The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 29
... shewn 27.1 . to be equal to it . Therefore , straight lines , & c . Q. E. D. PROP . XXXIV . THEOR . The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into ...
... shewn 27.1 . to be equal to it . Therefore , straight lines , & c . Q. E. D. PROP . XXXIV . THEOR . The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into ...
Page 30
... shewn to be equal to the angle BDC ; therefore the opposite sides and angles of parallelograms are equal to one another . Also , their diameter bisects them : for AB being equal to CD , and BC common , the two AB , BC are equal to the ...
... shewn to be equal to the angle BDC ; therefore the opposite sides and angles of parallelograms are equal to one another . Also , their diameter bisects them : for AB being equal to CD , and BC common , the two AB , BC are equal to the ...
Page 59
... shewn to be equal to EF ; therefore EF is equal to EG , the less to the greater , which is impossible . Therefore D +15 Def . 1 . † 15 Def . 1 . E † 1 Ax . E is not the centre of the circles ABC , CDG . Where- fore , if two circles ...
... shewn to be equal to EF ; therefore EF is equal to EG , the less to the greater , which is impossible . Therefore D +15 Def . 1 . † 15 Def . 1 . E † 1 Ax . E is not the centre of the circles ABC , CDG . Where- fore , if two circles ...
Page 62
... shewn , that DL is less than DH . Therefore DG is the least , and DK less than DL , and DL less than DH . Also there can be drawn only two equal straight lines from the point D to the circumference , one upon each side of the least line ...
... shewn , that DL is less than DH . Therefore DG is the least , and DK less than DL , and DL less than DH . Also there can be drawn only two equal straight lines from the point D to the circumference , one upon each side of the least line ...
Page 66
... shewn to be double of AF , and CD double of CG ; wherefore AB is equal + to CD . There- fore equal straight lines , & c . Q. E. D. + Hyp . † 3 Ax . † 6 Ax . See N. † 12. 1 . PROP . XV . THEOR . The diameter is the greatest straight line ...
... shewn to be double of AF , and CD double of CG ; wherefore AB is equal + to CD . There- fore equal straight lines , & c . Q. E. D. + Hyp . † 3 Ax . † 6 Ax . See N. † 12. 1 . PROP . XV . THEOR . The diameter is the greatest straight line ...
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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