## The Elements of Euclid |

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Page 16

IF two triangles have two sides of the one equal to two sides of the other , each to each ; and have likc . wise the angles contained by those sides equal to one another ; they shall likewise bave their bases , or

IF two triangles have two sides of the one equal to two sides of the other , each to each ; and have likc . wise the angles contained by those sides equal to one another ; they shall likewise bave their bases , or

**third**sides , equal ... Page 28

ANY two sides of a triangle are together greater Soe Nate . than the

ANY two sides of a triangle are together greater Soe Nate . than the

**third**side . a 3. 1 . F b 5. 1 . Let ABC be a triangle ; any two sides of it together are greater than the**third**side , viz . the sides BA , AC greater than the « side ... Page 29

Therefore , if from the ends of , & c . Q. E. D. 3 PROP . XXII . PROB . ។ See Note . TO make a triangle of which the sides shall be equal to three giyen straight lines , but any two whatever of these must be greater than the

Therefore , if from the ends of , & c . Q. E. D. 3 PROP . XXII . PROB . ។ See Note . TO make a triangle of which the sides shall be equal to three giyen straight lines , but any two whatever of these must be greater than the

**third**. a ... Page 32

AB to DE , and AC to DF : and the

AB to DE , and AC to DF : and the

**third**angle BAC to the**third**, angle EDF . For , if AB be not B с Е equal to DE , one of them must be the greater . Let AB be the greater of the two , and make BG equal to DE and join GC ; therefore ... Page 33

... equal to the angle DEF ; the base therefore AC is equal a to the base D ?, and the

... equal to the angle DEF ; the base therefore AC is equal a to the base D ?, and the

**third**angle BAC to the**third**angle EDF . Next , let the sides A D which are opposite to equal angles in each triangle be equal to one another , viz .### 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