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Let AB be the fame multiple of C, that DE is of F : C is to F, as AB to DE. Becaufe AB is the fame multiple of C that DE is of F ; there are as many magnitudes in AB equal to C, as there are in...
The Elements of Euclid: In which the Propositions are Demonstrated in a New ... - Page 69
by Euclid - 1776 - 264 pages

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

Euclid - Geometry - 1765 - 464 pages
...PROP. XV. THEOR. Magnitudes have the fame ratio to one another wbitt their equimultiples have *. For let AB be the fame multiple of C, that DE is of F I fay c is to F, as AB is to D E. For becaufe AB is the fame multiple of C, that DE is of F : there...

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

John Keill - Geometry - 1772 - 462 pages
...to D E. But AG is equal to C, and D K. to F. Whence, as C is to F, fo fhall AB be to D E. Therefore, Parts have the fame Proportion as their like Multiples, if taken correfpondently ; which Was to b» demonftrated, PROPROPOSITION XVI. THEOREM. Jf four Magnitudes of the fame Kind are...

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

Robert Simson - Trigonometry - 1775 - 520 pages
...'PROP. XV. THEO R. M AGNITUDES- have the fame ratio to one another which their equimultiples have. O Let AB be the fame multiple of C, that DE is of F : C is to F, as AB to DE. Becaufe AB is the fame multiple of C that DE is of F ; there are as many...

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

Euclid - Geometry - 1776 - 318 pages
...is equal to' C, B js equal to D ; and, if lefs, lefs. Wherefore, &c> P BOOK V. PROP. XV. THEOR, ARTS have the fame proportion as their like multiples^...each equal to F ; then AG, GH, HB are equal to one another3-, and likewife DK, KL, LE equal to one another ;« A*. therefore AG is to DK as GH is to KL,...

The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 550 pages
...PRO P. XV. THEO R. M AGNITUDES have the fame ratio to one another •which their equimultiples have. Let AB be the fame multiple of C, that DE is of F : C is t» F, as AB to DE. Becaufe AB is the fame multiple of C, that DE is of F; there are as many...

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

John Keill - Geometry - 1782 - 399 pages
...; which was to be demonftrated. D PROPOSITION XV. THEOREM. Paris have the Jame Proportion as tbeir like Multiples, if taken correfpondently. LET AB be the fame Multiple of C, as DE is of F. I fay, as C is to F, fo is AB to D E. For, becaufe AB and DE are A Equimultiples of...