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www.tapatalk.com/groups/ufo4afterglow/euclid-39-s-47th-problem-eureka-t2091.html

For this reason, axiomatic introductions to geometry usually employ another proof based on the similarity of triangles (see above). A third graphic illustration of the Pythagorean theorem (in yellow and blue to the right) fits parts of the sides' squares into the hypotenuse's square.

en.wikipedia.org/wiki/Euclidean_geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms , and deducing many other propositions ( theorems ) from these.

www.tapatalk.com/groups/ufo4afterglow/euclid-39-s-47th-problem-eureka-t2091-s...

What I find very interesting from a historical perspective is the point BSG has made by revealing/reminding us how Euclidian Geometry changed the ay many people and cultures ho followed it carried out it's construction projects.

www.humanistictexts.org/euclid.htm

Book XI covers elementary solid geometry; Book XII formally proves the theorem of Hippocrates (not the practitioner of healing) for the area of a circle—pi times the radius squared. Book XIII provides and proves the constructions for the five regular solids of Pythagoras.

www.algebra.com/algebra/homework/Pythagorean-theorem/Pythagorean-theorem.faq...

Question 203766This question is from textbook Discoverig geometry an investigative approach: Euclid's Proof: the area of the whole square equals the sum of its parts. 1) Write an expression for the area of the large square. Then simplified your expression. 2) write an expression for each part of the diagram and sum them up.

mathcs.clarku.edu/~djoyce/java/elements/elements.html

Euclid’s Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty lies in its logical development of geometry and other branches of mathematics. It has influenced all branches of science but none so much as mathematics and the exact sciences.

www.questarter.com/q/proof-of-euclid-39-s-formula-for-primitive-pythagorean...

I have been reading about Pythagorean triples from the wiki page link here.. It says that a pythagorean triple consists of 3 positive integer's $ a, b, c $ such that $ a^2 + b^2 = c^2 $.. Also if all the integers in a triple say $ a, b, c $ are relatively prime then the triplet is called Primitive Pythagorean triplet.. As I was reading more in this article it also described about generating .....

encyclopedia2.thefreedictionary.com/Euclid's+Elements.

Euclid’s Elements a scientific work written by Euclid in the third century B.C. containing the fundamentals of ancient mathematics—elementary geometry, number theory, algebra, the general theory of proportions, and a method for determining areas and volumes, including elements of the theory of limits. In this work, Euclid summarized three centuries ...

www.thefreedictionary.com/Euclid's+axiom

Euclid's axiom synonyms, Euclid's axiom pronunciation, Euclid's axiom translation, English dictionary definition of Euclid's axiom. Noun 1. Euclid's axiom - any of five axioms that are generally recognized as the basis for Euclidean geometry Euclidean axiom, Euclid's postulate math,...

en.wikipedia.org/wiki/Euclid's_Elements

The Elements (Ancient Greek: Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions.The books cover plane and solid Euclidean geometry ...