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 |
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Resultat 6-10 av 95
Side 174
... fimilar , and fimilarly fituated to a given rectilineal figure . Let AB be the given ftraight line , and CDEF the given rec- tilineal figure of four fides ; it is required upon the given firaight line AB to describe a rectilineal figure ...
... fimilar , and fimilarly fituated to a given rectilineal figure . Let AB be the given ftraight line , and CDEF the given rec- tilineal figure of four fides ; it is required upon the given firaight line AB to describe a rectilineal figure ...
Side 175
... fimilar to one another e . Next , let it be required to defcribe upon a given straight line AB , a rectilineal figure fimilar , and fimilarly fituated to the rectilineal figure CDKEF . · • ad e I. Def . 6 . Join DE , and upon the given ...
... fimilar to one another e . Next , let it be required to defcribe upon a given straight line AB , a rectilineal figure fimilar , and fimilarly fituated to the rectilineal figure CDKEF . · • ad e I. Def . 6 . Join DE , and upon the given ...
Side 176
... fimilar triangles , & c . Q. E. D. COR . From this it is manifeft , that if three straight lines be ' proportionals , as the first is to the third , fo is any triangle up- on the first to a fimilar , and fimilarly described triangle ...
... fimilar triangles , & c . Q. E. D. COR . From this it is manifeft , that if three straight lines be ' proportionals , as the first is to the third , fo is any triangle up- on the first to a fimilar , and fimilarly described triangle ...
Side 177
... fimilar to the polygon FGHKL , the angle BAE is equal to the Book VI . angle GFL a , and BA is to AE , as GF to FL : Wherefore , because the triangles ABE , FGL have an angle in one équal to an angle in the other , and their fides about ...
... fimilar to the polygon FGHKL , the angle BAE is equal to the Book VI . angle GFL a , and BA is to AE , as GF to FL : Wherefore , because the triangles ABE , FGL have an angle in one équal to an angle in the other , and their fides about ...
Side 178
... fimilar polygons , & c . Q. E. D. g 12. 5 . COR . I. In like manner , it may be proved , that fimilar four fided figures , or of any number of fides , are one to another in the duplicate ratio of their homologous fides , and it has ...
... fimilar polygons , & c . Q. E. D. g 12. 5 . COR . I. In like manner , it may be proved , that fimilar four fided figures , or of any number of fides , are one to another in the duplicate ratio of their homologous fides , and it has ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1781 |
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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