The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 8
... to DF ; and the angle BAC equal to the angle EDF : the AA CE base BC shall be equal to the base EF ; and the tri- angle ABC to the triangle DEF ; and the other angles A 1 to which the equal sides are opposite , shall 8 EUCLID'S ELEMENTS .
... to DF ; and the angle BAC equal to the angle EDF : the AA CE base BC shall be equal to the base EF ; and the tri- angle ABC to the triangle DEF ; and the other angles A 1 to which the equal sides are opposite , shall 8 EUCLID'S ELEMENTS .
Page 9
... 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 line AB upon DE ; the point B shall coincide with the point E , because AB is equal ...
... 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 line AB upon DE ; the point B shall coincide with the point E , because AB is equal ...
Page 10
... angle ACF to the angle ABG , and the angle AFC to the an- gle AGB : and because the whole AF is equal to the whole ... ABC is equal + to the remaining angle ACB , which are the angles at the base of the triangle ABC : and it has also ...
... angle ACF to the angle ABG , and the angle AFC to the an- gle AGB : and because the whole AF is equal to the whole ... ABC is equal + to the remaining angle ACB , which are the angles at the base of the triangle ABC : and it has also ...
Page 12
... angle BDC is equal to the angle BCD ; but BDC has been proved to be greater than the same BCD ; which is impossible ... ABC , DEF be two triangles , having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB to DE ...
... angle BDC is equal to the angle BCD ; but BDC has been proved to be greater than the same BCD ; which is impossible ... ABC , DEF be two triangles , having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB to DE ...
Page 15
... angle CHF is equal to the angle 8. 1 . CHG ; and they are adjacent angles : but when a straight line , standing on ... ABC ; therefore the angles DBA , ABC are equal to the three angles DBE , EBA , † 2 Ax . ABC : but the angles CBE , EBD ...
... angle CHF is equal to the angle 8. 1 . CHG ; and they are adjacent angles : but when a straight line , standing on ... ABC ; therefore the angles DBA , ABC are equal to the three angles DBE , EBA , † 2 Ax . ABC : but the angles CBE , EBD ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr 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 logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn 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