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 119
... equimultiples whatsoever of the first and third being taken , and any equimultiples whatfoever of the fecond and fourth ; if the multiple of the firft be lefs than that of the fecond , the multiple of the third is alfo less than that of ...
... equimultiples whatsoever of the first and third being taken , and any equimultiples whatfoever of the fecond and fourth ; if the multiple of the firft be lefs than that of the fecond , the multiple of the third is alfo less than that of ...
Side 120
... equimultiples of four magnitudes ( taken as in the fifth definition ) the multiple of the firft is greater than that of the fecond , but the multiple of the third is not greater than the multiple of the fourth ; then the firft is faid ...
... equimultiples of four magnitudes ( taken as in the fifth definition ) the multiple of the firft is greater than that of the fecond , but the multiple of the third is not greater than the multiple of the fourth ; then the firft is faid ...
Side 123
... equimultiples of as many , each of each ; what multiple foever any one of them is of its part , the fame multiple fhall all the firft magnitudes be of all the other . Let any number of magnitudes AB , CD be equimultiples of as many ...
... equimultiples of as many , each of each ; what multiple foever any one of them is of its part , the fame multiple fhall all the firft magnitudes be of all the other . Let any number of magnitudes AB , CD be equimultiples of as many ...
Side 125
... equimultiples , thefe fhall be equi- multiples , the one of the fecond , and the other of the fourth . Let A the first , be the fame multiple of B the second , that C the third is of D the fourth ; and of A , C let the equimul- tiples ...
... equimultiples , thefe fhall be equi- multiples , the one of the fecond , and the other of the fourth . Let A the first , be the fame multiple of B the second , that C the third is of D the fourth ; and of A , C let the equimul- tiples ...
Side 126
... equimultiples whatever of the firft and third fhall have the fame ratio to any equimultiples of the fecond and fourth , viz . the equimultiple of the firft shall have the fame ratio to that of the fecond , which the equi- multiple of ...
... equimultiples whatever of the firft and third fhall have the fame ratio to any equimultiples of the fecond and fourth , viz . the equimultiple of the firft shall have the fame ratio to that of the fecond , which the equi- multiple of ...
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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