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

### From inside the book

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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 B 3 BOOK I. - DEFINITIONS . 5 XXX. ... Page 30

Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles AEF , EFD equal to one another : AB shall be

Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles AEF , EFD equal to one another : AB shall be

**parallel**to CD . For , if it be not**parallel**, AB and CD being produced will meet either ... Page 31

angle EGB equal to the interior and opposite angle GHD upon the same side ; or make the interior E angles on the same side G BGH , GHD together equal AB to two right angles : AB C-D shall be

angle EGB equal to the interior and opposite angle GHD upon the same side ; or make the interior E angles on the same side G BGH , GHD together equal AB to two right angles : AB C-D shall be

**parallel**to CD . H Because the angle EGB is ... Page 32

Ax . right angles , will meet * together if continually produced ; therefore the straight lines AB , CD , if produced far enough , will meet : but they position never meet , since they are

Ax . right angles , will meet * together if continually produced ; therefore the straight lines AB , CD , if produced far enough , will meet : but they position never meet , since they are

**parallel**by the hypothesis ; therefore the ... Page 33

is equal to the angle GHF ; therefore also AGK is equal * to GKD : and they are alternate +1 Ax . angles ; therefore AB is

is equal to the angle GHF ; therefore also AGK is equal * to GKD : and they are alternate +1 Ax . angles ; therefore AB is

**parallel*** to CD . * 27. 1 . Wherefore , straight lines , & c . Q. E. D. PROP . XXXI . PROB .### 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

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 equimultiples 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 Q. E. D. PROP ratio reason 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