Euclid's Elements - Table of Content
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![Euclid Teaching](../euclid_teaching_geometry.jpg) |
Euclid's Elements is a mathematical and geometric treatise consisting of
13 books written by the Greek mathematician Euclid in Alexandria circa
300 BC. It comprises a collection of definitions, postulates (axioms),
propositions (theorems and constructions), and proofs.
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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 I, Proposition 1](euclid_book_i_1_17.jpg) |
Euclid's Elements Book I, Proposition 1: On a given finite line to
construct an equilateral triangle |
![Euclid's Elements Book I, Proposition 2](euclid_book_i_2_17.jpg) |
Euclid's Elements Book I, Proposition 2: To place at a given point (as
an extremity) a straight line equal to a given straight line |
![Euclid's Elements Book I, Proposition 3](../geometry/euclid_book_i_3_17.jpg) |
Euclid's Elements Book I, Proposition 3: Given two unequal straight
lines, to cut off from the greater a straight line equal to the less |
![a](euclid_book_i_4_sas_17.jpg) |
Euclid's Elements Book I, Proposition 4: (Side-Angle-Side SAS) |
![Euclid's Elements Book I,1 Proposition 5, Isosceles Triangle](euclid_book_i_5_isosceles_1.jpg) |
Euclid's Elements Book I, Proposition 5: (Pons Asinorum) Isosceles
triangles |
![Euclid's Elements Book I Proposition 6](euclid_book_i_6_triangle_1.jpg) |
Euclid's Elements Book I, Proposition 6: Converse of I.5
"Proof by contradiction," also called reductio ad absurdum. |
![Euclid's Elements Book I,1 Proposition 7](euclid_book_i_7_congruence.jpg) |
Euclid's Elements Book I, Proposition 7
Given two straight lines constructed on a straight line (from its
extremities) and meeting in a point,... |
![Euclid's Elements Book i,1 Proposition 8 SSS](euclid_book_i_8_sss_1.jpg) |
Euclid's Elements Book I, Proposition 8: (Side-Side-Side SSS Congruence) |
![Bisect an angle](euclid_elements_book_i_9_17.jpg) |
Book I, Proposition 9: Bisect a given angle
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![Classical Pythagorean Theorem](../pythagoras/pythagoras_theorem_17.jpg) |
Book I,
Proposition 47th: Pythagoras
Pythagorean Theorem.
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![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. |
![Euclid's Elements Book I](euclid_book_i_word_cloud_17.jpg) |
Euclid's Elements Book I Word Cloud.
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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 V, inscribed, circumscribed, polygon](euclid_book_5_word_cloud_1.jpg) |
Euclid's Elements Book V Word Cloud.
A treatise on proportions of magnitudes. Proposition 25 has as a special case
the inequality of arithmetic and geometric means. |
![Euclid's Elements Book IV, inscribed, circumscribed, polygon](euclid_book_4_word_cloud_1.jpg) |
Euclid's Elements Book IV Word Cloud.
Constructs the incircle and circumcircle of a triangle, and constructs regular
polygons with 4, 5, 6, and 15 sides |
![Euclid's Elements Book III, geometrical algebra](euclid_book_3_word_cloud_1.jpg) |
Euclid's Elements Book III Word Cloud.
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![Euclid's Elements Book II](euclid_book_ii_word_cloud_1.jpg) |
Euclid's Elements Book II Word Cloud.
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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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![Angle Bisector Theorem](euclid_elements_vi_3_bisect.jpg) |
Euclid's Elements Book VI, Proposition 3: Angle Bisector Theorem
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![Euclid Elements Book X, Lemma for Proposition 33](euclid_book_x_33_17.jpg) |
Euclid's
Elements, Book X, Lemma for Proposition 33 One page visual illustration. |
![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. |
![](../mindmap/mindmap_elements_170.jpg) |
MindMap of
Euclid's Elements. A mindmap is an excellent learning tool for
visual communication, organization, content sequencing, and navigation
on Internet. |
![](../mindmap/euclid_elements_book_1_170.jpg) |
MindMap of Euclid's Elements Book I
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![The School of Athens.](../geometric_art/school_athens_perspective_1.jpg) |
The School of Athens
Euclid and Pythagoras together!
Video |
![Twin Prime Number Conjecture Euclid](twin_prime_euclid_17.jpg) |
Twin
Prime Conjecture. is a famous unsolved problem in number theory
discovered by Euclid.
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![The School of Athens](../euclid_teaching_geometry.jpg) |
Euclid's Quotes. |