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 CorrectedT. Desilver and R. Desilver, 1825 - 516 sider |
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Side 117
... fourth , when any equimul- tiples whatsoever of the first and third being taken , and any equi- multiples whatsoever of the second and fourth ; if the multi- ple of the first be less than that of the second , the multiple of the third ...
... fourth , when any equimul- tiples whatsoever of the first and third being taken , and any equi- multiples whatsoever of the second and fourth ; if the multi- ple of the first be less than that of the second , the multiple of the third ...
Side 118
... fourth . VI . Magnitudes which have the same ratio are called proportionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying , the first is to the second , as the third to the fourth . ' VII . When of ...
... fourth . VI . Magnitudes which have the same ratio are called proportionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying , the first is to the second , as the third to the fourth . ' VII . When of ...
Side 119
... fourth ; or that the first is to the third , as the second to the fourth ; as is shown in the 16th prop . of this 5th book . XIV . Invertendo , by inversion ; when there are four proportionals , and it is inferred , that the second is ...
... fourth ; or that the first is to the third , as the second to the fourth ; as is shown in the 16th prop . of this 5th book . XIV . Invertendo , by inversion ; when there are four proportionals , and it is inferred , that the second is ...
Side 120
... fourth . Prop . E , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance when there is any number of magnitudes more than two , and as many others , so that they are proportionals when taken two and two ...
... fourth . Prop . E , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance when there is any number of magnitudes more than two , and as many others , so that they are proportionals when taken two and two ...
Side 122
... fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second , that the third together with the sixth is of the fourth . A D Let ...
... fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second , that the third together with the sixth is of the fourth . A D Let ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore