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In geometry, the segment addition postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle.
The new axiom is Lobachevsky's parallel postulate (also known as the characteristic postulate of hyperbolic geometry): [75] Through a point not on a given line there exists (in the plane determined by this point and line) at least two lines which do not meet the given line. With this addition, the axiom system is now complete.
In particular it is important to assure that for two given line segments, a new line segment can be constructed, such that its length equals the product of lengths of the other two. Similarly one needs to be able to construct, for a line segment of length , a new line segment of length . The intercept theorem can be used to show that for both ...
For the general quadrilateral (with four sides not necessarily equal) Euler's quadrilateral theorem states + + + = + +, where is the length of the line segment joining the midpoints of the diagonals. It can be seen from the diagram that x = 0 {\displaystyle x=0} for a parallelogram, and so the general formula simplifies to the parallelogram law.
In geometry, the isotomic conjugate of a point P with respect to a triangle ABC is another point, defined in a specific way from P and ABC: If the base points of the lines PA, PB, PC on the sides opposite A, B, C are reflected about the midpoints of their respective sides, the resulting lines intersect at the isotomic conjugate of P.
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements.Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions from these.
The Kutta condition is a principle in steady-flow fluid dynamics, especially aerodynamics, that is applicable to solid bodies with sharp corners, such as the trailing edges of airfoils.