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 17
... angle BAC equal A to the angle EDF , the bafe BC fhall be equal to the bafe EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the angle ABCB to ...
... angle BAC equal A to the angle EDF , the bafe BC fhall be equal to the bafe EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the angle ABCB to ...
Side 20
... angle ACB ; produce AC , AD to E , F ; therefore , becaufe AC is equal to AD in the triangle ACD , the angles ECD ... BAC is e qual to the angle EDF . For , if the tri- DG angle ABC be ap- B CE plied to DEF , fo F that the point B be on ...
... angle ACB ; produce AC , AD to E , F ; therefore , becaufe AC is equal to AD in the triangle ACD , the angles ECD ... BAC is e qual to the angle EDF . For , if the tri- DG angle ABC be ap- B CE plied to DEF , fo F that the point B be on ...
Side 21
... angle BAC coincides with the angle EDF , and is equal to it . There- b . 8. Ax fore if two triangles , & c . Q. E. D. T PROP . IX . PRO B. O bifect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be ...
... angle BAC coincides with the angle EDF , and is equal to it . There- b . 8. Ax fore if two triangles , & c . Q. E. D. T PROP . IX . PRO B. O bifect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be ...
Side 26
... BAC . Bifect a AC in E , join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle ... angle ACB ; ...
... BAC . Bifect a AC in E , join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle ... angle ACB ; ...
Side 27
... BAC , ACB , as also CAB , ABC are less than two right angles . Therefore any two angles , & c . Q. E. D. THE PRO P. XVIII . THEOR . HE greater fide of every triangle is oppofite to the greater angle . Let ABC be a triangle , of which ...
... BAC , ACB , as also CAB , ABC are less than two right angles . Therefore any two angles , & c . Q. E. D. THE PRO P. XVIII . THEOR . HE greater fide of every triangle is oppofite to the greater angle . Let ABC be a triangle , of which ...
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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