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单词 infinitesimal
释义

infinitesimaln.adj.

/ɪnfɪnɪˈtɛsɪməl/
Forms: Also infinitessimal.
Etymology: < modern Latin infīnītesimus, < Latin infīnītus (compare centesimus hundredth, millesimus thousandth): compare French infinitésime (1752 in Dict. Trévoux), infinitésimal (1762 in Dict. Acad.). The form. of the modern Latin word shows that it was originally meant as an ordinal, viz. the ‘infiniteth’ in order, that which is at an infinite distance from the first; but the ordinals are also used to name fractions, e.g. hundredth (part), 1/ 100, thousandth (part) 1/ 1000; hence, infinitesima pars, infinitesimal part or infinitesimal, came to mean unity divided by infinity, 1/ , and thus an infinitely small part or quantity. Although essentially an adjective, our earliest example shows the word used absolutely as a noun.
A. n. (or absol.)
1. As ordinal: The ‘infiniteth’ member of a series. Obsolete. rare.
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > series > designating place in
numberc1350
extreme1571
numero1649
infinitesimal1655
No.1753
Z1842
majorant1925
seed1972
1655 H. More Antidote against Atheism (ed. 2) xiii. 391 But for us whose capacities are finite, if we would venture to name a first in infinite succession, we should call it πρῶτον ἀπειραστὸν, the first infinitessimal, and acknowledge our selves unable to go through, our understandings being finite.
2.
a. (Chiefly Mathematics) As a fraction or fractional quantity. The inverse or reciprocal of an infinite quantity; †an infinitely small fraction or part of anything (obsolete).
ΘΚΠ
the world > relative properties > number > ratio or proportion > fraction > [noun] > numerator or denominator relationships
improper fraction1552
proper fractiona1630
infinitesimal1706
complex fraction1827
the world > relative properties > wholeness > incompleteness > part of whole > [noun] > a small part or proportion > infinitesimal
infinitesimal1706
zillionth1940
1704 C. Hayes Treat. Fluxions 1 These infinitely little Parts of an infinitely little Part of a given Quantity are..called Infinitesimæ Infinitesimarum or Fluxions of Fluxions.]
1706 H. Ditton Inst. Fluxions 20 Let m denote an infinite Quantity, d any finite one; then is d/ m the Infinitesimal of d, according to Mr. Nieuwentyt.
1710 G. Berkeley Treat. Princ. Human Knowl. §130 Some..not content with holding that finite lines may be divided into an infinite number of parts, do yet farther maintain that each of these infinitesimals is itself subdivisible into an infinity of other parts or infinitesimals of a second order, and so on ad infinitum. These, I say, assert there are infinitesimals of infinitesimals of infinitesimals, etc., without ever coming to an end.
1745 J. T. Needham Acct. New Microsc. Discov. Introd. 3 A little Ant-hill..would appear to its Inhabitants..an Infinitesimal of the terraqueous Globe.
b. (Mathematics) An infinitely small quantity or amount, a quantity less than any assignable quantity.Chiefly used of the infinitesimal differences or differentials treated of in the differential and integral calculus: see differential adj. 3, 1. Mathematicians distinguish different orders of infinitesimals; thus, if we make x infinite, 1/ x is an infinitesimal of the first order, 1/ x2 being infinitely less than 1/ x an infinitesimal of the second order, and so on.
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > [noun] > infinitesimal
infinitesimal1734
1734 G. Berkeley Analyst §6 An infinite succession of infinitesimals, each infinitely less than the foregoing.
1743 Philos. Trans. (Royal Soc.) 42 349 In the Method of Infinitesimals, the Element, by which any Quantity increases or decreases, is supposed to become infinitely small.
1816 tr. S. F. Lacroix Elem. Treat. Differential & Integral Calculus 78 A very simple explanation of the various orders of infinitesimals admitted by Leibnitz.
1831 Hind Princ. Differ. Calc. 116 The method of Infinitesimals adopted by Leibnitz as the foundation of his Differential Calculus.
1873 B. Williamson Elem. Treat. Differential Calculus (ed. 2) ii. §36.
3. In loose or hyperbolical use: An extremely small quantity or amount; something excessively minute or insignificant.
ΘΚΠ
the world > relative properties > quantity > smallness of quantity, amount, or degree > [noun] > a small quantity or amount > a very small amount
shredc1000
farthingsworthc1325
pennyworthc1330
incha1350
sliverc1374
chipa1393
gnastc1440
Jack1530
spoonful1531
crumba1535
spark1548
slight1549
pin's worth1562
scruple1574
thought1581
pinch1583
scrap1583
splinter1609
ticket1634
notchet1637
indivisible1644
tinyc1650
twopence1691
turn of the scale(s)1706
enough to swear by1756
touch1786
scrimptiona1825
infinitesimal1840
smidgen1841
snuff1842
fluxion1846
smitchel1856
eyelash1860
smidge1866
tenpenceworth1896
whisker1913
tidge1986
the world > space > extension in space > measurable spatial extent > smallness > [noun] > that which is small > a small thing > extremely small thing
hilum1659
whatkin1674
scuddick1823
infinitesimal1840
teensy-weensy1872
1840 T. Hood Up Rhine 233 Hahnemann, having hit on the advantage of small doses, never rested till he had reduced them to infinitesimals.
1876 R. W. Emerson Resources in Lett. & Social Aims 124 What power does Nature not owe to her duration of amassing infinitesimals into cosmical forces!
B. adj.
1. (Chiefly Mathematics.)
a. Infinitely or indefinitely small; smaller than any assignable fraction or magnitude. (Correlative to infinite, and, with it, opposed to finite.)
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > [adjective] > infinitesimal
infinitesimal1710
elementary1882
the world > space > extension in space > measurable spatial extent > smallness > [adjective] > extremely small > smaller than any assignable magnitude
infinitesimal1710
dimensionless1752
sizeless1874
indimensional1875
1710 G. Berkeley Treat. Princ. Human Knowl. §132 It will not be found..necessary to make use of or conceive infinitesimal parts of finite lines.
1771 S. Horsley in Philos. Trans. 1770 (Royal Soc.) 60 435 (note) The infinitesimal segments of that line.
1862 H. Spencer First Princ. i. iii. §17. 57 It is quite possible to think of its motion as diminishing insensibly until it becomes infinitesimal.
1871 J. Tyndall Fragm. Sci. (1879) I. ii. 58 The aqueous vapour it contains is of almost infinitesimal amount.
b. transferred. Relating to infinitesimal quantities; esp. in infinitesimal calculus, a name for the differential and integral calculuses considered as one (corresponding to the direct and inverse methods of fluxions).
ΘΚΠ
the world > relative properties > number > calculus > [noun]
calculus1672
fluxions1702
summatory calculus1704
infinitesimal calculus1801
rheometry1841
1801 W. Dickson (title) Reflections on the Infinitesimal Calculus. From the French of Carnot, with Notes.
2. In loose or hyperbolical use (cf. A. 3): Too small to be measured or reckoned; extremely minute or insignificant.
ΘΚΠ
the world > relative properties > quantity > smallness of quantity, amount, or degree > [adjective] > very small in amount or degree
superfine1575
tiny1598
minute1606
exiguous1630
myriate1665
delicate1692
miniature1714
infinitesimal1733
diminutive1741
weeny1790
inappreciable1802
teeny1802
scrumptious1834
teeny-weeny1842
teeny-tiny1849
tee-tiny1872
minuscule1878
the world > space > extension in space > measurable spatial extent > smallness > [adjective] > extremely small
tinea1400
little weea1525
undersmall?1527
little little1542
perpusil1598
tiny1598
punctual1605
minute1606
pygmya1616
exiguous1630
atomical1646
minutulous1651
puncticular1658
arenulous1664
myriate1665
minimal1666
minim1671
infinitesimal1733
minutissim1768
weeny1790
midgety1798
teeny1802
pinpoint1807
atomic1809
homuncular1822
minnow1824
weeshy1825
pinhead1835
finitesimal1836
homoeopathic1838
teeny-weeny1842
teenty1844
teenty-taunty1844
teeny-tiny1849
submolecular1854
teensy1856
super-compact1860
midget1865
ultramicroscopic1870
pilulous1871
teensy-weensy1872
tee-tiny1872
minuscule1878
smitchy1888
eeny-weeny1894
eensy-weensy1904
pygmean1904
ultramicroscopical1904
bitsy1905
bitty1905
totty1906
millimetric1909
miniscule1909
minuscular1911
insectual1912
micro1931
eeny1933
eensy1940
submicrogram1941
submillimetre1954
diddy1963
mini1963
micro-mini1967
1733 G. Cheyne Eng. Malady iii. iv. 337 I was not reduc'd to such extreme Weakness, that infinitesimal Errors, could do great Hurt.
1749 D. Hartley Observ. Man i. iii. 393 An Obstruction of the infinitesimal Vessels of the Nervous System.
1830 C. Lyell Princ. Geol. I. 474 No river can push forward its delta without raising the level of the whole ocean, although in an infinitesimal degree.
1834 T. Carlyle Sartor Resartus ii. ix. 71/1 Were it but the pitifullest infinitesimal fraction of a Product, produce it in God's name!
1884 Times (Weekly ed.) 19 Sept. 6/4 Each infinitesimal right of grazing..had to be surveyed, examined into.

Derivatives

infiniˈtesimalist n. one who supports the method of infinitesimals (sense A. 2).
ΘΚΠ
the world > relative properties > number > mathematics > [noun] > theories or branches of > one who holds theory
infinitesimalist1863
momentarian1863
number theorist1912
formalist1913
frequentist1949
game theorist1950
finitist1960
constructivist1979
chaologist1987
1863 A. De Morgan Let. 14 Nov. in R. P. Graves Life Sir W. R. Hamilton (1889) III. 598 Cotes was an infinitesimalist; so was Newton, till he abjured in 1706. But he continued a momentarian—which I take to be a (dx)-man—all his life.
1937 Mind 46 227 Berkeley's penetrating criticism of the postulates of the fluxionists and infinitesimalists of his day.
infinitesiˈmality n. an infinitesimally small matter.
ΘΚΠ
the world > space > extension in space > measurable spatial extent > smallness > [noun] > extreme
perpusillity1598
minuteness1661
tininess1674
diminutiveness1727
infinitesimality1867
infinitesimalness1897
mininess1964
the mind > attention and judgement > importance > unimportance > [noun] > that which is unimportant > of little importance or trivial
gnatc1000
ball play?c1225
smalla1250
triflec1290
fly1297
child's gamec1380
motec1390
mitec1400
child's playc1405
trufferyc1429
toyc1450
curiosity1474
fly-winga1500
neither mass nor matins1528
boys' play1538
nugament1543
knack?1544
fable1552
nincety-fincety1566
mouse1584
molehill1590
coot1594
scoff1594
nidgery1611
pin matter1611
triviality1611
minuity1612
feathera1616
fillip1621
rattle1622
fiddlesticka1625
apex1625
rush candle1628
punctilio1631
rushlight1635
notchet1637
peppercorn1638
petty John1640
emptiness1646
fool-fangle1647
nonny-no1652
crepundian1655
fly-biting1659
pushpin1660
whinny-whanny1673
whiffle1680
straw1692
two and a plack1692
fiddle1695
trivial1715
barley-strawa1721
nothingism1742
curse1763
nihility1765
minutia1782
bee's knee1797
minutiae1797
niff-naff1808
playwork1824
floccinaucity1829
trivialism1830
chicken feed1834
nonsensical1842
meemaw1862
infinitesimality1867
pinfall1868
fidfad1875
flummadiddle1882
quantité négligeable1885
quotidian1902
pipsqueak1905
hickey1909
piddle1910
cream puff1920
squat1934
administrivia1937
chickenshit1938
cream puff1938
diddly-squat1963
non-issue1965
Tinkertoy1972
1867 Good Words 8 801/1 The infinitesimality (I am sorry to have to coin a word) of his influence.
1895 Columbus (Ohio) Dispatch 17 Oct. 11/3 It is well sometimes to let the mind dwell on such infinitesimalities.
infiniˈtesimalness n. infinitesimal smallness.
ΘΚΠ
the world > space > extension in space > measurable spatial extent > smallness > [noun] > extreme
perpusillity1598
minuteness1661
tininess1674
diminutiveness1727
infinitesimality1867
infinitesimalness1897
mininess1964
1897 N.Y. Voice 8 July 2/3 This infinitesimalness of the Church practise.
This entry has not yet been fully updated (first published 1900; most recently modified version published online June 2022).
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n.adj.1655
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