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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Resultat 1-5 av 47
Side 121
... excefs of the first above the fecond , is to the fecond , as the excefs of the third above the fourth , is to the fourth . 17th prop . book 5 . XVII . Conyertendo , by converfion ; when there are four proportion- als , and it is ...
... excefs of the first above the fecond , is to the fecond , as the excefs of the third above the fourth , is to the fourth . 17th prop . book 5 . XVII . Conyertendo , by converfion ; when there are four proportion- als , and it is ...
Side 122
... excefs above the fourth . Prop . E. book 5 . XVIII . Ex aequali ( fc . diftantia ) , or ex aequo , from equality of di- ftance ; when there is any number of magnitudes more than two , and as many others , fo that they are proportionals ...
... excefs above the fourth . Prop . E. book 5 . XVIII . Ex aequali ( fc . diftantia ) , or ex aequo , from equality of di- ftance ; when there is any number of magnitudes more than two , and as many others , fo that they are proportionals ...
Side 144
... ex- cefs above the fecond , as the third to its excess above the fourth . • Let AB be to BE , as CD to DF ; then BA is to AE , as DC to CF. A a 17. 5 . b B. S. c 18. s . Because AB is to BE , as CD to DF , by divi- fon , AE is to EB ...
... ex- cefs above the fecond , as the third to its excess above the fourth . • Let AB be to BE , as CD to DF ; then BA is to AE , as DC to CF. A a 17. 5 . b B. S. c 18. s . Because AB is to BE , as CD to DF , by divi- fon , AE is to EB ...
Side 149
... excefs of the firft and fifth fhall be to the fecond , as K 3 the a 22. 5 b 18. St Book V. the excefs of the third and fixth to OF EUCLID . 149.
... excefs of the firft and fifth fhall be to the fecond , as K 3 the a 22. 5 b 18. St Book V. the excefs of the third and fixth to OF EUCLID . 149.
Side 150
... excefs of the third and fixth to the fourth : The demonftra , tion of this is the fame with that of the propofition , if divifion be used instead of compofition . COR . 2. The propofition holds true of two ranks of magni- tudes ...
... excefs of the third and fixth to the fourth : The demonftra , tion of this is the fame with that of the propofition , if divifion be used instead of compofition . COR . 2. The propofition holds true of two ranks of magni- tudes ...
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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