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" Ratios that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F. "
A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the ... - Σελίδα 260
των Thomas Malton - 1774 - 440 σελίδες
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

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

Euclid - 1765 - 464 σελίδες
...R. fhofe ratios that are the fame to the fame ratio, are the fame between tbemf elves. fo is I For let A be to B, as c is to D, and as C is to D, E to F : I fay, as A is to B, fo is E to F. For take G, H, K equimultiples of A, c, E, and...

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

Robert Simson - 1775 - 520 σελίδες
...Ax 5. R PRO P. XI. THEO R. ATIOS that are the fame to the fame ratio, are the fame to one another. Let A be to B as C is to D ; and as C to D, fo let E be to F ; A is to B, as E to F. Take of A, C, E, any equimultiples whatever G, H,...

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

Robert Simson - 1781 - 466 σελίδες
...QED -. E R PRO P. XL THEO R. ATIOS that are the fame to the fame ratio, are the fame to one another. Let A be to B, as C is to D} and as C to D, fo let E be to F; A is to B, as E to F. Take of A, C, E any equimultiples whatever G, H, K...

The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 σελίδες
...Q^ED B R PROP. XI. T II EO R. AT1OS that are the fame to the fame ratio, are the fame to one another. Let A be to B, as C is to D ; and as C to D, fo let E be to ' F ; A is to B, as E to F. Take of A, C, E, any equimultiples whatever G, H,...

Elements of Geometry: Containing the Principal Propositions in the First Six ...

Euclid - 1789 - 272 σελίδες
...the antecedents is to the fum of all the confequents. i 61 1 HiBi— < j)i ( F>Li 1 Mi • 1 NiLet A be to B as c is to D, and as E is to F ; then will A be to B, as A, c and E together, are to B, D and F together. For, of A, c and...

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

Alexander Ingram - 1799 - 351 σελίδες
...&c. Q^ ED AC R PROP. XI. THEOR. ATIoS that are equal to the fame ratio, are equal to one another. M Let A be to B, as C is to D, and as C to D, fo let E be to F ; A is to B, as E to F. Take MA, MC, ME any equimultiples of A, C, E: and...

Elements of Geometry: Containing the Principal Propositions in the First Six ...

John Bonnycastle - 1803 - 279 σελίδες
...will be to its confequent, as the fum of all the antecedent* is to the fum of all the confequents. Let A be to B as c is to D, and as E is to F ; then will A be to B, as A, C and E together, are to s, D and F to. gether. , For, of A, c...

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

Robert Simson - 1804
...D C E PROP. XL THEOR. RATIOS that are the fame to the fame ratio, are the fame to one another, *' " Let A be to B, as C is to D; and as C to D, fo let E be to Fj A is to B, as E to F. Take of A, C, E any equimultiples whatever G, H, K;...

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

Euclides - 1816 - 528 σελίδες
...&c. QED F PROP. XI. THEOR. RATIOS that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F ; A is to B, as E to F. Take of A, C, E, any equimultiples whatever G, H,...

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

Robert Simson - 1827 - 513 σελίδες
...Def. 5. 1 4 PROP. XI. THEOR. Ratios that are the same to the same ratio, aj-e the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F : A shall be to B, as E to F. Take of A, C, E, any equimultiples whatever...




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