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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Αποτελέσματα 1 - 5 από τα 78.
Σελίδα 17
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz.the angle ABC to ...
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz.the angle ABC to ...
Σελίδα 20
... angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is ... BAC is e- qual to the angle EDF . For , if the tri- D G angle ABC be ap- plied to DEF , so B that the point B CE F be ...
... angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is ... BAC is e- qual to the angle EDF . For , if the tri- D G angle ABC be ap- plied to DEF , so B that the point B CE F be ...
Σελίδα 21
... 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 angles . Let BAC be ...
... 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 angles . Let BAC be ...
Σελίδα 26
... angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior oppositeangles CBA , BAC . Bisecta ACinE , join ...
... angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior oppositeangles CBA , BAC . Bisecta ACinE , join ...
Σελίδα 27
... BAC . ACB , as also CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. PROP . XVIII . THEOR . THE greater side of every triangle is opposite to the greater angle ... angle ABCis also greater than the ...
... BAC . ACB , as also CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. PROP . XVIII . THEOR . THE greater side of every triangle is opposite to the greater angle ... angle ABCis also greater than the ...
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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