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

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Page 13

**PROP**. IX . PROB . A To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle ; it is required to bisect it . Take any point D in AB , and from AC cut * off AE 3. Page 18

Q. E. D.

Q. E. D.

**PROP**. XVII . THEOR . A * 16 , 1 . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles together shall be less than two right angles . Page 19

B

B

**PROP**. XX . THEOR . D * 3.1 . B * 5. 1 . Any two sides of a triangle are together greater than the See N. third side . Let ABC be a triangle : any two sides of it together shall be greater than the third side , viz . the sides BA ... Page 21

... FG , GK , equal to the three given straight lines A , B , C. Which was to be done .

... FG , GK , equal to the three given straight lines A , B , C. Which was to be done .

**PROP**. XXIII . PROB . . * 22. 1 . At a given point in a given straight line , to make a rectilineal angle equal to a given rectilineal angle . Page 27

C

C

**PROP**. XXXI . PROB . To draw a straight line through a given point parallel to a given straight line . Let A be the given point , and BC the given straight line ; it is required to draw a straight line through the point A , parallel ...### 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