The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 17
... opposite angles . Let ABC be a triangle , and let its side BC be produced to D : the exterior angle ACD shall be greater than either of the interior opposite angles CBA , BAC . Bisect * AC in E , join BE and pro- duce it to F , and make ...
... opposite angles . Let ABC be a triangle , and let its side BC be produced to D : the exterior angle ACD shall be greater than either of the interior opposite angles CBA , BAC . Bisect * AC in E , join BE and pro- duce it to F , and make ...
Page 18
... opposite angle ABC ; to each of these add the angle ACB ; therefore the angles ACD , ACB are greater + than the angles ABC , ACB : but ACD , ACB are together equal to two right angles ; therefore the angles ABC , BCA- are less than two ...
... opposite angle ABC ; to each of these add the angle ACB ; therefore the angles ACD , ACB are greater + than the angles ABC , ACB : but ACD , ACB are together equal to two right angles ; therefore the angles ABC , BCA- are less than two ...
Page 20
... opposite angle , the exte- rior angle BDC of the triangle CDE is greater than CED : for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC : and it has been demonstrated , that the angle BDC is greater than ...
... opposite angle , the exte- rior angle BDC of the triangle CDE is greater than CED : for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC : and it has been demonstrated , that the angle BDC is greater than ...
Page 23
... opposite to equal angles in each ; then shall the other sides be equal , each to each , and also the third angle of the one to the third angle of the other . D Let ABC , DEF be two triangles which have the angles ABC , BCA equal to the ...
... opposite to equal angles in each ; then shall the other sides be equal , each to each , and also the third angle of the one to the third angle of the other . D Let ABC , DEF be two triangles which have the angles ABC , BCA equal to the ...
Page 24
... opposite to equal angles in each triangle be equal to one another , viz . AB to DE : likewise in this case , the other sides shall be equal , AC to DF , and BC to EF ; and also the third angle BAC to the third angle EDF . For , if BC be ...
... opposite to equal angles in each triangle be equal to one another , viz . AB to DE : likewise in this case , the other sides shall be equal , AC to DF , and BC to EF ; and also the third angle BAC to the third angle EDF . For , if BC be ...
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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