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 44
Side 13
... double of the fame , are equal to one another . VII . Things which are halves of the fame , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the fame space , are equal to one ...
... double of the fame , are equal to one another . VII . Things which are halves of the fame , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the fame space , are equal to one ...
Side 40
... double a of the triangle BDC ; and they are there- fore equal to one another D C F But , if the fides AD , EF , oppofite B to the bafe BC of the parallelograms ABCD , EBCF , be not terminated in the fame point ; then , be- cause ABCD is ...
... double a of the triangle BDC ; and they are there- fore equal to one another D C F But , if the fides AD , EF , oppofite B to the bafe BC of the parallelograms ABCD , EBCF , be not terminated in the fame point ; then , be- cause ABCD is ...
Side 43
... c . Q. E. D. PROP . XLI . THEOR . IF a parallelogram and triangle be upon the fame base , and between the fame parallels ; the parallelogram fhall be double of the triangle . Let 43 Book I. a 37. I. b34 . I. Let the OF EUCLID .
... c . Q. E. D. PROP . XLI . THEOR . IF a parallelogram and triangle be upon the fame base , and between the fame parallels ; the parallelogram fhall be double of the triangle . Let 43 Book I. a 37. I. b34 . I. Let the OF EUCLID .
Side 44
... double b of the triangle ABC , because the diameter AC di- vides it into two equal parts ; where- fore ABCD is alfo double of the tri- angle EBC . Therefore , if a parallelogram , & c . Q. E. D. B C PROP . XLII . PROB . a Io . I. b 23 ...
... double b of the triangle ABC , because the diameter AC di- vides it into two equal parts ; where- fore ABCD is alfo double of the tri- angle EBC . Therefore , if a parallelogram , & c . Q. E. D. B C PROP . XLII . PROB . a Io . I. b 23 ...
Side 49
... double of the triangle FBC , because these alfo are upon the fame bale FB , and between the fame parallels FB , GC But the doubles of equals are equal to one another : Therefore the parallelo- h 6. Ax . gram BL is equal to the fquare GB ...
... double of the triangle FBC , because these alfo are upon the fame bale FB , and between the fame parallels FB , GC But the doubles of equals are equal to one another : Therefore the parallelo- h 6. Ax . gram BL is equal to the fquare GB ...
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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