|SC|=|BS|\cdot |SD|} Next to the tangent-secant theorem and the intersecting secants theorem, the intersecting chords theorem represents one of the three basic...

geometry, the intersecting secants theorem or just secant theorem describes the relation of line segments created by two intersecting secants and the associated...

. For the intersecting secants theorem and chord theorem the power of a point plays the role of an invariant: Intersecting secants theorem: For a point...

tangent-secant theorem can be proven using similar triangles (see graphic). Like the intersecting chords theorem and the intersecting secants theorem, the...

Christopher Clavius demonstrated this result, sometimes called the intersecting secants theorem, in their commentaries on Euclid. For curves more complicated...

⁠1/2⁠arc(AQ). The chord theorem states that if two chords, CD and EB, intersect at A, then AC × AD = AB × AE. If two secants, AE and AD, also cut the...

the later tradition of Alexandria. In the Elements, Euclid deduced the theorems from a small set of axioms. He also wrote works on perspective, conic sections...

angle theorem (geometry) Intercept theorem (Euclidean geometry) Intersecting chords theorem (Euclidean geometry) Intersecting secants theorem (Euclidean...

including Thales' theorem (31-34), and intersecting chords and tangents, including the intersecting secants theorem and the tangent-secant theorem (35-39). Book...

In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its sides. It states that the sum of the...

proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi ( π {\displaystyle \pi } ) is a transcendental number...

be found in Book 3 of Euclid's Elements, as used e.g. in the intersecting secants theorem. 18th century sources in Latin called any non-tangential line...

Greek mathematics is obscure, and traditional narratives of mathematical theorems found before the fifth century BC are regarded as later inventions. It...

tangent functions. Their reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less used. Each of these six trigonometric...

theorem Intersecting chords theorem Intersecting secants theorem Law of cosines Pons asinorum Pythagorean theorem Tangent-secant theorem Thales's theorem Theorem...

of the Pythagorean theorem and the tangent secant theorem can be replaced by a single application of the power of a point theorem. Case of acute angle...

because a, b are neither zero nor parallel (the planes being distinct and intersecting). If point x satisfies both plane equations, then it also satisfies the...

astronomy as modeled by the celestial sphere. Primarily consisting of theorems which were known at least informally a couple centuries earlier, the Spherics...

chord theorem 1925 in the article sur deux cercles secants for the Belgian math journal Mathesis. Eight years later he published On Two Intersecting Spheres...

equal (this is sometimes called the Two Tangents Theorem, see Incircle). By the secant-tangent theorem, the square of this tangent length equals the power...

In spherical geometry, Lexell's theorem holds that every spherical triangle with the same surface area on a fixed base has its apex on a small circle...

extensions (secant lines) of chords AB and CD intersect at a point P, then their lengths satisfy AP·PB = CP·PD (power of a point theorem). The midpoints...

to the intersecting plane, the intersection curve will be a hyperbola (or degenerate hyperbola, if the two generatrices are in the intersecting plane)...

theorem Intersecting chords theorem Intersecting secants theorem Law of cosines Pons asinorum Pythagorean theorem Tangent-secant theorem Thales's theorem Theorem...

the secant intersecting y = x2 at (0,0) and (3,9) is 3. (The slope of the tangent at x = 3⁄2 is also 3 − a consequence of the mean value theorem.) By...

Kantorovich theorem Laguerre's method Methods of computing square roots Newton's method in optimization Richardson extrapolation Root-finding algorithm Secant method...

Riemann–Roch theorem to higher dimension is the Hirzebruch–Riemann–Roch theorem, as well as the far-reaching Grothendieck–Riemann–Roch theorem. Hilbert schemes...

segment for details. Using the intersecting chords theorem (also known as power of a point or secant tangent theorem) it is possible to calculate the...

The Method of Mechanical Theorems (Greek: Περὶ μηχανικῶν θεωρημάτων πρὸς Ἐρατοσθένη ἔφοδος), also referred to as The Method, is one of the major surviving...

line g {\displaystyle g} intersects an ellipse at 0, 1, or 2 points, respectively called an exterior line, tangent and secant. Through any point of an...