## The Elements of Euclid |

### From inside the book

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Page 17

AB to DE , and AC to DF ; A D Book I. and the angle BAC equal to the angle ÉDF , the

AB to DE , and AC to DF ; A D Book I. and the angle BAC equal to the angle ÉDF , 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 ... Page 18

1 . therefore the

1 . therefore the

**base**FC is equal to the**base**GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one pie jare equal to the remaining an- ja B C gles of the other , each to each , to which the equal sides ... Page 19

B с Wherefore , if two angles , & c , Q. E. D. Cox , Hence every equiangular triangle is also equilateral PROP . VII . THEOR . UPON the same

B с Wherefore , if two angles , & c , Q. E. D. Cox , Hence every equiangular triangle is also equilateral PROP . VII . THEOR . UPON the same

**base**, and on the same side of it , there cannot be two triangles that have their sides which ... Page 20

E fore , because AC is equal to AD in the triangle ACD , the angles ECD , FDC F upon the other side of the

E fore , because AC is equal to AD in the triangle ACD , the angles ECD , FDC F upon the other side of the

**base**CD are C a 5. 1 . equal to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is ... Page 21

BC is equal to EF ; therefore BC coinciding with EF , BA and Book I. AC shall coincide with ED and DF ; for , if the

BC is equal to EF ; therefore BC coinciding with EF , BA and Book I. 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 ...### What people are saying - Write a review

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### Other editions - View all

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid No preview available - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prisms produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole