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synthetical division - Übersetzung nach russisch
математика
сокращенное деление (многочленов, при котором выписываются только отрицательные коэффициенты)
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![Members of the Australian 6th Division at [[Tobruk]], 22 January 1941](https://commons.wikimedia.org/wiki/Special:FilePath/Awm 005392 2nd11th.jpg?width=200 "Members of the Australian 6th Division at [[Tobruk]], 22 January 1941")
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![Headquarter of 11th Infantry Division of Bangladesh Army near [[Bogra]]](https://commons.wikimedia.org/wiki/Special:FilePath/Monogram of Bogra Cantonment Majhira.jpg?width=200 "Headquarter of 11th Infantry Division of Bangladesh Army near [[Bogra]]")
![Priest 105mm self-propelled gun]] of British 3rd Infantry Division, 1944](https://commons.wikimedia.org/wiki/Special:FilePath/Priest of 3rd Infantry Division in UK, 1944 (H 37994).jpg?width=200 "Priest 105mm self-propelled gun]] of British 3rd Infantry Division, 1944")
Definition
Wikipedia
Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few basic properties initially called postulate, and presently called axioms.
The term "synthetic geometry" has been coined only after the 17th century, and the introduction by René Descartes of the coordinate method, which was called analytic geometry. So the term "synthetic geometry" was introduced to refer to the older methods that were, before Descartes, the only known ones.
According to Felix Klein
Synthetic geometry is that which studies figures as such, without recourse to formulae, whereas analytic geometry consistently makes use of such formulae as can be written down after the adoption of an appropriate system of coordinates.
The first systematic approach for synthetic geometry is Euclid's Elements. However, it appeared at the end of the 19th that Euclid's postulates were not sufficient for characterizing geometry. The first complete axiom system for geometry was given only at the end of the 19th century by David Hilbert. At the same time, it appeared that both synthetic methods and analytic methods can be used to built geometry. The fact that the two approches are equivalent has been proved by Emil Artin in his book Geometric Algebra.
Because of this equivalence, the distinction between synthetic and analytic geometry is no more in use, except at elementary level, or for geometries that are not related to any sort of numbers, such as some finite geometries and non-Desarguesian geometry.
