The Elements of Euclid: Viz. the First Six Books Together, with the Eleventh and Twelfth ... Also the Book of Euclid's Data ...A. & J. Duncan for Bell & Bradfute, 1817 - 538 σελίδες |
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Σελίδα 16
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal ...
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal ...
Σελίδα 17
... wherefore also the point C shall coincide with the point F , because the straight line AC is equal to DF : but the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF , because the point B ...
... wherefore also the point C shall coincide with the point F , because the straight line AC is equal to DF : but the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF , because the point B ...
Σελίδα 21
... wherefore likewise the angle BAC coincides with the angle EDF , and is equal to it . Therefore if two triangles , & c . b s . Ax . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to di- vide it into two equal ...
... wherefore likewise the angle BAC coincides with the angle EDF , and is equal to it . Therefore if two triangles , & c . b s . Ax . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to di- vide it into two equal ...
Σελίδα 33
... wherefore also the angle BCG is equal to the angle BCA , the less to the greater , which is im- possible ; therefore ... wherefore BC is not unequal to EF , b 16. 1 . that is , it is equal to it ; and AB is equal to DE ; therefore the ...
... wherefore also the angle BCG is equal to the angle BCA , the less to the greater , which is im- possible ; therefore ... wherefore BC is not unequal to EF , b 16. 1 . that is , it is equal to it ; and AB is equal to DE ; therefore the ...
Σελίδα 36
... Wherefore , if a straight , & 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 be each of them parallel to EF , AB is also pa- rallel to CD . a Let ...
... Wherefore , if a straight , & 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 be each of them parallel to EF , AB is also pa- rallel to CD . a Let ...
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altitude angle ABC angle BAC arch 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 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 meet multiple opposite parallel parallelogram perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third tiple triangle ABC vertex wherefore