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It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The Pythagoreans are credited with the first proof of the Pythagorean theorem, [44] though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers.
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. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's Elements.
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
Other common auxiliary constructs in elementary plane synthetic geometry are the helping circles. As an example, a proof of the theorem on the sum of angles of a triangle can be done by adding a straight line parallel to one of the triangle sides (passing through the opposite vertex).
Berger–Kazdan comparison theorem (Riemannian geometry) Bernstein's theorem (approximation theory) Bernstein's theorem (functional analysis) Berry–Esséen theorem (probability theory) Bertini's theorem (algebraic geometry) Bertrand–Diquet–Puiseux theorem (differential geometry) Bertrand's ballot theorem (probability theory, combinatorics)
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.
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