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 51
Side 141
... adding the common part HK to both , GK is greater than HX ; wherefore alfo LN is greater than MP ; and by taking away MN from both , LM is greater than NP : Therefore , if GH be E N B DM c 5. def . 5 . greater than KX , LM is greater ...
... adding the common part HK to both , GK is greater than HX ; wherefore alfo LN is greater than MP ; and by taking away MN from both , LM is greater than NP : Therefore , if GH be E N B DM c 5. def . 5 . greater than KX , LM is greater ...
Side 143
... adding NM to both , LM is greater K than NP : Therefore , if GH be greater than KO , LM is greater than N ° . In like manner it may be shown , that if GH be equal to KO , LM is equal to NP ; and if lefs , lefs . And in the cafe in which ...
... adding NM to both , LM is greater K than NP : Therefore , if GH be greater than KO , LM is greater than N ° . In like manner it may be shown , that if GH be equal to KO , LM is equal to NP ; and if lefs , lefs . And in the cafe in which ...
Side 150
... added equal magnitudes , viz . to GB the two AG and F , and CH and E to HD ; AB and F together are greater than CD and E. Therefore , if four magnitudes , & c . Q. E. D. See N. R ACEF PRO P. F. THEO R. ATIOS which are compounded of the ...
... added equal magnitudes , viz . to GB the two AG and F , and CH and E to HD ; AB and F together are greater than CD and E. Therefore , if four magnitudes , & c . Q. E. D. See N. R ACEF PRO P. F. THEO R. ATIOS which are compounded of the ...
Side 187
... adding SR to each , the f 34. T. whole OB is equal to the whole XB : But XB is equal g to TE , 8 36. I. because the bafe AE is equal to the bafe EB ; wherefore alfo TE is equal to OB : Add XS to each , then the whole TS is equal to the ...
... adding SR to each , the f 34. T. whole OB is equal to the whole XB : But XB is equal g to TE , 8 36. I. because the bafe AE is equal to the bafe EB ; wherefore alfo TE is equal to OB : Add XS to each , then the whole TS is equal to the ...
Side 299
... added at the end of this definition in all the copies , but are now left out as not belonging to the definition , being only a corollary from it . Proclus demonftrates it by conceiving one of the parts into which the diameter divides ...
... added at the end of this definition in all the copies , but are now left out as not belonging to the definition , being only a corollary from it . Proclus demonftrates it by conceiving one of the parts into which the diameter divides ...
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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