## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |

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**angle**BAC**equal**to the**angle**EDF , the base BC shall be**equal**to the base EF ; and the triangle ABC to the triangle DEF ; and the other**angles**, to which the**equal**sides are opposite , shall be**equal**each to each , viz . the R**angle**ABC to ... Page 16

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**equal**to the two GA , AB , each to each ; and they contain the**angle**FAG common to the two triangles AFC , AGB ; therefore the base FC is**equal**( 4. 1. ) to the base GB , and the triangle AFC to the triangle AGB ; and the remaining**angles**... Page 19

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**equal**to EF ; therefore BC coin- ciding with EF , BA and AC shall coincide with ED and DF ; for , if the base BC ...**angles**. it . Let BAC be the given rectilineal**angle**, it is required to bisect A Take any point D in AB , and from AC cut ( ... Page 20

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**equal**parts in the point D. Which was to be done . C A D B PROP . XI . PROB . To draw a straight line at right**angles**to a given straight line , from a given point in the same . Let AB be a given straight line , and C a point given in ... Page 21

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**angles**FHC , GHC , the two sides FH , HC are**equal**to the two GH , HC , each to each ; and the base CF is**equal**( 15. Def . 1. ) to the base CG ; therefore the**angle**CHF is ...**angle**CBA be**equal**to ABD BOOK I. 21 THE ELEMENTS OF EUCLID .### Other editions - View all

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |

### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore