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The proof of Proposition 1.16 given by Euclid is often cited as one place where Euclid gives a flawed proof. [5] [6] [7] Euclid proves the exterior angle theorem by: construct the midpoint E of segment AC, draw the ray BE, construct the point F on ray BE so that E is (also) the midpoint of B and F, draw the segment FC.
The pons asinorum in Oliver Byrne's edition of the Elements [1]. In geometry, the theorem that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (/ ˈ p ɒ n z ˌ æ s ɪ ˈ n ɔːr ə m / PONZ ass-ih-NOR-əm), Latin for "bridge of asses", or more descriptively as the isosceles triangle theorem.
An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it; this is the exterior angle theorem. [34]
The Elements (Ancient Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions.
The congruence theorems side-angle-side (SAS) and side-side-side (SSS) also hold on a sphere; in addition, if two spherical triangles have an identical angle-angle-angle (AAA) sequence, they are congruent (unlike for plane triangles). [9] The plane-triangle congruence theorem angle-angle-side (AAS) does not hold for spherical triangles. [10]
Lie's theorem (Lie algebra) Lie's third theorem ; Lie–Palais theorem (differential geometry) Lindemann–Weierstrass theorem (transcendental number theory) Lie–Kolchin theorem (algebraic groups, representation theory) Liénard's theorem (dynamical systems) Lindelöf's theorem (complex analysis) Lindström's theorem (mathematical logic)