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

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Page 30

If a straight line

If a straight line

**falling**upon two other straight lines makes the alternate angles equal to one another , these two straight lines shall be purallel . Let the straight line EF , which**falls**upon the two straight lines AB , CD , make ... Page 31

If a straight line

If a straight line

**fall**upon two parallel straight See the lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the position interior and opposite upon the sume side ; and Oct. Ed . likewise the ... Page 32

... are less than two right angles : but those straight lines which , with another straight line

... are less than two right angles : but those straight lines which , with another straight line

**falling**upon them , make the interior angles on the same side less than two * 12 Ax . right angles , will meet * together if continually ... Page 34

Again , because AB is parallel to CE , and BD

Again , because AB is parallel to CE , and BD

**falls**upon them , the exterior + 29. 1. angle ECD is equal t to the interior and opposite angle ABC : but the angle ACE was shown to be equal to the angle BAČ ; therefore the whole +2 Ax . Page 43

... so that BE be in the same straight line with AB ; and produce FG to H ; and through A draw * AH parallel * 31 . to BG or EF , and join HB . Then , because the straight line HF

... so that BE be in the same straight line with AB ; and produce FG to H ; and through A draw * AH parallel * 31 . to BG or EF , and join HB . Then , because the straight line HF

**falls**upon the parallels AH , * 42 . 1 .### 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 |

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altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole