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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Side 119
... fourth , when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the fecond and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is alfo ...
... fourth , when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the fecond and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is alfo ...
Side 120
... fourth . VI . Magnitudes which have the fame ratio are called proportionals . N. B. When four magnitudes are proportionals , it is • ufually expreffed by faying , the firft is to the fecond , as the third to the fourth . ' " VII . When ...
... fourth . VI . Magnitudes which have the fame ratio are called proportionals . N. B. When four magnitudes are proportionals , it is • ufually expreffed by faying , the firft is to the fecond , as the third to the fourth . ' " VII . When ...
Side 121
... fourth ; or that the first is to the third , as the fecond to the fourth ; As is fhewn in the 16th prop . of this 5th book . XIV . Invertendo , by inverfion ; When there are four proportionals , and it is inferred , that the second is ...
... fourth ; or that the first is to the third , as the fecond to the fourth ; As is fhewn in the 16th prop . of this 5th book . XIV . Invertendo , by inverfion ; When there are four proportionals , and it is inferred , that the second is ...
Side 124
... fourth , and the fifth the fame multiple of the fecond that the fixth is of the fourth ; then shall the first together with the fifth be the fame multiple of the fecond , that the third together with the fixth is of the fourth . A Let ...
... fourth , and the fifth the fame multiple of the fecond that the fixth is of the fourth ; then shall the first together with the fifth be the fame multiple of the fecond , that the third together with the fixth is of the fourth . A Let ...
Side 125
... fourth ; and if of the first and third there be taken equimultiples , these shall be equi- multiples , the one of the second , and the other of the fourth . Let A the first , be the fame multiple of B the fecond , that C the third is of ...
... fourth ; and if of the first and third there be taken equimultiples , these shall be equi- multiples , the one of the second , and the other of the fourth . Let A the first , be the fame multiple of B the fecond , that C the third is of ...
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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