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 98
Side 6
... fimilar folid Figures are thofe which are contained by " fimilar Planes of the fame Number and Magnitude . " Now , this Propofition is a Theorem , not a Definition ; because the equality of Figures of any kind must be demonftrated , and ...
... fimilar folid Figures are thofe which are contained by " fimilar Planes of the fame Number and Magnitude . " Now , this Propofition is a Theorem , not a Definition ; because the equality of Figures of any kind must be demonftrated , and ...
Side 87
... fimilar to the fegment A b a 10. 3 . ADB , and that fimilar fegments of circles contain equal an- b11 . def . 3 . gles ; the angle ACB is equal to the angle ADB , the exterior to the interior , which is impoffible . Therefore , there ...
... fimilar to the fegment A b a 10. 3 . ADB , and that fimilar fegments of circles contain equal an- b11 . def . 3 . gles ; the angle ACB is equal to the angle ADB , the exterior to the interior , which is impoffible . Therefore , there ...
Side 88
... fimilar fegments , & c . Q. E. D. a 23. 3 . See N. a 10. I. b 11. I. c 6. I. d 9.3 . A PROP . XXV . PROB . Segment of a circle being given , to describe the circle of which it is the fegment . Let ABC be the given fegment of a circle ...
... fimilar fegments , & c . Q. E. D. a 23. 3 . See N. a 10. I. b 11. I. c 6. I. d 9.3 . A PROP . XXV . PROB . Segment of a circle being given , to describe the circle of which it is the fegment . Let ABC be the given fegment of a circle ...
Side 89
... fimilar to the bIx . def .. fegment EDF ; and they are upon equal ftraight lines BC , EF ; but fimilar fegments of circles upon equal ftraight lines are e- qual to one another ; therefore the fegment BAC is equal 24. 3 . to the fegment ...
... fimilar to the bIx . def .. fegment EDF ; and they are upon equal ftraight lines BC , EF ; but fimilar fegments of circles upon equal ftraight lines are e- qual to one another ; therefore the fegment BAC is equal 24. 3 . to the fegment ...
Side 166
... fimilar : In the like b 4 . 6 . D C manner it may be demonftrated , that the triangle ADC is e- quiangular and fimilar to the triangle ABC : And the triangles ABD , ADC , being both equiangular and fimilar to ABC , are equiangular and ...
... fimilar : In the like b 4 . 6 . D C manner it may be demonftrated , that the triangle ADC is e- quiangular and fimilar to the triangle ABC : And the triangles ABD , ADC , being both equiangular and fimilar to ABC , are equiangular and ...
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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