 XIII. Permutando, or alternando, by permutation, or alternately; this word is used when there are four proportionals, and it is inferred, that the first has the same ratio to the third, which the second has to the ,fourth; or that the first is to the...  Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ... - Side 156av Euclides - 1861Uten tilgangsbegrensning - Om denne boken
 | Robert Potts - 1865 - 528 sider
...xm. Permutando, or alternando,by permutation, or alternately. This word is used when there are four proportionals, and it is inferred that the first has...is to the third as the second to the fourth : as is shewn in Prop. xvi. of this Fifth Book. XTV. Invertendo, by inversion ; when there are four proportionals,... | |
 | William Thomas Brande, George William Cox - 1865 - 978 sider
...the first of four lit? magnitudes be to the second as the third is to the fourth, then alternately the first is to the third as the second to the fourth. Alternation. A term formerly nsed for what is now called pcrnuttatitsn. [PERMCTV TIO3Î.] Althaea (Or.... | |
 | William Thomas Brande - 1867 - 974 sider
...if the first of four like magnitudes be to the second as the third is to the fourth, then ultimately the first is to the third as the second to the fourth. Alternation. A term formerly used for what is now called pi-rmutation. [Рвамвтд.TION.] Althaea... | |
 | Robert Potts - 1868 - 434 sider
...XIII. Permutando or alternando,by permutation or alternately. This word is used when there are four proportionals, and it is inferred that the first has...is to the third as the second to the fourth : as is shewn in Prop. xvI. of this Fifth Book. XIV. XV. Componendo, by composition ; when there are four proportionals,... | |
 | Archibald Sandeman - 1868 - 500 sider
...PROP. If of four magnitudes of the same kind the first be to the second as the third is to the fourth the first is to the third as the second to the fourth. (EuCL.v. 16). Let ABCD be four magnitudes of the same kind such that A:B=C:D. Then since (art.245)... | |
 | Euclid - 1872 - 284 sider
...Permutation, when it is inferred that if there be four magnitudes, of the same kind, proportional, the first is to the third as the second to the fourth ; as is shcvjn in Prop. 33, B. 5. Ex. gr. — A to B as C to Do, becomes A to C as B to Do. 15. By Inversion,... | |
 | Euclides - 1874 - 342 sider
...13. Permutando, or alternando ; by permutation or alternately. This word is used when there are four proportionals, and it is inferred that the first has...fourth ; as is shown, in Prop. 16 of this Fifth Book. 14. Invertendo, by inversion ; when there are four proportionals, and it is inferred, that the second... | |
 | Charles Lutwidge Dodgson - 1874 - 96 sider
...consequents. XIII. Alternando. This word is used when there are four proportionals, and it is inferred that the first is to the third as the second to the fourth. (Рвор. xvi.) XIV. Invertendo ; when there are four proportionals, an it is inferred, that the second... | |
 | Euclid, Lewis Carroll - 1874 - 80 sider
...consequents. XIII. Alternando. This word is used when there are four proportionals, and it is inferred that the first is to the third as the second to the fourth. (Ркор. xvi.) XIV. Invertendo ; when there are four proportionals, an it is inferred, that the second... | |
 | William Alexander Willock - 1875 - 196 sider
...given proportion : — BY ALTERNATION. — When the first is to the second as the third to the fourth, the first is to the third as the second to the fourth. By the first test of a proportion equisubmultiples of the first and third are contained an equal number... | |
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