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

### From inside the book

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Page 9

... and C with F , if the base BC does not coincide with the base EF , two straight . lines would inclose a space , which is impossible . * There- * 10 Ax .

... and C with F , if the base BC does not coincide with the base EF , two straight . lines would inclose a space , which is impossible . * There- * 10 Ax .

**fore**the base BC coincides with the base EF , and therefore is equal t to it . Page 15

... standing on another straight line , makes the adjacent angles equal to one another , each of them is a right angle , and the straight line which stands upon the other , is called a perpendicular + to it : there- +10 Def .

... standing on another straight line , makes the adjacent angles equal to one another , each of them is a right angle , and the straight line which stands upon the other , is called a perpendicular + to it : there- +10 Def .

**fore**... Page 22

... and ACť to DG , the + Constr . two sides , BA , AC are equal to the two ED , DG , each to each , and the angle BAC is + Constr . equalt to the angle EDG ; there* 4.1 .

... and ACť to DG , the + Constr . two sides , BA , AC are equal to the two ED , DG , each to each , and the angle BAC is + Constr . equalt to the angle EDG ; there* 4.1 .

**fore**the base BC is equal * to the base EG . Page 25

Because the angle EGB is equalt to the angle GHD , + Hyp . and the angle EGB is equal * to the angle AGH , there- * 15.1 .

Because the angle EGB is equalt to the angle GHD , + Hyp . and the angle EGB is equal * to the angle AGH , there- * 15.1 .

**fore**the angle AGH is equalt to the angle GHD : and +1 Ax . they are the alternate angles ; therefore AB is ... Page 30

... and BC meets them , the alternate angles ABC , BCD , are equal * to one another : and because AC is parallel to BD , and BC meets them , the alternate angles ACB , CBD , are equal " to one another : where

... and BC meets them , the alternate angles ABC , BCD , are equal * to one another : and because AC is parallel to BD , and BC meets them , the alternate angles ACB , CBD , are equal " to one another : where

**fore**the two triangles ABC ...### 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