## The Elements of Euclid |

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Page 16

**Wherefore**from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . sh E NO th 11 Y a A 1 В 2 с # 2 21 PROP . III . PROB . t + FROM the greater of two given straight lines to ... Page 17

**Wherefore**the whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the ... Page 21

... therefore , if the basc BC coincides with a 7.1 . the base ÉF , the sides BA , AC cannot but coincide with the sides ED , DF ;

... therefore , if the basc BC coincides with a 7.1 . the base ÉF , the sides BA , AC cannot but coincide with the sides ED , DF ;

**wherefore**likewise the angle BAC coincides . with the angle EDF , and is equal to it . Page 33

... and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GSB is equal to the angle DFE ; but DFE is , by the hypothesis , equal to the angle BCA ;

... and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GSB is equal to the angle DFE ; but DFE is , by the hypothesis , equal to the angle BCA ;

**wherefore**also the angle ... Page 42

**Wherefore**triangles , & c . Q. E. D. PROP . XXXVIII . THEOR . TRIANGLES upon equal bases , and between the same parallels , are equal to one another . a 31. 1 . H. b 36. 1 . Let the triangles ABC , DEF be upon equal bases BC , EF , and ...### 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