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 |
Inni boken
Resultat 1-5 av 53
Side 119
... 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 , the multiple of the third is alfo ...
... 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 , 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 thown in the 16th prop . of this 5th book . XIV . Invertendo , by inverfion : When there are four proportionals , and it is inferred , that the fecond is ...
... 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 , that the fecond is ...
Side 122
... fourth . Prop . E. book 5 . XVIII . Ex aequali ( fc . diftantia ) , or ex aequo , from equality of di- ftance ; when there is any number of magnitudes more than two , and as many others , fo that they are proportionals when taken two ...
... fourth . Prop . E. book 5 . XVIII . Ex aequali ( fc . diftantia ) , or ex aequo , from equality of di- ftance ; when there is any number of magnitudes more than two , and as many others , fo that they are proportionals when taken two ...
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 . Let AB ...
... 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 . Let AB ...
Andre utgaver - Vis alle
The Elements of Euclid: Viz. The First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1793 |
Vanlige uttrykk og setninger
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