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" That magnitude which has a greater ratio than another has unto the same magnitude, is the greater of the two : and that magnitude to which the same has a greater ratio than it has unto another magnitude, is the lesser of the two. "
Elements of Trigonometry, and Trigonometrical Analysis, Preliminary to the ... - Page 53
by Augustus De Morgan - 1837 - 230 pages
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The Elements of Euclid: The errors, by which Theon, or others, have long ago ...

Robert Simson, Euclid - Trigonometry - 1762 - 466 pages
...which the fame has a greater ratio than it has unto another magnitude is the leffer of the two. Let A have to C a greater ratio than B has to C ; A is greater than B. for becaufe A has a greater ratio to C, than B has to C, there are a fome equimultiples...
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The Elements of Euclid, viz: The errors, by which Theon, or others, have ...

Robert Simson, Euclid - Trigonometry - 1775 - 520 pages
...greater ratio than ij has unto another magnitude is the Icflerof the two. •THHAT 1 othe of the two Let A have to C a greater ratio than B has to C ; A is greater than B : For, becaufe A has a greater ratio to C, than 15 has to C, there are" fome...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 pages
...which the fame has a greater ratio than it has unto another magnitude is the leffer of the two. v Let A have to C a greater ratio than B has to C : A is greater than B : For, becaufe A has a greater ratio to C, than B has to C, there are* fome equimultiples...
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The elements of Euclid: viz. the first six books, with the eleventh and ...

Trigonometry - 1799 - 351 pages
...magnitude to which the fame has a greater ratio than it has to another, is the leiTer of the two. Let A have to C a greater ratio than B has to C ; A is greater than B : For, becaufe A has a greater ratio to C, than B has to C, there is fome multiple...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804
...which the fame has a greater ratio than it has unto another magnitude is the lefler of the two. Let A have to C a greater ratio than B has to C ; A is greater than B. for becaufe A has a greater ratio to C, than B has to C, there are a fome equimultiples...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - Geometry - 1816 - 528 pages
...which the same has a greater ratio than it has unto another magnitude, is the lesser of the two. Let A have to C a greater ratio than B has to C ; A is greater than B : For, because A has a greater ratio to C, than B has to C, there area some equimultiples...
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An elementary treatise on algebra: theoretical and practical

James Ryan, Robert Adrain - Algebra - 1824 - 516 pages
...the same has a greater ratio- than it has to another, is the less of the two. DEMONSTRATION'. 1. Let A have to C a greater ratio than B has to C, it is to be proved that A is greater than B. A o Since the ratios of A and B to C, are-^ and 37-. \*>...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...which the same has a greater ratio than it has unto another magnitude, is the lesser of the two. Let A have to C a greater ratio than B has to C : A shall be greater than B. For, because A has a greater ratio to C, than B has * 7 Def. 5. to c,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, John Davidson - Mathematics - 1835 - 513 pages
...to which the same has a greater ratio than it has to another magnitude, is the less of the tioo. Let A have to C a greater ratio than B has to C ; then is A greater than B : For, because A has a greater ratio to C, than B has to C, there are a some equimultiples...
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The Elements of Euclid

Robert Simson, Euclid - Mathematics, Greek - 1835 - 513 pages
...to which the same has a greater ratio than it has to another magnitude, is the less of the two. Let A have to C a greater ratio than B has to C ; then is A greater than B : For, because A has a greater ratio to C, than B has to C, there are a some equimultiples...
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