## The Elements of Euclid |

### From inside the book

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Page 18

Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG

Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG

**common**to the two triangles AFC , AGB ; as be 4. 1 . therefore the base FC is equal to the ... Page 19

1 . equal to AC , the less , and join DC ; thereА fore , because in the triangles DBC , ACB , DB is equal to AC , and BC

1 . equal to AC , the less , and join DC ; thereА fore , because in the triangles DBC , ACB , DB is equal to AC , and BC

**common**to D both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal ... Page 21

Because AD is equal to AE , and D E AF is

Because AD is equal to AE , and D E AF is

**common**to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the sides EA , AF , each to each ; ne base DF is equal to the " ' ; therefore the angle DAF is ty . c to the angle B ... Page 22

Bécause AC is equal to CB , and CD

Bécause AC is equal to CB , and CD

**common**to the two ' triangles ' ACD , BCD ; the two sides AC , CD are equal to BC , CD , each to each ; and the angle AGD is equal to the angle BCD ; therefore the base AD is equal to the base 6 DB ... Page 23

... the angle DBE is equal to the angle EBA ; where . fore the angle DBE is equal to the angle CBE , the less to the greater ; which is impossible ; therefore twostraight lines canA not have a

... the angle DBE is equal to the angle EBA ; where . fore the angle DBE is equal to the angle CBE , the less to the greater ; which is impossible ; therefore twostraight lines canA not have a

**common**segment . PROP . XII . PROB .### 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