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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.
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 ]
By the power-of-a-point theorem, the product of lengths PM · PN for any ray PMN equals to the square of PT, the length of the tangent line segment (red). No tangent line can be drawn through a point within a circle, since any such line must be a secant line. However, two tangent lines can be drawn to a circle from a point P outside of the circle.
Cut-elimination theorem (proof theory) D ... Monotone class theorem ... Thabit ibn Qurra's theorem (amicable numbers) Thales's theorem ...
Thales' theorem, named after Thales of Miletus states that if A, B, and C are points on a circle where the line AC is a diameter of the circle, then the angle ABC is a right angle. Cantor supposed that Thales proved his theorem by means of Euclid Book I, Prop. 32 after the manner of Euclid Book III, Prop. 31. [15] [16]
Thales' theorem states that an angle inscribed in a semicircle (with a vertex on the semicircle and its defining rays going through the endpoints of the semicircle) is a right angle. Two application examples in which the right angle and the Thales' theorem are included (see animations).
From January 2008 to May 2009, if you bought shares in companies when John L. Clendenin joined the board, and sold them when he left, you would have a -3.9 percent return on your investment, compared to a -38.2 percent return from the S&P 500.
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 ...