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

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Page 9

to which the equal sides are opposite , shall be equal each to each , viz . the

to which the equal sides are opposite , shall be equal each to each , viz . the

**angle ABC**to the angle DEF , and the**angle ACB**to DFE . For , if the**triangle ABC**be applied to DEF , so that the point A may be on D , and the straight ... Page 10

Let ABC be a triangle having the

Let ABC be a triangle having the

**angle ABC**equal to the**angle ACB**: the side AB shall be equal to the side AC . For , if AB be not equal to AC , one of them is greater than the other : let AB be the greater ; and from it cut * off DB ... Page 12

Again , because CB is equal t to DB , the angle BDC is equal * to the angle BCD ; but BDC has been proved to be greater ... For , if the

Again , because CB is equal t to DB , the angle BDC is equal * to the angle BCD ; but BDC has been proved to be greater ... For , if the

**triangle ABC**be applied to DEF , so that the point B may be on E , and the straight line BC upon EF ... Page 13

Describe * upon it an equilateral

Describe * upon it an equilateral

**triangle ABC**, and * 1. 1 . bisect * the**angle ACB**.by the straight line CD . AB * 9.1 . shall be cut into two equal parts in the point D. Because AC is equal † to CB , and CD common to the two ... Page 15

CHG ; and they are adjacent angles : but when a straight line , standing on another straight line , makes the adjacent ... Again , because the angle DBA is equal to the two angles VBE , EBA , add to each of these equals the

CHG ; and they are adjacent angles : but when a straight line , standing on another straight line , makes the adjacent ... Again , because the angle DBA is equal to the two angles VBE , EBA , add to each of these equals the

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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