The Elements of Euclid |
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Page 75
... less than the more remote , viz . DK than DL , and DL than DH . : 2 c H D LK GBN € 24. 1 . M d 4. Ax . Take M the ... less than KD : and because MK , DK are drawn to the point K within the triangle MLD from M , D , the extremi- ties of ...
... less than the more remote , viz . DK than DL , and DL than DH . : 2 c H D LK GBN € 24. 1 . M d 4. Ax . Take M the ... less than KD : and because MK , DK are drawn to the point K within the triangle MLD from M , D , the extremi- ties of ...
Page 80
... less . Let ABCD be a circle , of which the diameter is AD , and the centre E ; and let BC be nearer to the centre than FG ; AD is greater than any straight line BC . which is not a diameter , and BC greater than FG . From the centre ...
... less . Let ABCD be a circle , of which the diameter is AD , and the centre E ; and let BC be nearer to the centre than FG ; AD is greater than any straight line BC . which is not a diameter , and BC greater than FG . From the centre ...
Page 81
... less than the square of EK , because EH is less than EK ; therefore the square of BH is greater than the square of FK , and the straight line BH greater than FK ; and therefore BC is greater than FG ... Next , let BC be greater than FG ...
... less than the square of EK , because EH is less than EK ; therefore the square of BH is greater than the square of FK , and the straight line BH greater than FK ; and therefore BC is greater than FG ... Next , let BC be greater than FG ...
Page 82
... less than a right angle : DA is greater than DG : but DA is equal to DH ; therefore DH is greater than DG , the less than the greater , which is impossible : therefore . straight line can be drawn from the point A between AE and the ...
... less than a right angle : DA is greater than DG : but DA is equal to DH ; therefore DH is greater than DG , the less than the greater , which is impossible : therefore . straight line can be drawn from the point A between AE and the ...
Page 89
... less than a semicir- cle ; but if the angle ABD be less than BAD , the centre E falls within the segment ABC , which is therefore greater than a semicircle : wherefore a segment of a circle being given , the circle is described of which ...
... less than a semicir- cle ; but if the angle ABD be less than BAD , the centre E falls within the segment ABC , which is therefore greater than a semicircle : wherefore a segment of a circle being given , the circle is described of which ...
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Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid 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 pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore