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

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Page 8

From the

From the

**greater**of two given straight lines to cut off a part equal to the less . Let AB and C be the two given straight lines , whereof AB is the**greater**. It is required to cut off from AB , Е В the**greater**, a part equal to C ... Page 11

1 . each ; and the angle DBC is equal to the anglet ACB ; + Hyp . therefore the base DC is equal to the base AB , and the triangle DBC is equal to the triangle * ACB , the less to the

1 . each ; and the angle DBC is equal to the anglet ACB ; + Hyp . therefore the base DC is equal to the base AB , and the triangle DBC is equal to the triangle * ACB , the less to the

**greater**, which is absurd . Page 17

Let ABC be a triangle , and let its side BC be produced to D : the exterior angle ACD shall be

Let ABC be a triangle , and let its side BC be produced to D : the exterior angle ACD shall be

**greater**than either of the interior opposite angles CBA , BAC . Bisect * AC in E , join BE and produce it to F , and make EF equalt to BE ... Page 18

1 . that the angle BCG , that is , the angle * ACD , is

1 . that the angle BCG , that is , the angle * ACD , is

**greater**than the angle ABC . Therefore , if one side , & c . Q. E. D. PROP . XVII . THEOR . A * 16 , 1 . Any two angles of a triangle are together less than two right angles . Page 19

**greater**than the angle BCA : the side AC shall be**greater**than the side ÅB . For , if it be not**greater**, AC must either be equal to AB , or less than it : it is not equal , because then the angle ABC would be equal * to the angle CAB ...### 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 |

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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