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

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Page 9

Because AF is equal to + AG , and AB to | AC , the + Constr . two sides FA , AC are equal to the two GA , AB , each $ Hyp . to each : and they contain the angle FAG

Because AF is equal to + AG , and AB to | AC , the + Constr . two sides FA , AC are equal to the two GA , AB , each $ Hyp . to each : and they contain the angle FAG

**common**to ** 3. 1 . 1 А В , C * 4. 1 . FA G BOOK I. PROP . IV . V. 9. Page 10

... and the base BC is

... and the base BC is

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

Because AD is equal + to AE , and AF is

Because AD is equal + to AE , and AF is

**common**to the two triangles DAF , EAF ; the two sides DA , AF , are equal B F to the two sides EA , AF , each to each ; and the base DF is equal + to the base EF ; therefore + Constr . the angle ... Page 14

Because DC is equal t to CE , and FC

Because DC is equal t to CE , and FC

**common**to the two triangles DCF , ECF ; the two sides DC , CF , are equal to the two EC , CF , each to each ; and the base DF is equal t to the base EF ; therefore the angle DCF is equal * to the ... Page 15

HC

HC

**common**to the two triangles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the base CF is equal * to the base * 15 Def . CG : therefore the angle CHF is equal * to the angle * 8. 1 .### 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