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
... fecond , which the third has to the fourth , when any 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 ...
... fecond , which the third has to the fourth , when any 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 ...
Side 120
... fecond , as the third to the fourth . ' VII . When of the 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 ...
... fecond , as the third to the fourth . ' VII . When of the 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 ...
Side 121
... fecond has to the fourth ; or that the first is to the third , as the fecond to the fourth : As is thown in the 16th prop . of this 5th book . XIV . Invertendo , by inverfion : When there are four proportionals , and it is inferred ...
... fecond has to the fourth ; or that the first is to the third , as the fecond to the fourth : As is thown in the 16th prop . of this 5th book . XIV . Invertendo , by inverfion : When there are four proportionals , and it is inferred ...
Side 122
... fecond , as the third to its excefs above the fourth . Prop . E. book 5 . XVIII . Ex aequali ( fc . diftantia ) , or ... fecond of the first rank , as the firft to the fecond of the other rank ; and as the fe- cond is to the third of the ...
... fecond , as the third to its excefs above the fourth . Prop . E. book 5 . XVIII . Ex aequali ( fc . diftantia ) , or ... fecond of the first rank , as the firft to the fecond of the other rank ; and as the fe- cond is to the third of the ...
Side 124
... 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 . Let AB the firft , be the fame multiple of C the fecond ...
... 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 . Let AB the firft , be the fame multiple of C the fecond ...
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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