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 73
Side 6
... must be demonftrated , and not af- fumed ; and therefore , though this were a true Propofition , it ought to have been demonftrated . But , indeed , this Propo- fition , which makes the 10th Definition of the 11th Book , is not true ...
... must be demonftrated , and not af- fumed ; and therefore , though this were a true Propofition , it ought to have been demonftrated . But , indeed , this Propo- fition , which makes the 10th Definition of the 11th Book , is not true ...
Side 29
... must be greater than the third " . Let A , B , C be the three given straight lines , of which any two whatever are greater than the third , viz . A and B greater than C ; A and C greater than B ; and B and C than A. It is required to ...
... must be greater than the third " . Let A , B , C be the three given straight lines , of which any two whatever are greater than the third , viz . A and B greater than C ; A and C greater than B ; and B and C than A. It is required to ...
Side 32
... must either be equal to it , or lefs ; but the angle BAC is not equal to the angle EDF , because then the bafc BC would be equal to EF ; but it is not ; there- fore the angle BAC is not equal to the angle EDF ; neither is it lefs ...
... must either be equal to it , or lefs ; but the angle BAC is not equal to the angle EDF , because then the bafc BC would be equal to EF ; but it is not ; there- fore the angle BAC is not equal to the angle EDF ; neither is it lefs ...
Side 35
... must be greater than the other ; let AGH be the greater ; and because the angle AGH is greater than the angle GHD , add to each of them the angle BGH ; therefore the angles AGH , BGH are greater than the angles BGH , GHD ; but the ...
... must be greater than the other ; let AGH be the greater ; and because the angle AGH is greater than the angle GHD , add to each of them the angle BGH ; therefore the angles AGH , BGH are greater than the angles BGH , GHD ; but the ...
Side 77
... must pass through it . Therefore , if two circles , & c . Q. E. D. IF PROP . XII . THEOR . IF two circles touch each other externally , the ftraight line which joins their centres fhall pafs through the point of contact . a 20. I. Let ...
... must pass through it . Therefore , if two circles , & c . Q. E. D. IF PROP . XII . THEOR . IF two circles touch each other externally , the ftraight line which joins their centres fhall pafs through the point of contact . a 20. I. Let ...
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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