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" N ; and if equal, equal ; and if less, less : but if G be greater than L, it has been shown that L HC K E M F N H is greater than M ; and if equal, equal; and if less, less: therefore, if G be greater than L, K is greater than N ; and if equal, equal... "
The First Six Books of the Elements of Euclid, with a Commentary and ... - Σελίδα 107
των Euclid, Dionysius Lardner - 1828 - 324 σελίδες
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...V^"\°OM ; and if equal, equal ; and if lefs, lefs". Again, becaufe C is to a. 5. Def. 3. D, as E is to F, and H, K are taken equimultiples of C, E ; and M,'...K is greater than N ; and if equal, equal; and if lefs, lefs. but if G be greater than L, it has ACE BDF L M- Nbeen fhewn that H is greater than M ;...

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...lefs, lefs '. Again, bei 5- def. 5. caufe C is to I), as E is to F, and H, K are takf n equimultiple* of C, E; and M, N of D, F ; if H be greater than M,...K is greater than N ; and if equal equal ; and if lefs, lefs : But, if G GHI A.- — CE te greater than L, it has been fhewn, thatH is greater than M;...

The First Six Books: Together with the Eleventh and Twelfth

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...lefs, lefs'. Again, bo • 5. &(• S. caufe C. is to D, as E is to F, and H, K are taken equimultiple* of C, E ; and M, N, of D. F; if H be greater than...K is greater than N; and if equal, equal ; and if lels, lefs : But, if G GH A. • c ~ B D. be greater than L, it has been fhpwn that H is greater than...

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...eater than "v M; and if equal, equal; and if lefs, lefs •. Again, becaufe C is to D, as E is to F, and H, K are taken equimultiples of C, E; and M, N...K is greater than N ; and if equal, equal } and if lefs, lefs. but' if G be greater than L, it has GH KAC EBD FL M- N. been fhewn that H is greater than...

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...M, N, which have the same ratio taken two and two in a cross order; if G "be greater than L, d21. 5. K is greater than N; and if equal, equal; and if less, lessd; and G, K are any equimultiples whatever of A, D ; and L, N any whatever of C, F ; as, therefore,...

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...M; and if equal, equal; and if less, less ». Again, because a 5. del. o. C is to D, as E is to F, and H, K are taken equimultiples of C, E: and M, N, of D, F: if H be greater than M, K is greater ili. ii N; and if equal, equal; and if less, less: but if G be G HA CBD FLM Ngreater than L, it has...

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

Euclides - 1814
...S of C, E; and M, N, of D, F; v ^ v ~"' less, less3. Again, because C is to D, as E is to F, and H, if H be greater than M, K is greater than N; and if...if less, less: But if G be greater than L. it has G II KA f > t?B I> lfM— N been shown that H is greater than M; and if equal, equal; and if less,...

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...that H is greater than M ; and if equal, equal ; and if less, less; therefore if G be greater than L, K is greater than N ; and if equal, equal ; and if less, less : And G, K are any equimultiples whatever of A, E ; and L, N any whatever of B, F : Therefore, as A...

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...G, K, M, and other three H, L, N, which, two and two, have the same ratio: if G be greater than M, H is greater than N; and if equal, equal; and if less, less (20. 5.); and G, H are any equimultiples whatever of A, D, and M, N are any equimultiples whatever...

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...K, M, N, which have the same ratio, taken two ant) two, in a cross order : if G be greater than L, K is greater than N ; and if equal, equal ; and if less, K'ss : (21. 5.) and G, K are any equimultiples whatever of A, D ; and L, N any whatever of C, F ; as,...




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