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In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid 's Elements . [ 1 ]
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.
A special case of the theorem is Thales's theorem, which states that the angle subtended by a diameter is always 90°, i.e., a right angle. As a consequence of the theorem, opposite angles of cyclic quadrilaterals sum to 180°; conversely, any quadrilateral for which this is true can be inscribed in a circle.
Thales's theorem: if AC is a diameter and B is a point on the diameter's circle, the angle ∠ ABC is a right angle. Pamphila says that, having learnt geometry from the Egyptians, Thales was the first to inscribe in a circle a right-angled triangle, whereupon he sacrificed an ox . [ 54 ]
Greek mathematics allegedly began with Thales of Miletus (c. 624–548 BC). Very little is known about his life, although it is generally agreed that he was one of the Seven Wise Men of Greece . According to Proclus , he traveled to Babylon from where he learned mathematics and other subjects, coming up with the proof of what is now called ...
It was published in Oxford in 1921, in two volumes titled Volume I, From Thales to Euclid and Volume II, From Aristarchus to Diophantus. It got positive reviews and is still used today. Ten years later, in 1931, Heath published A Manual of Greek Mathematics, a concise version of the two-volume History.
Thabit ibn Qurra's theorem (amicable numbers) Thales's theorem ; The duality theorem ; Thébault's theorem ; Theorem of de Moivre–Laplace (probability theory) Theorem of the cube (algebraic varieties) Theorem of the gnomon ; Theorem of three moments ; Theorem on friends and strangers (Ramsey theory)
As for any right triangle, the converse of Thales' theorem says that the diameter of the circumcircle equals the hypotenuse; hence for primitive triples the circumdiameter is m 2 + n 2, and the circumradius is half of this and thus is rational but non-integer (since m and n have opposite parity).