integraladj.n.
/ˈɪntɪɡrəl/ A. adj.
1. Of or pertaining to a whole. Said of a part or parts: Belonging to or making up an integral whole; constituent, component; spec. necessary to the completeness or integrity of the whole; forming an intrinsic portion or element, as distinguished from an adjunct or appendage. (Cf. integrant adj. and n.) (Formerly distinguished from essential: see quots. 1697, 1728.)
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the world > existence and causation > existence > intrinsicality or inherence > [adjective]
propera1325
indwelling14..
resident1525
subsistenta1530
corporate1531
immanent1535
intrinsical?1545
integral1551
inexistent1553
internal1564
subjective1564
insident1583
inward1587
inherent1588
imminent1605
inhering1609
intern1612
subjectory1614
intimate1632
inhesive1639
intrinsic1642
implantate1650
medullary1651
implicit1658
inexisting1678
originala1682
indwelt1855
the world > relative properties > wholeness > incompleteness > part of whole > [adjective] > of or relating to components > forming (a) component part(s)
partiala1398
integral1551
integrant1637
constitutivea1640
elemental1639
constituting1641
integrating1654
constituent1660
component1664
compounding1682
contained1696
organical1770
inbuilt1961
1551 T. Wilson Rule of Reason sig. Kiijv The integrale partes, whiche make perfecte the whole, and cause the bignesse therof.
a1639 W. Whately Prototypes (1640) ii. xxvi. 43 The parts integrall, viz. as the severall members of the matter, head, heart, &c. in man.
1651 N. Bacon Contin. Hist. Disc. Govt. 134 In a mixt common wealth, they [kings] are integrall members.
1697 J. Locke 2nd Vindic. Reasonableness Christianity 247 (Seager) Integral parts..are contradistinguished to essential; and signify such parts, as the thing can be without, but without them will not be so complete and entire as with them.
1728 E. Chambers Cycl. Integral, among the Schoolmen, is understood of those Parts which enter the Composition of any Whole. Thus the Arms, Legs, &c. are integral Parts of the Body.
1786 E. Burke Articles of Charge against W. Hastings in Wks. (1842) II. 220 Forming no legal or integral part of the government.
1862 E. M. Goulburn Thoughts Personal Relig. (1873) iii. x. 238 Recreation must form an integral part of human life.
1867 E. A. Freeman Hist. Norman Conquest I. ii. 69 A dependency of the British Crown..not an integral part of the United Kingdom.
1923 R. Glazebrook Dict. Appl. Physics V. 165/1 This cylinder has an open-ended steel barrel with integral fins.
1958 Chambers's Techn. Dict. 987/1 Integral stiffeners, the stiffening ridges left when an aircraft skin panel is machined from a solid billet.
1968 Gloss. Formwork Terms (B.S.I.) 16 Integral facing, a special facing concrete or mortar cast simultaneously with the backing concrete so as to be monolithic with it.
1972 Sci. Amer. Jan. 49/2 (advt.) An integral peak-reading meter lets you optimize record level without using a scope. Options include a 5 to 30 foot loop adaptor, an interrupting voice channel, and an inverter for 12 or 28 VDC..all integrally mounted.
2. Made up of component parts which together constitute a unity; in Logic, said of a whole consisting of or divisible into parts external to each other, and therefore actually (not merely mentally) separable. Now rare or Obsolete except in technical use.
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the world > relative properties > wholeness > mutual relation of parts to whole > state of being composite > [adjective]
compoundc1400
jointc1400
pieced1419
mixed?a1425
complexionatec1430
partyc1500
concrete1536
compost?1541
united1567
composed1570
compounded1570
integral1588
compositive1601
integrate1601
complicate1638
complexa1652
complicated1667
composite1678
co-unala1711
conglomerate1835
polylithic1961
1588 A. Fraunce Lawiers Logike i. vi. f. 33 The whole Integrall cannot bee affirmed of any one of his parts, for a part is not the whole.
1628 T. Spencer Art of Logick 203 An Integrall whole is not in each part, neither according to their whole essence, nor vertue, and therefore it is no wayes predicated of the singular parts.
1649 Bp. J. Taylor Great Exemplar ii. vi. §19 In every Christian there are three parts concerning this integral Constitution, body and soul, and Spirit.
1725 I. Watts Logick i. vi. §10 As an integral Whole is distinguish'd into its several Parts by Division, so the Word Distribution is most properly used when we distinguish an universal Whole into its several Kinds of Species.
1725 I. Watts Logick i. vi. §10 Logicians have sometimes given a mark or sign to distinguish when it is an integral whole, that is, divided into its parts and members, or when it is a genus, an universal whole, that is, distributed into its species and individuals.
a1856 W. Hamilton Lect. Metaphysics (1859) II. xxxvii. 340 The Integral or, as it ought to be called, Integrate whole (totum integratum), is composed of integrant parts (partes integrantes) which are either homogeneous, or heterogeneous.
1864 F. C. Bowen Treat. Logic iv. 67 (note) The Essential or Physical whole is that which consists of Matter and Form, or substance and accident, as its essential parts. The characteristic of this whole is that, as its parts do not exist out of each other, they cannot be separated except in Thought..The Mathematical or Integral whole, on the other hand, has parts which are external to each other, so that they can be divided asunder.
1945 H. D. Smyth Gen. Acct. Devel. Atomic Energy Mil. Purposes xii. 132 Two ‘integral experiments’ (experiments on assembled or integrated systems comprising fissionable material, reflector, and perhaps moderator also) may be described.
1953 C. Wallace Photographer's Pocket-bk. 112 In modern colour materials the colours are achieved by building up on a suitable base..an ‘integral tri-pack’ of three separate emulsions.
3. † c. Grammar. Applied by Wilkins to a word or part of speech denoting a complete notion; see B. 3. Obsolete.
a. Having no part or element separated, taken away, or lacking; unbroken, whole, entire, complete. Now somewhat rare. [= modern French intégral.]
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the world > relative properties > wholeness > [adjective]
wholelOE
entirec1430
integera1509
integral1611
1611 J. Florio Queen Anna's New World of Words Integrale, whole or integrall.
1626 F. Bacon Sylua Syluarum §344 All Locall Motion keepeth Bodies Integrall, and their Parts together.
1651 N. Biggs Matæotechnia Medicinæ Praxeωs ⁋238 Thorow the integral porous pelt.
1659 D. Pell Πελαγος 484 Their hearts are not integral, and entire in prayer.
1798 T. J. Mathias Pursuits of Lit.: Pt. II (ed. 5) 115 Excerpta of Writers whose integral works are lost for ever.
1862 E. Bulwer-Lytton Strange Story II. i. 15 Who could expect that every link in a madman's tale would be found integral and perfect?
b. Of things immaterial.
ΚΠ
1651 Bp. J. Taylor XXVIII Serm. iv. 51 Repent with an integral, a holy and excellent repentance.
1656 Earl of Monmouth tr. T. Boccalini Ragguagli di Parnasso 281 They are thought by them to merit their Princes integral love.
1847 R. W. Hamilton Disq. Sabbath (1848) v. 181 It is felt that, if we would retain Christianity, we must hold fast the full, the integral, sabbath.
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the mind > language > linguistics > study of grammar > a part of speech > other parts of speech > [adjective] > other spec.
numerala1398
partitivea1398
gentile1542
indefinitive1598
illative1611
integral1668
collective1751
modal1845
parti-generic1939
1668 Bp. J. Wilkins Ess. Real Char. 305 They supply the room either, 1. Of some Integral word, as Pronouns, or 2. Of some Sentence or complex part of it, as Interjections.
4. Mathematics.
a. That is, or is denoted by, an integer, or involves only integers; consisting of a whole number or undivided quantity; not fractional, or not involving a fraction.
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the world > relative properties > number > mathematical number or quantity > [adjective] > prime > whole
whole?c1425
round1607
brown1611
integral1658
integer1660
1658 E. Phillips New World Eng. Words (at cited word) In Arithmetick integral numbers are opposed to fraction[s].
a1690 S. Jeake Λογιστικηλογία (1696) 15 To express the true content of any Number Integral.
1812 J. Smyth Pract. of Customs ii. 238 The fractional part of a foot..is to be given up in favour of the importer, and the duties to be charged only upon the integral feet.
1816 tr. S. F. Lacroix Elem. Treat. Differential & Integral Calculus 185 Q being a rational and integral function of x.
1875 I. Todhunter Algebra for Schools (ed. 7) xxxvi. §516 When n has any value positive or negative, integral or fractional.
b. Relating to or involving integrals (see B. 4); obtained by, belonging to, or proceeding by integration. integral calculus: the calculus of integrals (see B. 4); that branch of the infinitesimal calculus which deals with the finding and properties of integrals of functions (in this restricted sense, the inverse of the differential calculus, and corresponding to the ‘inverse method of fluxions’ in the Newtonian calculus), also used to include the solution of differential equations, and parts of the theory of functions and other branches of the higher mathematics. integral sign = sign of integration at integration n. 2.
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the world > relative properties > number > calculus > [noun] > integral calculus
integral calculus1728
Riemann integration1908
the world > relative properties > number > calculus > [adjective] > of integration
integrating1654
integrable1728
integral1728
subregular1887
Riemann integrable1918
1728 E. Chambers Cycl. at Calculus The Integral Calculus..is the Inverse of the Differential one.
1728 E. Chambers Cycl. at Calculus Suppose ∫ the Sign of the Sum, or Integral Quantity.
1802 Woodhouse in Philos. Trans. (Royal Soc.) 92 95 Expressions deduced from the true integral equations.
1875 C. P. Buckingham Elem. Different. & Int. Calculus (1880) §157 The..problem of the integral calculus is to pass from a given differential of a function to the function itself.
1881 J. C. Maxwell Treat. Electr. & Magnetism (ed. 2) I. 21 In the expression under the integral sign only the finite values..are to be considered.
1887 R. A. Roberts Integral Calculus 1 The principal object of the Integral Calculus is to find the value of a function of a single variable when its differential coefficient is given.
c. Applied to the entire or total amount of a continuous quantity (e.g. curvature) taken between definite limits, and thus expressible by a definite integral (see B. 4(a)).
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the world > relative properties > number > calculus > [adjective] > of integration > expressible by definite integral
integral1879
1879 W. Thomson & P. G. Tait Treat. Nat. Philos. (new ed.) I: Pt. i. §10 The integral curvature, or whole change of direction of an arc of a plane curve, is the angle through which the tangent has turned as we pass from one extremity to the other.
Categories »
d. integral domain: see domain n. 4d.
B. n.† 2. An integral part or element; a constituent, component: see A. 1. Obsolete.† 3. Grammar. Applied by Wilkins to those words or parts of speech which of themselves express a distinct notion, as distinct from those which express relations between notions. Obsolete.
1. Something entire or undivided; a whole, either as wanting no part, or as made up of parts: see A. 2, A. 3 Obsolete except as transferred from 4 = total sum.
ΘΚΠ
the world > relative properties > wholeness > [noun] > that which is whole
integral1620
integrity1620
wholenessa1681
unitarya1842
integera1848
1620 T. Granger Syntagma Logicum 177 A tree, a body, an house..are totall Integrals, whose integritie, or wholenesse..is made of their parts.
1657 R. Tomlinson tr. J. de Renou Physical Inst. i, in Medicinal Dispensatory sig. C In the third genus are contained all Animals, whether Integrals, or In-parts.
a1806 J. Barry in R. N. Wornum Lect. on Painting (1848) 152 Any other conjunction of parts, forming an integral or whole.
1834 W. S. Landor Citation & Exam. Shakespere in Wks. (1846) II. 299/2 No more..than breaking an eggshell is breaking an egg, the shell being a part, and the egg being an integral.
1881 Nature No. 625. 582 What is seen in a sun-spot is the integral, as it were, of all that is taking place..in many thousand miles of solar atmosphere.
ΘΚΠ
the world > relative properties > wholeness > incompleteness > part of whole > [noun] > constituent part or component
limbc1000
membera1382
elementc1386
parcelc1395
ingredientc1460
partc1530
ingredience1577
principle1594
simple1603
composer1610
partiment1641
component1644
constitutive1647
composite1657
integral1659
ingredient1674
aggregant1749
constituent1757
congredient1767
factor1816
integrant1825
inclusion1845
1659 T. Burton Diary (1828) III. 557 We must, therefore, be very circumspect in the materials of the other House. Let us, therefore, look to the integrals in this building.
a1676 M. Hale Primitive Originat. Mankind (1677) i. i. 21 Anatomy can give us the Position..of all the several Integrals of the Body of Man or Beast.
a1676 M. Hale Primitive Originat. Mankind (1677) iv. viii. 372 They all make up a most magnificent and stately Temple, and every Integral thereof full of wonder.
1680 R. Baxter Answer to Dr. Stillingfleet 82 Doth not every good Law and Rule distinguish between Essentials, Integrals, and Accidents, and make more Accidents than are Integrals, and Integrals, than are Essentials?
1685 R. Baxter Paraphr. New Test. 1 Cor. xii. 14 So wise, as besides the Essentials of Christianity, to know all the Integrals.
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the mind > language > linguistics > study of grammar > a part of speech > [adjective] > relating to content words
integral1668
notional1839
presentive1871
1668 Bp. J. Wilkins Ess. Real Char. iii. i. §2 By Integrals or Principal words, I mean such as signifie some entire thing or notion.
1688 R. Holme Acad. Armory iii. 251/2.
a1831 J. Stoddart Gram. in Encycl. Metrop. (1845) I. 124/1 Wilkins includes under the term integral both the noun and the verb.
4. Mathematics (a) (Of a function): That quantity of which the given function is the differential or differential coefficient (corresponding to the fluent of a given fluxion in Newton's method); so called because it may be regarded as the whole sum of a series of consecutive values assumed by an infinitesimal function (differential) of the variable while the latter changes continuously from any one value to any other. When such limits of variation are fixed or determinate, it is called a definite integral: see quot. 1877. An integral is denoted by the sign ∫ (originally a long s, for Latin summa sum); in a definite integral the inferior and superior limits are indicated at the bottom and top of the sign, thus ∫ba. (Formerly sometimes applied to the quantity from which a given ‘finite difference’ or ‘increment’ is derived, as in quot. 1763; cf. quot. 1832 at integrate v. 3a.) (b) (Of a differential equation, or a system of such equations): An equation or system of equations from which the given equation or system can be derived by differentiation. (In relation to a system of equations, any quantity which that system makes constant is sometimes called its integral.)
ΘΚΠ
the world > relative properties > number > calculus > [noun] > integral calculus > integration or integrability > integral
fluent1706
integral1728
gamma function1834
surface integral1867
Riemann integral1894
Cauchy's integral1898
Lebesgue integral1905
Stieltjes integral1914
convolution1934
1728 E. Chambers Cycl. at Calculus ∫ydx will denote the Sum, or Integral of the Differential ydx.
1763 W. Emerson Method of Increments Pref. p. vii Some Increments have no integrals, but what infinite series afford.
1802 Woodhouse in Philos. Trans. (Royal Soc.) 92 90 The integral or fluent of Px· is that function from which Px· is derived.
1877 B. Williamson Elem. Treat. Integral Calculus (ed. 3) vi. §91 The expression ∫X/ x0 ϕ(x)dx is called the definite integral of ϕ(x)dx between the limits x0 and X, and represents the limit of the sum of the infinitely small elements ϕ(x)dx, taken between the proposed limits... In contradistinction, the name indefinite integrals is often applied to integrals..in which the form of the function is merely taken into account, without regard to any assigned limits.
1881 J. C. Maxwell Treat. Electr. & Magnetism (ed. 2) I. 27 The double integrals destroy each other.
This entry has not yet been fully updated (first published 1900; most recently modified version published online March 2022).
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adj.n.1551