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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.
The elements of plane geometry; or, The first six books of Euclid, ed. by W ... - Σελίδα 68
των Euclides - 1863
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## A Dictionary of Science, Literature, & Art: Comprising the ..., Τόμος 1

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...

## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

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,...

## Pelicotetics, Or, The Science of Quantity: An Elementary Treatise on Algebra ...

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's Elements of Geometry

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,...

## The Elements of Euclid, containing the first six books, with a selection of ...

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...

## Euclid, book v. proved algebraically, so far as it relates to commensurable ...

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, Book V. Proved Algebraically, So Far as it Relates to Commensurable ...

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...

## The Elementary Geometry of the Right Line and Circle ... With Exercises

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...

## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

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,...

## The Harpur Euclid: An Edition of Euclid's Elements

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...