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 69
Side 45
... diameter of any parallelogram , are equal to one another . Let ABCD be a parallelogram , of which the diameter is AC , and EH , FG the parallelo- grams about AC , that is , thro ' which AC paffes , and BK , KD the other parallelograms E ...
... diameter of any parallelogram , are equal to one another . Let ABCD be a parallelogram , of which the diameter is AC , and EH , FG the parallelo- grams about AC , that is , thro ' which AC paffes , and BK , KD the other parallelograms E ...
Side 46
... diameter is HK , and AG , ME are the parallelograms about HK ; and LB , BF are the complements ; therefore LB is equal e to BF : But BF is equal to the triangle C ; wherefore LB is equal to the triangle C ; and because the angle GBE is ...
... diameter is HK , and AG , ME are the parallelograms about HK ; and LB , BF are the complements ; therefore LB is equal e to BF : But BF is equal to the triangle C ; wherefore LB is equal to the triangle C ; and because the angle GBE is ...
Side 54
... rectangle AC , CB . Wherefore if a straight line , & c . Q. E. D. COR . From the demonftration , it is manifest that the pa rallelograms about the diameter of a square are likewise squares . PROP 1 Book II . I ' PROP . V : 54 THE ELEMENTS.
... rectangle AC , CB . Wherefore if a straight line , & c . Q. E. D. COR . From the demonftration , it is manifest that the pa rallelograms about the diameter of a square are likewise squares . PROP 1 Book II . I ' PROP . V : 54 THE ELEMENTS.
Side 67
... diameters are equal , Book ILL or from the centres of which the ftraight lines to the cir- cumferences are equal . This is not a definition but a theorem , the truth of which is evident ; for , if the circles be applied to one another ...
... diameters are equal , Book ILL or from the centres of which the ftraight lines to the cir- cumferences are equal . This is not a definition but a theorem , the truth of which is evident ; for , if the circles be applied to one another ...
Side 73
... diameter of a circle which is not the centre , of all the straight lines which can be drawn from it to the circumference , the great- eft is that in which the centre is , and the other part of that diameter is the leaft ; and , of any ...
... diameter of a circle which is not the centre , of all the straight lines which can be drawn from it to the circumference , the great- eft is that in which the centre is , and the other part of that diameter is the leaft ; and , of any ...
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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