The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 34
... parallelogram ABCD and the triangle EBC be upon the same base BC , and between the same parallels BC , AE : the parallelogram ABCD shall be double of the triangle EBC . * DE Join AC : then the triangle ABC is equal to the triangle EBC ...
... parallelogram ABCD and the triangle EBC be upon the same base BC , and between the same parallels BC , AE : the parallelogram ABCD shall be double of the triangle EBC . * DE Join AC : then the triangle ABC is equal to the triangle EBC ...
Page 35
... parallelograms which are about the diameter of any parallelogram , are equal to one another . E A H Let ABCD be a parallelogram , of which the diameter is AC ; and EH , GF parallelograms about AC , that is , through which AC passes ...
... parallelograms which are about the diameter of any parallelogram , are equal to one another . E A H Let ABCD be a parallelogram , of which the diameter is AC ; and EH , GF parallelograms about AC , that is , through which AC passes ...
Page 36
... parallelogram , of which the diameter is HK , and AG , ME are parallelograms about HK ; and LB , BF are the complements : therefore LB is equal to BF : but BF is equal to the triangle C : wherefore LB is equal + to the triangle C : and ...
... parallelogram , of which the diameter is HK , and AG , ME are parallelograms about HK ; and LB , BF are the complements : therefore LB is equal to BF : but BF is equal to the triangle C : wherefore LB is equal + to the triangle C : and ...
Page 37
... parallelogram HFt , 1 . and the triangle DBC to the parallelogram GM ; the + Constr . whole rectilineal figure ABCD is equal † to the whole +2 Ax . parallelogram KFLM . Therefore the parallelogram KFLM has been described equal to the ...
... parallelogram HFt , 1 . and the triangle DBC to the parallelogram GM ; the + Constr . whole rectilineal figure ABCD is equal † to the whole +2 Ax . parallelogram KFLM . Therefore the parallelogram KFLM has been described equal to the ...
Page 38
... parallelogram that has one right angle , has all its angles right angles . PROP . XLVII . THEOR . In any right - angled triangle , the square which is described upon the side subtending the right angle , is equal to the squares ...
... parallelogram that has one right angle , has all its angles right angles . PROP . XLVII . THEOR . In any right - angled triangle , the square which is described upon the side subtending the right angle , is equal to the squares ...
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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