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

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Page 15

CHG ; and they are adjacent angles : but when a straight line , standing on another straight line , makes the adjacent ... Again , because the angle DBA is equal to the two angles VBE , EBA , add to each of these equals the

CHG ; and they are adjacent angles : but when a straight line , standing on another straight line , makes the adjacent ... Again , because the angle DBA is equal to the two angles VBE , EBA , add to each of these equals the

**angle ABC**... Page 18

1 . that the angle BCG , that is , the angle * ACD , is greater than the

1 . that the angle BCG , that is , the angle * ACD , is greater than the

**angle ABC**. Therefore , if one side , & c . Q. E. D. PROP . XVII . THEOR . A * 16 , 1 . Any two angles of a triangle are together less than two right angles . Page 19

greater than the angle BCA : the side AC shall be greater than the side ÅB . ... AB : neither is it less ; because then the

greater than the angle BCA : the side AC shall be greater than the side ÅB . ... AB : neither is it less ; because then the

**angle ABC**would be less than the**angle ACB**; but it is not ; therefore the side AC is not less than AB : and it ... Page 24

... therefore the two AB , BC are equal to the two DE , EF , each to each ; and the

... therefore the two AB , BC are equal to the two DE , EF , each to each ; and the

**angle ABC**is equalt to the angle DEF ... Next , let the sides which are opposite to equal angles in each triangle be equal to one another , viz . Page 28

Again , because AB is parallel tó CË , and BD falls upon them , the exterior angle ECD is equal + to the interior and opposite

Again , because AB is parallel tó CË , and BD falls upon them , the exterior angle ECD is equal + to the interior and opposite

**angle ABC**: but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exterior angle ACD ...### 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