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

### From inside the book

Results 1-5 of 100

Page 8

1 Ax . that BC is equal to BG ;

1 Ax . that BC is equal to BG ;

**wherefore**AL and BC are each of them equal to BG : and things that are equal to the same thing are equalt to one another ; therefore the straight line AL is equal to BC .**Wherefore**from the given point A ... Page 9

DE , AC shall coincide with DF , because the angle BAC is equal t to the angle EDF ;

DE , AC shall coincide with DF , because the angle BAC is equal t to the angle EDF ;

**wherefore**also the + Hyp . point C shall coincide with the point F , because the straight line AC + is equal to DF : but the point B was + Hyp . proved ... Page 14

But when the adjacent angles which one straight line makes with another straight line , are equal to one another , each of them is called a right * angle ; therefore each of the angles DCF , ECF , is a right angle .

But when the adjacent angles which one straight line makes with another straight line , are equal to one another , each of them is called a right * angle ; therefore each of the angles DCF , ECF , is a right angle .

**Wherefore**, from the ... Page 17

Again , because the straight line DE makes with AB the angles AED , DEB , these also are together equal to two right angles ; and CEA , AED have been demonstrated to be equal to two right angles ;

Again , because the straight line DE makes with AB the angles AED , DEB , these also are together equal to two right angles ; and CEA , AED have been demonstrated to be equal to two right angles ;

**wherefore**the angles CEA , AED are ... Page 24

... which is impossible * :

... which is impossible * :

**wherefore**BC is not unequal to EF , that is , it is equal to it : and AB is equal to DE ... equal angles ;**wherefore**the base AC is equal + to the base DF , and the third angle BAC to the third angle EDF .### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

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