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 O F Euclid's Data in Like Manner CorrectedF. Wingrave, 1809 - 531 sider |
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Side 112
... proportion- als . 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 the equimultiples of four magnitudes ( taken as in the fifth ...
... proportion- als . 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 the equimultiples of four magnitudes ( taken as in the fifth ...
Side 113
... proportionals , so as that they continue still to be ' proportionals . ' . XIII . Permutando , or alternando , by permutation , or alternately ! This word is used when there are four proportionals , and it See N. is inferred , that the ...
... proportionals , so as that they continue still to be ' proportionals . ' . XIII . Permutando , or alternando , by permutation , or alternately ! This word is used when there are four proportionals , and it See N. is inferred , that the ...
Side 114
... proportionals when taken two and two of each rank , and it is inferred , that the first is to the last of the first rank of magnitudes , as the first is to the last of the others : Of this there are the two fol lowing kinds , which ...
... proportionals when taken two and two of each rank , and it is inferred , that the first is to the last of the first rank of magnitudes , as the first is to the last of the others : Of this there are the two fol lowing kinds , which ...
Side 121
... proportionals , they are pro- portionals also when taken inversely . If the magnitude A be to B , as C is to D , then also inversely Bis to A , as D to C. Take of B and D any equimultiples whatever E and F ; and of A and C any ...
... proportionals , they are pro- portionals also when taken inversely . If the magnitude A be to B , as C is to D , then also inversely Bis to A , as D to C. Take of B and D any equimultiples whatever E and F ; and of A and C any ...
Side 128
... proportionals , as one of the antecedents is to its consequent , so shall all the antecedents taken together be to all the con- sequents . Let any number of magnitudes A , B , C , D , E , F , be pro- portionals ; that is , as A is to B ...
... proportionals , as one of the antecedents is to its consequent , so shall all the antecedents taken together be to all the con- sequents . Let any number of magnitudes A , B , C , D , E , F , be pro- portionals ; that is , as A is to B ...
Andre utgaver - Vis alle
The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid Ingen forhåndsvisning tilgjengelig - 2016 |
The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
ABCD altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABC circumference common logarithm cone cylinder demonstrated described diameter 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 logarithm multiple opposite parallel parallelogram perpendicular point F polygon prism proportionals proposition pyramid 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 tiple triangle ABC triplicate ratio vertex