different between porism vs axiom

English

Etymology

Ancient Greek ??????? (pórisma, “a deduction from a previous demonstration”).

Noun

porism (plural porisms)

1. (geometry, number theory) A proposition affirming the possibility of finding such conditions as will render a certain determinate problem indeterminate or capable of innumerable solutions.
2. A corollary.
   • 1845, Robert Potts, Euclid's Elements

     Porism: something between a problem and a theorem or that in which something is proposed to be investigated.

     A Porism is a proposition in which it is proposed to demonstrate that some one thing, or more things than one, are given, to which, as also to each of innumerable other things, not given indeed, but which have the same relation to those which are given, it is to be shewn that there belongs some common affection described in the proposition.

   • 1845, Robert Potts, Euclid's Elements

     In the original Greek of Euclid's Elements the corollaries to the propositions are called porisms.

   • 1893, Florian Cajori, A History of Mathematics

     The term porism is vague in meaning. The aim of a porism is not to state some property or truth, like a theorem, nor to effect a construction, like a problem, but to find and bring to view a thing which necessarily exists with given numbers or a given construction, as, to find the centre of a given circle, or to find the G.C.D. of two given numbers.

References

• Porism: "A proposition affirming the possibility of finding one or more of the conditions of an indeterminate theorem." - Dugald Stewart
• Porism: "A proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate or capable of innumerable solutions." - John Playfair
• porism on Wikipedia.Wikipedia
• porism at OneLook Dictionary Search

Anagrams

• impros, primos

English

Etymology

From Middle French axiome in the 15th century, from Latin axi?ma (“axiom; principle”), from Ancient Greek ?????? (axí?ma, “that which is thought to fit, a requisite, that which a pupil is required to know beforehand, a self-evident principle”), from ????? (axió?, “to think fit or worthy, to require, to demand”), from ????? (áxios, “fit, worthy”, literally “weighing as much as; of like value”), from ??? (ág?, “I drive”).

Pronunciation

• (Received Pronunciation) IPA^(key): /?aks.?.?m/
• (General American) enPR: ?k's??m, IPA^(key): /?æks.i.?m/
• Hyphenation: ax?i?om

Noun

axiom (plural axioms or axiomata) (the latter is becoming less common and is sometimes considered archaic)

1. (philosophy) A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
2. (logic, mathematics, proof theory) A fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from postulates as being universally applicable, whereas postulates are particular to a certain science or context).
3. An established principle in some artistic practice or science that is universally received.

Synonyms

• (philosophy, mathematics): axioma (now rare)
• (logic, mathematics): postulate

Hypernyms

• (logic): well-formed formula, wff, WFF

Hyponyms

• (mathematics): axiom of choice, axiom of infinity, axiom of pairing, axiom of power set, axiom of regularity, axiom of union, completeness axiom, parallel axiom

Holonyms

• (logic): formal system

Derived terms

• axiomatic
• axiomatical
• axiomatically
• axiomatise, axiomatize
• axiomatisation, axiomatization

Translations

See also

References

• axiom in The Century Dictionary, New York, N.Y.: The Century Co., 1911.
• axiom in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.

Further reading

• axiom on Wikipedia.Wikipedia

Anagrams

• amoxi

Czech

Noun

axiom m

1. axiom

Derived terms

• axiom výb?ru m

Related terms

• axiomatický
• axiomatizovat
• axiomatizace

Swedish

Noun

axiom n

1. axiom

Declension

Related terms

• axiomatisk