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

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Page 10

AB to DE , and AC to DF ; CE F the angle BAC equal to the angle EDF , the

AB to DE , and AC to DF ; CE F the angle BAC equal to the angle EDF , the

**base BC**shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite , shall be equal ... Page 12

... and the

... and the

**base BC**is common to the two triangles BFC , CGB ; wherefore these triangles are equal * , and their remaining angles each to each , to which the equal sides are opposite : therefore the angle FBC is equal to the angle GCB ... Page 13

mon to both , the two sides , DB ,

mon to both , the two sides , DB ,

**BC**are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle + ACB ; therefore the fIlyp .**base**DC is equal to the**base**AB , and the triangle DBC is equal to the triangle ... Page 14

Therefore , upon the same

Therefore , upon the same

**base**, and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of ... AB to DE , and AC to DF ; and also the**base**A D G**BC**equal to the**base**EF . Page 15

Therefore BC coinciding with EF , BA and AC shall coincide with ED and DF : for , if the

Therefore BC coinciding with EF , BA and AC shall coincide with ED and DF : for , if the

**base BC**coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation as EG ...### What people are saying - Write a review

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### 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

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