The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 9
... , GB . Because AF is equal to † AG , and AB to ‡ AC , the + Constr . two sides FA , AC are equal to the two GA , AB , each to each : and they contain the angle FAG common to Hyp . * 4 . 1 . * 3 Ax . * BOOK I. PROP . IV . V. 9.
... , GB . Because AF is equal to † AG , and AB to ‡ AC , the + Constr . two sides FA , AC are equal to the two GA , AB , each to each : and they contain the angle FAG common to Hyp . * 4 . 1 . * 3 Ax . * BOOK I. PROP . IV . V. 9.
Page 10
... common to the two triangles BFC , CGB ; wherefore these triangles are equal , * and their remaining angles each to each , to which the equal sides are opposite : therefore the angle FBC is equal to the angle GCB , and the angle BCF to ...
... common to the two triangles BFC , CGB ; wherefore these triangles are equal , * and their remaining angles each to each , to which the equal sides are opposite : therefore the angle FBC is equal to the angle GCB , and the angle BCF to ...
Page 13
... common to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; and the base DF is equal to the base EF ; therefore + Constr . the angle DAF is equal to the angle EAF : wherefore 8.1 ...
... common to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; and the base DF is equal to the base EF ; therefore + Constr . the angle DAF is equal to the angle EAF : wherefore 8.1 ...
Page 14
... common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B draw + BE at right angles to AB ; and because ABC is a straight line , the angle CBE is equal to the ...
... common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B draw + BE at right angles to AB ; and because ABC is a straight line , the angle CBE is equal to the ...
Page 15
... common to the two triangles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the base CF is equal to the base * 15 Def . CG : therefore the angle CHF is equal to the angle 8. 1 . CHG ; and they are ...
... common to the two triangles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the base CF is equal to the base * 15 Def . CG : therefore the angle CHF is equal to the angle 8. 1 . CHG ; and they are ...
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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