incommensurableadj.n.
/ɪnkəˈmɛnsjʊərəb(ə)l//ɪnkəˈmɛnʃərəb(ə)l//ɪŋkəˈmɛnsjʊərəb(ə)l//ɪŋkəˈmɛnʃərəb(ə)l/ A. adj.
1.
a. Mathematics. Not commensurable; having no common measure (integral or fractional). Said of two or more quantities or magnitudes, or of one quantity or magnitude in relation to another (const. with, †to); also sometimes absol. = incommensurable with ordinary or ‘rational’ quantities, as the natural numbers; the same as irrational or surd (but not usually said, like these, of roots).
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > [adjective] > describing relationships between quantities > incommensurable
incommensurable?a1560
heterogeneous1656
incommensuratea1687
?a1560 L. Digges Geom. Pract.: Pantometria (1571) iii. viii. sig. R j v These lines for that they are some of them incommensurable, can not exactly be expressed, saue only in surde numbers.
1570 H. Billingsley tr. Euclid Elements Geom. x. f. 229 Incommensurable magnitudes are such, which no one common measure doth measure.
a1688 R. Cudworth Treat. Eternal & Immutable Morality (1731) iv. v. 271 That the Diameter of every Square is Incommensurable with the Sides.
1723 J. Clarke tr. Rohault's Syst. Nat. Philos. I. i. ix. 33 Suppose ABCD to be a Square, it may be geometrically demonstrated, that the Side AB, is incommensurable to the Diagonal AC.
1837 H. Hallam Introd. Lit. Europe I. iii. 332 The rules as to surd roots are referrible to incommensurable magnitudes.
1900 N.E.D. at Incommensurable Mod. The ratio of the circumference of a circle to its diameter (denoted by π) is an incommensurable quantity.
b. (in Arithmetic): Having no (integral) common measure except unity; prime to one another.
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > [adjective] > describing relationships between quantities > other
incommensurable1557
minor1571
reflexive1903
biunique1941
dyadic1962
1557 R. Record Whetstone of Witte sig. Bi If thei haue no suche common diuisor, then are thei called incommensurable, as 18 and 25.
1806 C. Hutton Course Math. (ed. 5) I. 53 If it happen that the common measure thus found is 1; then the numbers are said to be incommensurable, or not having any common measure.
2.
a. gen. Having no common standard of measurement; not comparable in respect of magnitude or value.
ΚΠ
1660 R. Coke Justice Vindicated 12 Whether such things so apprehended by the Senses, be pleasant, profitable, just or unjust..commensurable, or incommensurable.
1664 H. More Apol. in Modest Enq. Myst. Iniquity 539 Will not this Position prove as incommensurable to humane affairs and be laden with as great inconveniences?
1796 E. Burke Let. to Noble Lord 6 Between them and money there is no common measurer. Such services, if done by abler men than I am, are, quantities incommensurable.
1845 T. De Quincey On Temperance Movement in Tait's Edinb. Mag. Oct. 663/2 The two states are incommensurable on any plan of direct comparison.
1881 B. F. Westcott & F. J. A. Hort New Test. in Orig. Greek II. Introd. ii. 46 The rival probabilities represented by relative number of attesting documents must be treated as incommensurable.
b. spec. Not worthy to be measured with; not coming up to the standard of measurement of (something); utterly disproportioned to.
ΘΚΠ
the world > relative properties > order > disorder > disharmony or incongruity > unsuitability or inappropriateness > [adjective] > disproportionate
unproportioneda1500
unproportionate1535
misproportioned1552
disproportionate1555
disproportionated1572
unproportionable1576
improportionate1581
disproportionable1589
disproportioned1597
improportionable1601
disproportional1609
asymmetral1615
unproportional1628
overproportionated1647
improportioned1656
improportionala1662
over-proportioned1662
overproportionate1672
uncommensurate1676
incommensurate1684
incommensurable1820
1820 S. Turner Hist. Anglo-Saxons (ed. 3) I. iii. iv. 303 The forces of either were so incommensurable with the numbers and bravery of the people they attacked.
1856 P. E. Dove Logic Christian Faith vi. §2. 340 His past life is incommensurable with infinity.
1892 R. L. Stevenson & L. Osbourne Wrecker x. 173 Solutions, which I still dismissed as incommensurable with the facts.
B. n.
An incommensurable quantity, etc.: usually in plural.
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > [noun] > relationship between quantities > incommensurable
incommensurability1570
asymmetrya1652
incommensurableness1681
incommensurable1741
the world > relative properties > number > enumeration, reckoning, or calculation > [noun] > capability of calculation > instance of
incommensurable1741
1741 I. Watts Improvem. Mind i. i. 8 Puzzling Enquiries concerning..Incommensurables.
1812 Edinb. Rev. 20 94 Omitting to introduce any thing concerning the nature of incommensurables.
1845 H. Rogers Ess. I. iii. 125 Melancthon was ‘cutting and contriving’ to perform impossibilities, to find a common measure of incommensurables.
This entry has not yet been fully updated (first published 1900; most recently modified version published online September 2020).
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adj.n.1557