The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 104
... excess of the first above the second , is to the second , as the excess of the third above the fourth , is to the fourth . Prop . Book 5 . XVII . 17th Convertendo , by conversion ; when there are four pro- portionals , and it is ...
... excess of the first above the second , is to the second , as the excess of the third above the fourth , is to the fourth . Prop . Book 5 . XVII . 17th Convertendo , by conversion ; when there are four pro- portionals , and it is ...
Page 124
... excess above the fourth . Let AB be to BE , as CD to DF : then BA shall be to AE , as DC to CF. Because AB is to BE , as CD to DF , there- fore by division * , AE is to EB , as CF to FD ; and by inversion * , BE is to EA , as DF to FC ...
... excess above the fourth . Let AB be to BE , as CD to DF : then BA shall be to AE , as DC to CF. Because AB is to BE , as CD to DF , there- fore by division * , AE is to EB , as CF to FD ; and by inversion * , BE is to EA , as DF to FC ...
Page 128
... excess of the first and fifth shall be to the second , as the excess of the third and sixth to the fourth . The demonstration of this is the same with that of the proposition , if division be used instead . of composition . COR . 2. The ...
... excess of the first and fifth shall be to the second , as the excess of the third and sixth to the fourth . The demonstration of this is the same with that of the proposition , if division be used instead . of composition . COR . 2. The ...
Page 162
... excess of EF above C , and similar and similarly situated to D : then , since D is similar + to EF , therefore * also KM is si- milar to EF : let KL be the homologous side to EG , * 26.6 . and LM to GF : and because 162 EUCLID'S ELEMENTS .
... excess of EF above C , and similar and similarly situated to D : then , since D is similar + to EF , therefore * also KM is si- milar to EF : let KL be the homologous side to EG , * 26.6 . and LM to GF : and because 162 EUCLID'S ELEMENTS .
Page 163
... excess of the one to be applied above that upon the given line is required to be similar . It is required to apply a parallelogram to the given straight line AB which shall be equal to the figure C , exceeding by a parallelogram similar ...
... excess of the one to be applied above that upon the given line is required to be similar . It is required to apply a parallelogram to the given straight line AB which shall be equal to the figure C , exceeding by a parallelogram similar ...
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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