The Elements of Euclid |
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Page 28
... less than the other two sides of the tri- angle , but shall contain a greater angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are less ...
... less than the other two sides of the tri- angle , but shall contain a greater angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are less ...
Page 32
... less ; because then the base BC would be less b than the base EF ; but it is not ; there- fore the angle BAC A B D E is not less than the angle EDF ; and it was shown that it is not equal to it ; therefore the angle BAC is greater than ...
... less ; because then the base BC would be less b than the base EF ; but it is not ; there- fore the angle BAC A B D E is not less than the angle EDF ; and it was shown that it is not equal to it ; therefore the angle BAC is greater than ...
Page 46
... less than two right angles : but straight lines which with another straight line make the interior angles upon d 12. Ax . the same side less than two right angles , do meet if produced far enough : therefore HB , FE shall meet , if ...
... less than two right angles : but straight lines which with another straight line make the interior angles upon d 12. Ax . the same side less than two right angles , do meet if produced far enough : therefore HB , FE shall meet , if ...
Page 72
... less to the greater , which is impos- sible : therefore E is not the centre of the circles ABC , CDG . Where- fore , if two circles , & c . Q. E. D. D F E B 34 PROP . VI . THEOR . IF two cireles touch one another internally , they shall ...
... less to the greater , which is impos- sible : therefore E is not the centre of the circles ABC , CDG . Where- fore , if two circles , & c . Q. E. D. D F E B 34 PROP . VI . THEOR . IF two cireles touch one another internally , they shall ...
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 ...
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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