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Webster 1913 Edition
Incommensurable
Inˊcom-men′su-ra-ble
,Adj.
[Pref.
in-
not + commensurable
: cf. F. incommensurable
.] Not commensurable; having no common measure or standard of comparison;
– as, quantities are
incommensurable
when no third quantity can be found that is an aliquot part of both; the side and diagonal of a square are incommensurable
with each other; the diameter and circumference of a circle are incommensurable
.Inˊcom-men′su-ra-ble-ness
, Noun.
Inˊcom-men′su-ra-bly
, adv.
Inˊcom-men′su-ra-ble
,Noun.
One of two or more quantities which have no common measure.
Webster 1828 Edition
Incommensurable
INCOMMEN'SURABLE
,Adj.
Having no common measure. Two lines are incommensurable, when, compared to each other, they have no common measure,that is, no measure that will exactly measure both. oth. Quantities are incommensurable, when no third quantity can be found that is an aliquot part of both.
Definition 2024
incommensurable
incommensurable
English
Adjective
incommensurable (comparative more incommensurable, superlative most incommensurable)
- (mathematics) Of two real numbers, such that their ratio is not a fraction of two integers.
- (arithmetic) Of two integers, having no common integer divisor except 1.
- Not able to be measured by the same standards as another term in the context; see measurement; contrast with unmeasurable or immeasurable, each of which means not able to be measured at all, the former more generally, the latter generally due to some infinite quality of the thing being described
- The side and diagonal of a square are incommensurable with each other; the diameter and circumference of a circle are incommensurable.
Related terms
Translations
having no common divisor except 1
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not able to be measured by same standards
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Noun
incommensurable (plural incommensurables)
- An incommensurable value or quantity; an irrational number.
- 1946, Bertrand Russell, History of Western Philosophy, ch. 3:
- Unfortunately for Pythagoras, his theorem led at once to the discovery of incommensurables, which appeared to disprove his whole philosophy.
- 1946, Bertrand Russell, History of Western Philosophy, ch. 3: