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Molecular Koch's postulates are a set of experimental criteria that must be satisfied to show that a gene found in a pathogenic microorganism encodes a product that contributes to the disease caused by the pathogen. Genes that satisfy molecular Koch's postulates are often referred to as virulence factors.
Koch's postulates (/ k ɒ x / KOKH) [2] are four criteria designed to establish a causal relationship between a microbe and a disease. The postulates were formulated by Robert Koch and Friedrich Loeffler in 1884, based on earlier concepts described by Jakob Henle , and the statements were refined and published by Koch in 1890. [ 3 ]
Hammond's postulate (or alternatively the Hammond–Leffler postulate), is a hypothesis in physical organic chemistry which describes the geometric structure of the transition state in an organic chemical reaction. [1] First proposed by George Hammond in 1955, the postulate states that: [2]
Saccheri quadrilaterals. A Saccheri quadrilateral is a quadrilateral with two equal sides perpendicular to the base.It is named after Giovanni Gerolamo Saccheri, who used it extensively in his 1733 book Euclides ab omni naevo vindicatus (Euclid freed of every flaw), an attempt to prove the parallel postulate using the method reductio ad absurdum.
The first systematic approach for synthetic geometry is Euclid's Elements. However, it appeared at the end of the 19th century 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 ...
The classical equivalence between Playfair's axiom and Euclid's fifth postulate collapses in the absence of triangle congruence. [18] This is shown by constructing a geometry that redefines angles in a way that respects Hilbert's axioms of incidence, order, and congruence, except for the Side-Angle-Side (SAS) congruence.
Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry , there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two).
If "line" is taken to mean great circle, spherical geometry only obeys two of Euclid's five postulates: the second postulate ("to produce [extend] a finite straight line continuously in a straight line") and the fourth postulate ("that all right angles are equal to one another"). However, it violates the other three.