The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 3
... segment of a circle is the figure contained by a " straight line , and the circumference it cuts off . " XX . Rectilineal figures are those which are contained by straight lines . XXI . Trilateral figures , or triangles , by three ...
... segment of a circle is the figure contained by a " straight line , and the circumference it cuts off . " XX . Rectilineal figures are those which are contained by straight lines . XXI . Trilateral figures , or triangles , by three ...
Page 14
... 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 angle ...
... 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 angle ...
Page 55
... segment is that which is contained by the straight line and the circumference . " VIII . An angle in a segment is the angle con- tained by two straight lines drawn from any point in the circumference of the segment to the extremities of ...
... segment is that which is contained by the straight line and the circumference . " VIII . An angle in a segment is the angle con- tained by two straight lines drawn from any point in the circumference of the segment to the extremities of ...
Page 71
... segment BAED : the angles BAD , BED shall be equal to one another . B E 71. 3 . First , let the segment BAED be greater than a semicircle . Take + F , the centre of the circle ABCD , and join BF , FD : and because the angle BFD is at ...
... segment BAED : the angles BAD , BED shall be equal to one another . B E 71. 3 . First , let the segment BAED be greater than a semicircle . Take + F , the centre of the circle ABCD , and join BF , FD : and because the angle BFD is at ...
Page 72
... segments must fall within the other : let ACB fall within ADB : draw the straight line BCD , and join CA , DA . And because the segment ACB is similar to the segment ADB , and that similar seg- ments of circles contain * equal angles ...
... segments must fall within the other : let ACB fall within ADB : draw the straight line BCD , and join CA , DA . And because the segment ACB is similar to the segment ADB , and that similar seg- ments of circles contain * equal angles ...
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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