Povzetek

This is page 225 of the Arithmetica Integra (1544), by Michael Stifel (1487-1567). Stifel is "one of the best-known German cossists of the sixteenth century. Stifel's work covered the basics of algebra, using the German symbols for powers of the unknown and also considering negative exponents for one of the first times in a European book. He also presented the Pascal triangle as a tool for finding roots of numbers and was one of the first to present one combined form of the algorithm for solving quadratic equations." [1]

"The diagram here on p. 255 represents the solution to the pair of simultaneous equations

x2 + y2 - (x + y) = 78, xy + (x + y) = 39.

Here, the two unknowns are represented by AC and BC, while the sum AB is called "B" by Stifel. Also, the script z is Stifel's notation for the square of the (first) unknown, namely x2. Note that therefore the smaller square (on the upper right) is labeled with the script z, the two rectangles are labeled 39 - 1B (since their areas are each xy, which is equal to 30 - (x + y)), and the larger square, which is equal to y2, is labeled 78 + B - z, that is 78 + (x + y) - x2. Stifel completes the problem as follows: The sum of the areas of all four regions of the diagram is equal to 156 - B, and this equals B2. It follows that B = 12. Therefore the larger square has area 90 - x2, and the two rectangles each have area 27. But either of those rectangles is the mean proportional between the larger square and the smaller square. Therefore, (90 - x2):27 = 27:x2. It follows that 90x2 - x4 = 729. So x2 = 9 and x = 3. Then y = 9 and the problem is solved." [2]

Licenca

To delo je v javni domeni tudi v državah in na območjih, kjer trajajo avtorske pravice za časa avtorjevega življenja in še 70 let ali manj po tem. Na stran morate dodati tudi oznako za javno domeno v Združenih državah Amerike, s katero razložite, zakaj je delo v javni domeni v Združenih državah Amerike. V nekaterih državah trajajo avtorske pravice več kot 70 let: v Mehiki trajajo 100 let, na Jamajki 95 let, v Kolumbiji 80 let, v Gvatemali in na Samoi trajajo 75 let. Avtorske pravice se lahko podaljšajo na delih Francozov, ki so umrli za Francijo v drugi svetovni vojni (več o tem), Ruse, ki so služili na vzhodni fronti druge svetovne vojne (v Rusiji poznani kot velika domoljubna vojna) in posmrtno za rehabilitirane Ruse (več o tem).

Datoteka je bila prepoznana kot prosta omejitev po avtorskem pravu, vključno z vsemi povezanimi in sorodnimi pravicami.

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