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 Restored : Also the Book of Euclid's Data, in Like Manner CorrectedJ. Nourse, London, 1781 - 520 sider |
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Side 5
... given ; and by taking out of this Book , befides other things , the good Definition which Eudoxus or Euclid had given of Compound Ratio , and giving an abfurd one in place of it in the 5th Definition of the 6th Book , which neither ...
... given ; and by taking out of this Book , befides other things , the good Definition which Eudoxus or Euclid had given of Compound Ratio , and giving an abfurd one in place of it in the 5th Definition of the 6th Book , which neither ...
Side 175
... given straight line fimilar to one given , and so on . Which was to be done . PRO P. XIX . THEOR . IMILAR triangles are to one another in the duplicate ratio of their homologous fides . STH Let ABC , DEF be fimilar triangles , having ...
... given straight line fimilar to one given , and so on . Which was to be done . PRO P. XIX . THEOR . IMILAR triangles are to one another in the duplicate ratio of their homologous fides . STH Let ABC , DEF be fimilar triangles , having ...
Side 312
... give a gene- " ral and fummary idea of ratio to beginners , by premifing " this metaphyfical definition , to the more accurate defini- " tions of ratios that are the fame to one another , or one of which is greater , or lefs than the ...
... give a gene- " ral and fummary idea of ratio to beginners , by premifing " this metaphyfical definition , to the more accurate defini- " tions of ratios that are the fame to one another , or one of which is greater , or lefs than the ...
Side 320
... ratio to C , than B has to C , there muft , by the 7th def . of Book 5. be certain equimultiples of A and B , and ... given the demonftration of the 10th propofition as we now have it , instead of that which Eudoxus or Euclid had given ...
... ratio to C , than B has to C , there muft , by the 7th def . of Book 5. be certain equimultiples of A and B , and ... given the demonftration of the 10th propofition as we now have it , instead of that which Eudoxus or Euclid had given ...
Side 329
... ratio might have been made after the fame manner in which the definitions of duplicate and triplicate ratio are given , viz . " That as in feveral magni- " tudes that are continual proportionals , Euclid named the " ratio of the first ...
... ratio might have been made after the fame manner in which the definitions of duplicate and triplicate ratio are given , viz . " That as in feveral magni- " tudes that are continual proportionals , Euclid named the " ratio of the first ...
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The Elements of Euclid: Viz. The First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1793 |
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alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle bifected Book XI cafe centre circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated diameter drawn equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fides BA 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 oppofite parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC vertex wherefore