The Elements of Euclid: Viz. The First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner CorrE. Wingrove, London, and J. Balfour, Edinburgh, 1793 - 520 sider |
Inni boken
Resultat 6-10 av 60
Side 140
... proportionals , they shall also be proportionals when taken separately ; that is , if two magnitudes together have to one of them the fame ratio which two others have to one of thefe , the remaining one of the first two shall have to ...
... proportionals , they shall also be proportionals when taken separately ; that is , if two magnitudes together have to one of them the fame ratio which two others have to one of thefe , the remaining one of the first two shall have to ...
Side 141
... proportionals , they śce N. fhall also be proportionals when taken jointly , that is , if the firft be to the fecond , as the third to the fourth , the first and fecond together fhall be to the fecond , as the third and fourth together ...
... proportionals , they śce N. fhall also be proportionals when taken jointly , that is , if the firft be to the fecond , as the third to the fourth , the first and fecond together fhall be to the fecond , as the third and fourth together ...
Side 144
... proportionals , they are b 17. 5. alfo proportionals b when taken feparately ; there- ' fore , as BE is to DF , fo is EA to FC ; and alter- nately , as BE is to EA , fo is DF to FC : But , as E- AE to CF , fo by the hypothefis , is AB ...
... proportionals , they are b 17. 5. alfo proportionals b when taken feparately ; there- ' fore , as BE is to DF , fo is EA to FC ; and alter- nately , as BE is to EA , fo is DF to FC : But , as E- AE to CF , fo by the hypothefis , is AB ...
Side 149
... proportionals , they fhall likewise be proportionals when taken jointly b ; as therefore AG is to GB , fo is B E H ACDF DH to HE ; but as GB to C , fo is HE to F. Therefore , ex æquali a , as AG is to C , fo is DH to F. Wherefore , if ...
... proportionals , they fhall likewise be proportionals when taken jointly b ; as therefore AG is to GB , fo is B E H ACDF DH to HE ; but as GB to C , fo is HE to F. Therefore , ex æquali a , as AG is to C , fo is DH to F. Wherefore , if ...
Side 150
... proportionals , the greatest and leaft of them together are greater than the other two together . Let the four magnitudes AB , CD , E , F be proportionals , viz . AB to CD , as E to F ; and let AB be the greatest of them , a A. & 14 ...
... proportionals , the greatest and leaft of them together are greater than the other two together . Let the four magnitudes AB , CD , E , F be proportionals , viz . AB to CD , as E to F ; and let AB be the greatest of them , a A. & 14 ...
Andre utgaver - Vis alle
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1781 |
Vanlige uttrykk og setninger
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe centre circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated diameter drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fecond fegment fhall fide BC fides fimilar firft firſt folid angle fome fore fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs leſs likewife line BC muſt oppofite parallel parallelepiped parallelogram perpendicular plane angles PROP propofition proportionals pyramid rectangle contained rectilineal figure right angles ſame ſhall ſphere ſquare THEOR theſe tiple triangle ABC wherefore