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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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## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 410 σελίδες
...Alternately : f this word is used when there are four proportionals of the same kind : and it is inferred, that the first has the same ratio to the third, which...third, as the second to the fourth : as is shown in the 16th proposition of this book. 15. By inversion : when there are four proportionals, and it is...

## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1838 - 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...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,...

## Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 σελίδες
...terms of a proportion are all of the same kind, they are proportional when taken ALTERNATELY, that is, the first is to the third as the second to the fourth. Let the proportion be A : B :: C : D; then also A : C :: B : D. For take mA, mB any equimultiples of...

## The elements of algebra

Andrew Bell (writer on mathematics.) - 1839 - 500 σελίδες
...inversion, when the second is to the first as the fourth to the third ; (328.) By alternation, when the first is to the third as the second to the fourth ; (329.) By composition, when the sum of the first and second is to the second, as the sum of the third...

## The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 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...third, as the second to the fourth; as is shown in the 16th Prop, of this fifth Book. XIV. Invertendo, by inversion: when there are four proportionals,...

## The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - 1841 - 140 σελίδες
...alternando, by permutation or alternately, is used when there are four proportionals, and it is inferred that the first has the same ratio to the third which...; or that the first is to the third as the second is to the fourth : as is shown in the following proposition : — Let • : A : : О : Д, by " permuntando...

## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 332 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...first is to the third as the second to the fourth : See Prop. 16. of this Book. 15. Invertendo, by inversion : When there are four proportionals, and...

## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 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...as the second to the fourth : as is shown in Prop. xvi. of this fifth book. XIV. Invertendo, by inversion ; when there are four proportionals, and it...

## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 218 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...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,...

## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclides, James Thomson - 1845 - 382 σελίδες
...Alternately:* this word is used when there are four proportionals of the same kind : and it is inferred that the first has the same ratio to the third, which...third, as the second to the fourth : as is shown in the 16th proposition of this book. 15. By inversion: when there are four proportionals, and it is inferred,...