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![College Geometry Online, eLearning](../machu_picchu_h1_810.jpg)
Discover the Fascinating World of Euclidean Geometry: Explore Classical Theorems and Their Applications Today!
![Euclidean Geometry](euclidean_geometry_17.jpg)
Lines stretch infinitely,
Circles embrace symmetry,
Angles speak their truth.
Geometry's timeless grace,
A testament to our world.
Classical geometry is a branch of mathematics that deals
with the study of geometry based on Euclid's Elements.
Euclid's Elements is a widely influential book in mathematics
that lays out a comprehensive system of geometry that has been
studied for thousands of years. Classical geometry is
concerned with the study of points, lines, and shapes in two
and three dimensions, as well as their relationships and
properties. Classical geometry has many applications in fields
such as architecture, engineering, physics, and computer
graphics.
This index includes definitions, formulas,
and interactive illustrations to help users understand and
explore each theorem. It is a useful resource for students,
teachers, and anyone interested in mathematics and geometry.
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Classical Theorems - Page 1
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![Dynamic Geometry 1478](../school-college/5/p1478-reuschle-terquem-theorem-3-cevians-circumcircle-concurrent-geogebra-ipad-1.jpg) |
Dynamic Geometry 1478.
Cyclocevian, Reuschle-Terquem Theorem, Concurrent Cevians, Triangle, Circumcircle, Secant line, Step-by-step Illustration. GeoGebra,
iPad. |
![Dynamic Geometry 1477](../school-college/5/p1477-miquel-pentagram-theorem-circumcircle-5-concyclic-geogebra-ipad-1.jpg) |
Dynamic Geometry 1477.
Miquel's Pentagram Theorem, Pentagon, Triangle, Circumcircles, Concyclic Points, Step-by-step Illustration. GeoGebra,
iPad. |
![Dynamic Geometry 1476](../school-college/5/p1476-droz-farny-line-theorem-orthocenter-collinear-midpoint-geogebra-1.jpg) |
Dynamic Geometry 1476.
Droz-Farny Line Theorem, Triangle, Orthocenter, Perpendicular, Collinear Midpoints, Step-by-step Illustration. GeoGebra,
iPad. |
![Dynamic Geometry 1475](../school-college/5/p1475-clifford-intersecting-circles-theorem-geogebra-1.jpg) |
Dynamic Geometry 1475.
Clifford Intersecting Circles Theorem, Step-by-step Illustration, GeoGebra, iPad. |
![Dynamic Geometry 1474](../school-college/5/p1474-butterfly-theorem-circle-chord-midpoint-geogebra-ipad-1.jpg) |
Dynamic Geometry 1474.
Butterfly Theorem, Circle, Chords, Midpoints, Step-by-step Illustration. |
![Dynamic Geometry 1473](../school-college/5/p1473-kosnita-theorem-triangle-circumcenter-concurrent-geogebra-1.jpg) |
Dynamic Geometry 1473.
Kosnita's Theorem, Triangle, Four Circumcenters, Concurrent Line, Step-by-step Illustration. |
![Dynamic Geometry 1468](../school-college/5/p1468-steiner-theorem-triangle-inradius-exradius-circumradius-ipad-geogebra-1.jpg) |
Dynamic Geometry 1468.
Steiner's Theorem, Triangle, Circumradius, Inradius, Sum of Exradii, Step-by-step Illustration. |
![Geometry Problem 1466](../school-college/5/p1466-tangential-quadrilateral-newton-line-incenter-geogebra-ipad-1.jpg) |
Geometry Problem 1466.
Tangential Quadrilateral, Newton Line, Incenter, Midpoint, Diagonal, Collinear Points.
Step-by-step Illustration using GeoGebra. |
![Geometry Problem 1462](../school-college/5/p1462-newton-theorem-gauss-line-quadrilateral-midpoint-side-diagonal-geogebra-1.jpg) |
Geometry Problem 1462.
Newton-Line, Newton-Gauss Line, Complete Quadrilateral, Midpoints of Sides and Diagonals,
Collinear Points. Step-by-step Illustration using GeoGebra. |
![Geometry Problem 1460](../school-college/5/p1460-newton-gauss-line-dynamic-complete-quadrilateral-1.jpg) |
Dynamic Geometry
1460.
Newton-Gauss Line, Complete Quadrilateral, Midpoints of Diagonals,
Collinear Points, Step-by-step Illustration using GeoGebra. |
![Geometry Problem 1455](../school-college/5/p1455-nagel-point-incircle-congruence-geogebra-ipad-1.jpg) |
Geometry
Problem 1455.
Nagel Point, Excircles, Incircle, Congruent Segments,
iPad. Step-by-step illustration using GeoGebra. |
![Dynamic Geometry 1452](../school-college/5/p1452-cyclic-quadrilateral-sangaku-japanese-theorem-geogebra-1.jpg) |
Dynamic Geometry 1452.
Japanese Theorem, Sangaku,
Cyclic Quadrilateral, Incenter, Rectangle, Inradius. Step-by-step
illustration using GeoGebra. |
![Dynamic Geometry 1451](../school-college/5/p1451-orthopole-geogebra-triangle-perpendicular-concurrency-1.jpg) |
Dynamic Geometry 1451.
Orthopole of a Line. Step-by-step
illustration using GeoGebra. |
![Dynamic Geometry 1450](../school-college/5/p1450-ortholine-complete-quadrilateral-geogebra-dynamic-igs-1.jpg) |
Dynamic Geometry 1450.
Ortholine, Steiner Line, Complete Quadrilateral, Collineal Orthocenters. Step-by-step
illustration using GeoGebra. |
![Dynamic Geometry 1449](../school-college/5/p1449-salmon-line-geogebra-dynamic-geometry-igs-1.jpg) |
Dynamic Geometry 1449.
Salmon Line. Step-by-step
illustration using GeoGebra. |
![Dynamic Geometry 1448](../school-college/5/p1448-simson-line-geogebra-dynamic-1.jpg) |
Dynamic Geometry 1448.
Simson Line. Step-by-step
illustration using GeoGebra. |
![Problem 1447](../school-college/5/p1447-vecten-point-outer-geogebra-dynamic-1.jpg) |
Dynamic Geometry Problem 1447.
Outer Vecten Point. Step-by-step
illustration using GeoGebra. |
![Problem 1446](../school-college/5/p1446-lemoine-line-tangent-geogebra-dynamic-1.jpg) |
Dynamic Geometry Problem 1446.
Lemoine Line, triangle, circumcircle, tangent, collinear points. Step-by-step animation using GeoGebra. |
![Problem 1444](../school-college/5/p1444-asymmetric-propeller-equilateral-triangle-geogebra-1.jpg) |
Dynamic Geometry Problem 1444.
The Asymmetric Propeller Theorem, Equilateral Triangles, Midpoints. Step-by-step animation using GeoGebra. |
![Classical Pythagorean Theorem](../pythagoras/pythagoras_theorem_17.jpg) |
Pythagorean Theorem.
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![Euclid's Elements, Book II, Proposition 12](euclid_elements_ii_12_17.jpg) |
Euclid's Elements Book II, Proposition 12: Law of Cosines.
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![Euclid's Elements: Book II, Proposition 13: Law of Cosines](euclid_elements_ii_13_17.jpg) |
Euclid's Elements Book II, Proposition 13: Law of Cosines.
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![Median Length theorem](median_length_17.jpg) |
Median
length, Apollonius' Theorem |
![Pythagoras Theorem, 47th Proposition of Euclid's Book I](../pythagoras/pythagoras_euclid_theorem_170.jpg) |
The significance of the Pythagorean theorem by Jacob
Bronowski.
Pythagorean Theorem, 47th Proposition of Euclid's Book I. |
![Geometry Problem 889](../school-college/p889-carnot-theorem-acute-triangle-inradius-circumradius-html5-ipad-1.jpg) |
Carnot's Theorem. Geometry Problem 889
Carnot's Theorem in an acute triangle, Circumcenter, Circumradius, Inradius. GeoGebra, HTML5 Animation for Tablets. |
![Ceva's Theorem](ceva_theorem_cl_17.jpg) |
Ceva's Theorem.
Concurrency. Interactive proof with animation. Key concept:
Menelaus Theorem. |
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Menelaus' Theorem. Interactive proof with
animation and key concepts..
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![van Aubel theorem](van_aubel_theorem_cl_17.jpg) |
van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation. |
![van Aubel theorem for Tablets, iPad, Nexus, Galaxy](van-aubel-theorem-quadrilateral-square-ipad-nexus-galaxy-1.jpg) |
van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation for Tablets, iPad,
Nexus, Galaxy. |
![Problem 1445](../school-college/5/p1445-van-aubel-theorem-quadrilateral-geogebra-step-1.jpg) |
Dynamic Geometry Problem 1445.
Van Aubel's theorem, Quadrilateral and Four Squares, Centers. Step-by-step animation using GeoGebra. |
![](../heron/heron__proof_170x100.jpg) |
Heron's Formula.
Key facts and
a purely geometric
step-by-step proof.
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![Euclid's Elements 23 definitions](euclid_elements_definition_170.jpg) |
Euclid's Elements
Book I, 23 Definitions. One-page visual illustration.
Euclid's Elements Book.
Index |
![Angle Bisector Theorem](euclid_elements_vi_3_bisect.jpg) |
Euclid's Elements Book VI, Proposition 3: Angle Bisector Theorem |
![Euclid's Elements Book XIII, Proposition 10](euclid_elements_book_xiii_10_17.jpg) |
Euclid's
Elements, Book XIII, Proposition 10 One page visual illustration. |
![](../equilic/cyclic_ptolemy_theorem_170.jpg) |
Ptolemy's Theorem.
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![Brahmagupta's Theorem](../software/dynamic-geometry-brahmagupta-theorem-cyclic-quadrilateral-ipad-1.jpg) |
Dynamic Geometry: Brahmagupta Theorem,
. GeoGebra, HTML5 Animation for Tablets |
![Brianchon Theorem](brianchon_theorem_hexagon_1.jpg) |
Brianchon's Theorem in a Circumscribed Hexagon. |
![Brianchon Corollary](brianchon_corol_hexagon_1.jpg) |
Brianchon Corollary, Circumscribed Hexagon, Concurrency lines. |
![Carnot's Theorem, Acute Triangle](carnot_acute_1.jpg) |
Carnot's
Theorem in an Acute Triangle. |
![Carnot's Theorem, Obtuse Triangle](carnot_obtuse_triangle_1.jpg) |
Carnot's
Theorem in an Obtuse Triangle. |
![Clifford's theorem](clifford_theorem_17.jpg) |
Clifford's Circle Chain
Theorems. This is a step by step presentation of the first theorem.
Clifford discovered, in the ordinary Euclidean plane, a "sequence or
chain of theorems" of increasing complexity, each building on the last
in a natural progression.
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![](../equilic/cyclic_ptolemy_ratio_170.jpg) |
Cyclic
Quadrilateral: Ratio of the Diagonals
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![Euler Line, Nine Point Circle](euler_nine_point_circle_cl_.jpg) |
Nine-Point Center, Nine-Point Circle, Euler Line.
Interactive illustration.
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![Soddy Circles and Descartes Theorem](../geometry/soddy_descartes_circle_17.jpg) |
Soddy
Circles and Descartes Theorem.
Three tangent circles, Inscribed and Circumscribed Circles, Radii. |
![Elearning 155](../problem/p155_triangle_circle_17.jpg) |
Euler's Problem, Problem 155. Distance between the Incenter to the Circumcenter. |
![The Simson Line Index](simson_line_i.jpg) |
The Simson Line, Theorems
and Problems - Index. |
![Casey Theorem](../equilic/casey_theorem_ptolemy_170.jpg) |
Casey's Theorem. Generalized Ptolemy's Theorem.
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![](../circle/brahmagupta_formula_170.jpg) |
Brahmagupta's Formula
Area of a cyclic quadrilateral.
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![](../circle/brahmagupta_theorem_170.jpg) |
Brahmagupta's Theorem
Cyclic quadrilateral.
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![](../solid/platonic_solid_170.jpg) |
Platonic
Solids, Interactive animation.
HTML5 Animation for iPad and Nexus
Flash Animation. |
![Theaetetus Theorem, Platonic Solids](../solid/theaetetus_theorem_17.jpg) |
Theaetetus' Theorem, Platonic Solids, Interactive animation |
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Last updated: Jun 14, 2023
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