
	Where results make sense

Topic: Euclids lemma

Related Topics

Euclid computer program

South Euclid

South Euclid, Ohio

Euclid v Amber

Euclid Madden

Euclid of Alexandria

Euclid Township, Cuyahoga County, Ohio

Euclid Drafter

Euclid Township, Minnesota

Euclid of Megara

Euclid Road Machinery Company

Diagonal lemma

In the News (Fri 17 Feb 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Porism - Wikipedia, the free encyclopedia
		The treatise which has given rise to the controversies on this subject is the Porisms of Euclid, the author of the Elements.
		On the "porism" in the other sense he adds nothing to the definition of "the older geometers" except to say (what does not really help) that the finding of the center of a circle and the finding of the greatest common measure are porisms (Proclus, ed.
		It is a fact that Lemma 31 (though it makes no mention of a conic) corresponds exactly to Apollonius's method of determining the foci of a central conic (Conics, iii.
	en.wikipedia.org /wiki/Porism (1559 words)

	[No title]
		These are Pappus's thirty-eight lemmas relating to the porisms, ten cases of the proposition concerning four straight lines, twenty-nine porisms, two problems in illustration and some preliminary lemmas.
		Thus, in view of the ancillary relation in which Pappus's lemmas generally stand to the works to which they refer, it seems incredible that the first seven out of thirty-eight lemmas should be really equivalent (as Chasles makes them) to Euclid's first seven Porisms.
		Observing, e.g., that the intercept-Porism is still true if the two fixed points are points on a conic, and the straight lines drawn through them intersect on the conic instead of on a fixed straight line, Zeuthen conjectures that the Porisms were a by-product of a fully developed projective geometry of conics.
	encyclopedia.jrank.org /correction/edit?locale=en&content_id=53769 (1246 words)

	80-110: The Nature of Mathematical Reasoning
		Mathematical theories are systematized by axioms and definitions in a way exemplified by Euclid in his famous compilation of geometric knowledge in the Elements.
		Euclids theory of geometry had 5 short axioms, and from these axioms hundreds of pages of theorems follow.
		Euclid's geometry was taken to be the paradigm of a good theory.
	www.andrew.cmu.edu /user/scheines/scheines.006/scheines.006/80-110/lectures/jan22/jan22.html (939 words)

	List of lemmas: Encyclopedia topic (Site not responding. Last check: 2007-10-13)
		Fatou's lemma (Fatou's lemma: fatous lemma establishes an inequality relating the integral (in the sense of lebesgue)...
		Noether's normalization lemma (commutative algebra (commutative algebra: in abstract algebra, commutative algebra is the field of study of commutative rings,...
		Schreier's subgroup lemma (Schreier's subgroup lemma: schreiers subgroup lemma is a theorem in group theory used in the schreier-sims...
	www.absoluteastronomy.com /reference/list_of_lemmas (960 words)

	Math Refresher: Euclid's Method for the Greatest Common Denominator
		The method for finding the greatest common denominator is found in Euclid's Elements and is therefore known today as Euclid's algorithm.
		Here is the proof (note: in the example referenced, it refers to Gaussian Integers, but the same proof applies to Eisenstein Integers and other types of quadratic integers that are characterized by a division algorithm).
		One result of this is that for any two Euclidean integers (quadratic integers that have a division algorithm) that are not relatively prime, it is possible to derive two smaller integers which are relatively prime.
	mathrefresher.blogspot.com /2005/07/euclids-method-for-greatest-common.html (507 words)

	Pappus of Alexandria - Crystalinks
		Pappus also wrote commentaries on Euclids Elements (of which fragments are preserved in Proclus and the Scholia, while that on the tenth Book has been found in an Arabic MS.), and on Ptolemy's Apuovtth.
		Pappus then enumerates works of Euclid, Apollonius, Aristaeus and Eratosthenes, thirty-three books in all, the substance of which he intends to give, with the lemmas necessary for their elucidation.
		With the mention of the Porisms of Euclid we have an account of the relation of porism to theorem and problem.
	www.crystalinks.com /pappus.html (1234 words)

	Theorem: Free Encyclopedia Articles at Questia.com Online Library
		A lemma is a theorem that is demonstrated as an intermediate step in the proof of another, more basic theorem.
		A corollary is a theorem that follows as a direct consequence of another theorem or an axiom.
		This theorem was known to the Greek mathematician Euclid...
	www.questia.com /library/encyclopedia/theorem.jsp?l=T&p=2 (1477 words)

	PORISM - Online Information article about PORISM
		Pappus states that the porisms of Euclid are neither theorems nor problems, but are in some sort intermediate, so that they may be presented either as theorems or as problems; and they were regarded accordingly by many geometers, who looked merely at the See also:
		thirty-eight lemmas for the three books of porisms; and these include 171 theorems.
		The lemmas which Pappus gives in connexion with the porisms are interesting historically, because he gives (1) the fundamental theorem that the See also:
	encyclopedia.jrank.org /POL_PRE/PORISM.html (1855 words)

	INFINITESIMAL CALCULUS - LoveToKnow Article on INFINITESIMAL CALCULUS (Site not responding. Last check: 2007-10-13)
		If from the greater of two magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there will at length remain a magnitude less than the smaller of the proposed magnitudes.
		It may be described ~as the enclosure of the magnitude to be evaluated between two others which can be brought by a definite process to differ from each other by less than any assigned magnitude.
		In the Philosophiae naturalis principia mathensatica (1687), commonly called the Principia, the words fluxion and moment occur in a lemma in the second book; but the notation which is characteristic of the calculus of fluxions is nowhere used.
	www.1911encyclopedia.org /I\IN\INFINITESIMAL_CALCULUS.htm (21110 words)

	SIR ISAAC NEWTON - LoveToKnow Article on SIR ISAAC NEWTON (Site not responding. Last check: 2007-10-13)
		Up to the time of the publication of the Principia in 1687 thi method of fluxions which had been invented by Newton, and had been of great assistance to him in his mathematical investigations, was still, except to Newton and his friends, a secret.
		One of the most important rules of the method forms the second lemma of the second book of the Princi pie.
		Though this new and powerful method was of great help to Newton in his work, he did not exhibit it in the results.
	43.1911encyclopedia.org /N/NE/NEWTON_SIR_ISAAC.htm (9689 words)

	Talk:Euclid's lemma - Wikipedia, the free encyclopedia
		I'd be interested in seeing Euclids proof of proposition 30 on there.
		Is bezout's identity so obvious or well-known that it can be used in the proof of Euclid's lemma without further ado?
		This page was last modified 15:30, 11 March 2006.
	en.wikipedia.org /wiki/Talk:Euclid's_lemma (69 words)

	KyleM.xwell » Blog Archive » Euclid’s Algorithm
		We focused al most entirely on Euclid’s Algorithm.
		Osvath is still kind of a dotte ring old man, and it turns out that I’m not the only one who thinks he’s harder to understand (I believe his voice has gotten weaker).
		You may use Markdown in your comment, or post as plain text.
	kylem.xwell.org /blog/archives/2003/01/17/personal/class/euclids-algorithm (379 words)

	Who Invented The Fundamental Theorem Of Arithmetic Mathematics The Free Encyclopedia / / / / Founder Jimmy Waless ... (Site not responding. Last check: 2007-10-13)
		Proving that the list is always the same is what the Fundamental Theoremis all about.Euclids LemmaThe critical element in the proof of the Fundamental Theorem is a lemma calledEuclids Lemma.A lemma is a minor theorem which is useful only to help prove some other more importanttheorem.
		Sometimes a minor theorem is originally developed as a lemma and then everyonedecides that the lemma is actually quite important for its own sake but they keepon calling it a lemma anyway.Euclids Lemma states that if a prime number p divides a number N i.e.
		Now you might be thinking: what if the knife cuts the raisin in half does that stillcount and to avoid that problem well replace the raisins with marbles and use a plastic knife so thatthe knife cant possibly cut the marbles in half.
	www.4teenagers.net /cgi/who_invented_the_fundamental_theorem_of_arithmetic.htm (1998 words)

	Re: Newbie question(s)...
		I would recommend you look at starting with something along the level of Discrete Mathematics, focusing on topics like understanding the basic language of mathematics (e.g.
		conjecture, theorm, proof, lemma), and the basic types of proofs (induction, proof by contradiction -- reductio ad absurdum), and learn some classic proofs in topics like geometry (just because it's fun), number theory, and abstract (aka modern) algebra.
		Modern cryptography (and cryptanalysis) is based upon mathematics, so if you seriously want to learn all the details and really understand cryptography you need strong math skills.
	www.usenet.com /newsgroups/sci.crypt/msg02179.html (756 words)

	The Fundamental Theorem Of Arithmetic Fundamental Theorem Of Arithmetic The Free Encyclopedia / / / / Founder Jimmy ... (Site not responding. Last check: 2007-10-13)
		This is a minimal counterexample argument.The uniqueness part of the proof hinges on the following fact: if a prime number p divides a product ab then it divides a or it divides b Euclids lemma.
		Does such a factorization always exist And isthis factorization unique About 350 BC Euclid answeredyes in his Elements.
		Today we word his answer asfollows:The Fundamental Theorem of ArithmeticEvery positive integer greater than one can be expresseduniquely as a product of primes apart from therearrangement of terms.
	www.4teenagers.net /cgi/the_fundamental_theorem_of_arithmetic.htm (1032 words)

	CS6110 Term Project: Formal Verification of IDEA with HOL
		To prove it, we need prove the Euclids' Algorithm, some clever encoding and decoding algorithm and some attributes related to the prime number 65537 (2^16+1, the mode).
		With the assistance of these lemmas, we can prove that the effect of a even round operation can be inversed by simply run the same operation with the same key again.
		To prove the correctness of the encryption and decryption, we simply apply the definition of the ecryption and decryption to the goal, and then apply the lemma we just proved.
	www.cs.utah.edu /~slind/papers/lpar05/IDEA/report.htm (3058 words)

	List of number theory topics: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-13)
		Euclidean algorithm (The euclidean algorithm (also called euclids algorithm) is an algorithm to determine the greatest common...)
		Euclid's lemma (Euclids lemma is a generalisation of proposition 30 of book vii of euclids elements....)
		Gauss lemma (In mathematics, there is more than one gauss lemma; all are named after carl friedrich gauss....)
	www.absoluteastronomy.com /ref/list_of_number_theory_topics (6033 words)

	Martindale's Calculators On-Line Center: Mathematics - E-H (Site not responding. Last check: 2007-10-13)
		EUCLID'S ELEMENTS (JAVA APPLETS) - D.E. Joyce, Department of Mathematics and Computer Science, Clark University, Worcester, Massachusetts Euclids Elements Course (Text, Images, Applets & Simulations).
		"...Euclid's Elements form one of the most beautiful and influential works of science in the history of humankind.
		EUCLID'S ELEMENTS: TRANSLATION OF JOYCE'S "EUCLID'S ELEMENTS" INTO SPANISH & CATALAN (JAVA APPLETS) - JDL euclides.org & Development Network Services Presence with permission from D.E. Joyce, Department of Mathematics and Computer Science, Clark University, Worcester, Massachusetts Euclids Elements Course (Text, Images, Applets & Simulations).
	www.martindalecenter.com /Calculators2_6_EH.html (7277 words)

	Usenet Archive (Site not responding. Last check: 2007-10-13)
		You mean for prime p > 2 of course.
		If you accept this lemma, then the proof of the thing you're after is pretty straightforward.
		The lemma itself is a simple exercise in homological algebra, as covered for instance in the book on homological algebra by Hilton and Stammbach.
	www.all-usenet-archive.com /File.asp?service=43422 (9323 words)

	Interactive Real Analysis Guest Book
		Wachsmuth, I was looking at the "Interactive Real Analysis" and I noticed something (I think is) wrong with Euclid's Theorem (There is no largest prime number.
		GREAT pages, I'm in 11th grade and have been challenged with proving Euclids Theory e^(i*pi)=-1.
		Little did I realize that when I wanted to remember his proof of the abel theorem of convergence (together with the summation by parts lemma), all I had to do was check your site on the world wide web.
	pirate.shu.edu /projects/reals/about/real-bk.html (12146 words)

	IRA: Read Guest Book
		Thanks for all the help with my paper on Lebesgue Integration and Measure.
		I am a student of b.sc first year and i tried to gain knowledge about graph theory and its application and partial order lattice and zorns lemma but i was unable to do so sir please give me the possible knowledge of above soon i will be waiting for it please Email to me.
		I hope to see a similar text for abstract algebra soon.
	pirate.shu.edu /~wachsmut/ira/about/real-bk.html (15116 words)

Try your search on: Qwika (all wikis)