## 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 |

### From inside the book

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**less**" than two right angles , these straight lines being continual- " ly produced , shall at length meet upon that side on which " are the angles which are**less**than two right angles . See " the notes on prop . 29. of Book I ... Page 17

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**less**, and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ... Page 25

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**less**than two right angles . Therefore any two angles , & c . Q. E. D .. 1 PROP . XVIII . THEOR . THE greater side ...**less**than it ; it is not equal , because then the angle . ABC would be equal ( 5. 1. ) to the an- gle ACB ; but it is ... Page 26

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**less**than the other two sides of the triangle , but shall contain a greater angle . * Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are**less**... Page 30

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**less**; because then the base BC would be**less**( 24. 1. ) than the base EF ; but it is not ; therefore the angle BAC is not**less**than the angle EDF ; and it was shown that it is not equal to it ; therefore the angle BAC is greater than ...### 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