The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 24
... wherefore BC is not unequal to EF , that is , it is equal to it : and AB is equal + to DE ; therefore the two , AB , BC are equal to the two DE , EF , each to each ; and they contain + equal angles ; wherefore the base AC is equal to ...
... wherefore BC is not unequal to EF , that is , it is equal to it : and AB is equal + to DE ; therefore the two , AB , BC are equal to the two DE , EF , each to each ; and they contain + equal angles ; wherefore the base AC is equal to ...
Page 31
... wherefore AD is equal to * 1 Ax . EF ; and DE is common ; therefore the whole , or the remainder , AE is equal to the whole , or the remainder DF : AB also is equal + to DC ; therefore the two EA , AB are equal to the two FD , DC , each ...
... wherefore AD is equal to * 1 Ax . EF ; and DE is common ; therefore the whole , or the remainder , AE is equal to the whole , or the remainder DF : AB also is equal + to DC ; therefore the two EA , AB are equal to the two FD , DC , each ...
Page 32
... Wherefore triangles , & c . Q. E. D. • PROP . XXXVIII . THEOR . Triangles upon equal bases , and between the same paral- lels , are equal to one another . Let the triangles ABC , DEF be upon equal bases BC , EF , and between the same ...
... Wherefore triangles , & c . Q. E. D. • PROP . XXXVIII . THEOR . Triangles upon equal bases , and between the same paral- lels , are equal to one another . Let the triangles ABC , DEF be upon equal bases BC , EF , and between the same ...
Page 43
... wherefore the angle CGB is equal + to the angle CBG ; and therefore the side BC is equal to the side CG : but CB is equal also to GK , and CG H to BK ; wherefore the figure CGKB is + equilateral : it is likewise rectangular ; for ...
... wherefore the angle CGB is equal + to the angle CBG ; and therefore the side BC is equal to the side CG : but CB is equal also to GK , and CG H to BK ; wherefore the figure CGKB is + equilateral : it is likewise rectangular ; for ...
Page 45
... Wherefore , if a straight line , & c . Q. E. D. PROP . VII . THEOR . If a straight line be divided into any two parts , the squares of the whole line , and of one of the parts , are equal to twice the rectangle contained by the whole ...
... Wherefore , if a straight line , & c . Q. E. D. PROP . VII . THEOR . If a straight line be divided into any two parts , the squares of the whole line , and of one of the parts , are equal to twice the rectangle contained by the whole ...
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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