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... viz. as A is to B, fo is E to F, and B to C as D to E ; and if the firft A be greater than the third C, then the fourth D will be greater than the fixth F ; if equal, equal ; and, if lefs, lefs.
The Elements of Euclid,: In which the Propositions are Demonstrated in a New ... - Σελίδα 78
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - 1723 - 444 σελίδες
...be proportional ; • •Lj and others D, E, F, equal to them in Number. Let their Analogy likewife be perturbate, viz. as A is to B, fo is E to F ; and as B fe to C, fo is D to E ; if the firft Magfiitude A be greater than the third C. I fay, the fourth...

Euclid's Elements of Geometry,: From the Latin Translation of Commandine. To ...

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...Magnitudes, A, B, C, be proportional; and others D, E, F, equal to them in Number, Let their Analogy likewife be perturbate, viz. as A is to B, fo is E to F; and as B is to C, fo is D to E ; if the firft Magnitude A be greater than the third C. I fay, the fourth...

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

Robert Simson - 1762 - 488 σελίδες
...there be four magnitudes A, B, C, D, and other four E, F, G, H, which two and two have the fame ratio, viz. as A is to B, fo is E to F ; and as H to C, fo F to G ; and as C to D, fo G to H. A fhall be to D, as E to H. Becaufe A, B, C are three...

Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

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...B, c, and other three D, E, F which taken two and two are in the fame ratio, but in a crofs order ; viz. as A is to B, fo is E to F, and as B is to c, fo is D to E. And A be greater than c : I fay D is greater than F ; if A be equal to...

Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - 1772 - 462 σελίδες
...proportional ; •*-' and others, D, E, F, equal to them in Number. Let their Analogy likewife be perturbate j viz. as A is to B, fo is E to F ; and as B is to C, fo is D to E : If the firft Magnitude A be greater than the third C, I fay, the fourth...

The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 534 σελίδες
...there be four magnitudes A, B, C, D, and other four E, F, G, H, which two and two have the lime ratio, viz. as A is to B, fo is E to F; and as B to C, fo F to G ; and as C to D, fo G to A : H ilia! I be to D, as E to H. Becaufe A, B, C are...

The Elements of Euclid: In which the Propositions are Demonstrated in a New ...

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...magnitude be greater than the third, then the fourth will be greater than the Jixth ; and if thefirftbe equal to the third, then the fourth will be equal...A has a greater ratio to B than ^ *• C has to B " ; but A is to B as E is to F ; therefore E has to F a greater ratio than C hath to B ; and inverfely...

The First Six Books: Together with the Eleventh and Twelfth

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...magnitudes, and D, E, F other three, which have the fame ratio, taken two and two, but in a crofs order, viz. as A is to B, fo is E to F, and as B is to C, fo is D to E. If A be greater than C, D fhall be greater than F ; and if equal, equal;...

The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

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...magnitudes, and D, E, F other three, which have the fame ratio, taken two and two, but in a crofs order, viz. as A is to B, fo is E to F, and as B is to C, fo is D to E. If A be greater than C, D fhall be greater than F i and if equal ; equal,...

The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

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...magnitudes, and D, E, F other three which have the fame ratio taken two and two, but in a crofs order, viz. as A is to B, fo is E to F, and as B is to C, fo is D to E. If A be greater than C, D fhall be greater than F; and if equal, equalj...