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 CorrectedP. Wogan, 1803 - 520 sider |
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Resultat 1-5 av 37
Side 121
... excess of the first above the fecond , is to the fecond , as the excess of the third above the fourth , is to the fourth . 17th Prop . Book 5 . XVII . Convertendo , by converfion ; when there are four propor tionals , and it is inferred ...
... excess of the first above the fecond , is to the fecond , as the excess of the third above the fourth , is to the fourth . 17th Prop . Book 5 . XVII . Convertendo , by converfion ; when there are four propor tionals , and it is inferred ...
Side 144
... excess above the fourth . Let AB be to BE , as CD to DF ; then BA is to AE , as DC to CF. Because AB is to BE , as CD to DF , by divifion " , AE is to EB , as CF to FD ; and by inverfion b , BE is to EA , as DF to FC . Wherefore , by ...
... excess above the fourth . Let AB be to BE , as CD to DF ; then BA is to AE , as DC to CF. Because AB is to BE , as CD to DF , by divifion " , AE is to EB , as CF to FD ; and by inverfion b , BE is to EA , as DF to FC . Wherefore , by ...
Side 149
... Q. E. D. ACDF COR . I. If the fame hypothefis be made as in the propofi- tion , the excess of the first and fifth fhall be to the fecond , as the a 22. S. b 18 . Book V. the excefs of the third and fixth to OF EUCLID . 149.
... Q. E. D. ACDF COR . I. If the fame hypothefis be made as in the propofi- tion , the excess of the first and fifth fhall be to the fecond , as the a 22. S. b 18 . Book V. the excefs of the third and fixth to OF EUCLID . 149.
Side 186
... parallelogram KLMN equal to the excess of EF above C , and fimilar and fimilarly fituated to D ; but D is fimilar to EF , therefore alfo KM is fimilar to EF : Let KL d be be the homologous fide to EG , and LM to 186 THE ELEMENTS.
... parallelogram KLMN equal to the excess of EF above C , and fimilar and fimilarly fituated to D ; but D is fimilar to EF , therefore alfo KM is fimilar to EF : Let KL d be be the homologous fide to EG , and LM to 186 THE ELEMENTS.
Side 187
... excess of the one to be applied above that upon the given line is required to be fimilar . It is required to apply a parallelogram to the given ftraight line AB which fhall be equal to the figure C , exceeding by a parallelogram Gimilar ...
... excess of the one to be applied above that upon the given line is required to be fimilar . It is required to apply a parallelogram to the given ftraight line AB which fhall be equal to the figure C , exceeding by a parallelogram Gimilar ...
Andre utgaver - Vis alle
The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2015 |
The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |
Vanlige uttrykk og setninger
AC is equal alfo alſo angle ABC angle BAC bafe baſe BC is given becauſe the angle becauſe the ratio bifected Book XI cafe centre circle ABCD circumference cone confequently cylinder defcribed demonftrated diameter drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fide BC fides fimilar fince firft firſt folid angle fome fore fphere 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 parallel parallelogram parallelopipeds perpendicular polygon prifms propofition proportionals pyramid rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe tiple triangle ABC vertex wherefore