 | William Thomas Brande - 1867 - 974 σελίδες
...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 σελίδες
...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...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 - 498 σελίδες
...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 σελίδες
...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 σελίδες
...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...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 σελίδες
...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 σελίδες
...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 σελίδες
...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... | |
 | Robert Potts - 1876 - 446 σελίδες
...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...is to the third as the second to the fourth : as is shewn in Prop. xvi. of this Fifth Book, XIV. Invertendo, by inversion ; when there are four proportionals,... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 σελίδες
...alternando,' by permutation or alternately; 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. It is demonstrated in V. 16 that if A, B, C, D be four quantities of the same kind such that A : B... | |
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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 third as the second to the fourth : as is shown in Prop. 
