The Elements of Euclid |
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Page 29
... given straight lines , of which any two whatever are greater than the third ... line DE terminated at the point D , but un- limited towards E , and b make a ... straight lines A , B , C. See Note . a_20.1 . a 3. 1 . E G H b 3. Post . L ...
... given straight lines , of which any two whatever are greater than the third ... line DE terminated at the point D , but un- limited towards E , and b make a ... straight lines A , B , C. See Note . a_20.1 . a 3. 1 . E G H b 3. Post . L ...
Page 30
... straight line A ; there . fore FK is equal to A : again , because G is the centre of the 15. Def . circle LKH , GH ... given straight lines A , B , C. Which was to be done . a 22. 1 . PROP . XXIII . PROB . AT a given point to a given ...
... straight line A ; there . fore FK is equal to A : again , because G is the centre of the 15. Def . circle LKH , GH ... given straight lines A , B , C. Which was to be done . a 22. 1 . PROP . XXIII . PROB . AT a given point to a given ...
Page 36
... straight line , & c . Q. E. D .. PROP . XXX . THEOR . STRAIGHT lines which are parallel to the same straight line are parallel to one another . Let AB , CD ... straight line EAF is drawn through the given point A parallel to THE ELEMENTS.
... straight line , & c . Q. E. D .. PROP . XXX . THEOR . STRAIGHT lines which are parallel to the same straight line are parallel to one another . Let AB , CD ... straight line EAF is drawn through the given point A parallel to THE ELEMENTS.
Page 45
... given angle D. Which was to be done . PROP . XLIII . THEOR . THE complements ... straight line to apply a parallelogram , which shall be equal to a given ... a 42. 1 . Make a the parallelogram OF EUCLID . 45.
... given angle D. Which was to be done . PROP . XLIII . THEOR . THE complements ... straight line to apply a parallelogram , which shall be equal to a given ... a 42. 1 . Make a the parallelogram OF EUCLID . 45.
Page 47
... straight line GH B C K II M the two straight lines KH , HM , upon the opposite sides of it , make the adjacent ... given rec- tilineal figure ABCD , having the angle FKM equal to the gi ven angle E. Which was to be done . e COR . From this it ...
... straight line GH B C K II M the two straight lines KH , HM , upon the opposite sides of it , make the adjacent ... given rec- tilineal figure ABCD , having the angle FKM equal to the gi ven angle E. Which was to be done . e COR . From this it ...
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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