单词 | infinitesimal |
释义 | infinitesimaln.adj. A. n. (or absol.) 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). < n.adj.1655 |
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