line , & c . Q. E. D. G PROP . XXVIII . Page 26

H D F If a straight line fall upon two

H D F If a straight line fall upon two

**parallel**straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles ... Page 27

1 , A 2 -B HA Let the straight line GHK cut AB , EF , CD : and because GHK cuts the

1 , A 2 -B HA Let the straight line GHK cut AB , EF , CD : and because GHK cuts the

**parallel**straight lines AB , EF , the angle AGH is equal * to the angle ĞHF . Again , because the straight line GK cuts the**parallel**straight lines EF ...### What people are saying - Write a review

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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid sphere square square of AC taken THEOR third triangle ABC wherefore whole