Also 5 subtraccio(u)n, 5–6 -tractioun(e, sotraccion. [ad. late L. subtractio, -ōnem (in Vulgate trans. Gr. ὑποστολή), n. of action f. subtrahĕre to SUBTRACT. Cf. It. sottrazione, Pg. subtracção. See also SUBSTRACTION.]
† 1. Withdrawal or removal from a place. Obs.
c. 1400. Sc. Trojan War (Horstm.), II. 369. He … wylfully in-to þat stede Hath graunted þe subtractioune Of þat relyk of gret renowne To Anthenor.
1432–50. trans. Higden (Rolls), II. 155. As in the subtraccion of Danes as vn to the maner and chaunce þer of croniclers make noo mencion [etc.].
2. The withdrawal or withholding of something due, necessary or useful. Also, an instance of this. Obs. exc. arch.
c. 1450. trans. De Imitatione, II. x. 53. He þat is tauȝt wiþ þe ȝifte of grace, and lerned wiþ þe betyng of subtraccion [orig. subtractionis verbere].
1552. Abp. Hamilton, Catech. (1884), 33. This plaige of subtractioun of grace.
1598. in Archpriest Controv. (Camden), I. 96. By ye addicions & sotraccions affirmacions & negacions, etc., of the particulrs of his autority.
a. 1656. Bp. Hall, Rem. Wks. (1660), 163. A subtraction or diminution of the maintenance of studied Divines.
1818. Hallam, Mid. Ages (1872), II. 242. A second subtraction of obedience, or at least declaration of neutrality.
1833. Waddington, Hist. Ch., xxiii. 524. The party in France, which for some time had been opposed to the subtraction of obedience … declared its adhesion.
b. Law. The withdrawal or withholding from a person of any right or privilege to which he is lawfully entitled.
1660. R. Coke, Power & Subj., 21. Ecclesiastical laws relate to … subtraction and right of tythes, oblations, &c.
1768. Blackstone, Comm., III. 94. The suit for restitution of conjugal rights … is brought whenever either the husband or wife is guilty of the injury of subtraction, or lives separate from the other without any sufficient reason. Ibid., 231. The subtraction or non-observance of any of these conditions, by neglecting to swear fealty, to do suit of court, [etc.] is an injury to the freehold of the lord.
1835. Tomlins’ Law. Dict., Subtraction of Rents and Services.
c. Logic. The exception of one class from another in which the excepted class is naturally included.
In recent Dicts.
3. Math. The taking of one quantity from († out of) another; the operation of finding the difference between two quantities, the result being termed the remainder. Also, an instance of this.
Compound subtraction: see COMPOUND a. 2 b.
c. 1425. Crafte Nombrynge (E.E.T.S.), 10. Þou most know þat subtraccion is drawynge of one nowmber oute of anoþer nomber.
1542. Recorde, Gr. Artes (1575), 95. Subtraction or Rebating is nothing els, but an arte to withdrawe and abate one summe from another, that the Remainer may appeare.
1571. Digges, Pantom., I. xviii. F j. Nowe by subtraction subduce 100 from 120, there remayneth your diuisor 20.
1612. Drayton, Poly-olb., iv. 390, note. Subtraction of this number, and, in some, addition … will rectifie many gross absurdities in our Chronologies.
1706. Phillips (ed. Kersey), s.v., Compound Subtraction, is the Method of taking a Summ compounded of several different Species, from another Summ Compounded likewise of the same sorts of Species.
1854. Orr’s Circ. Sci., Math., 22. Proceed in like manner with each denomination till the subtraction is finished.
1910. Encycl. Brit. (ed. 11), II. 538/2. We … perform the subtractions independently, and then regroup the results as the remainder.
b. transf. and fig. Abstraction, deduction, removal.
1534. Whitinton, Tullyes Offices, I. (1540), 27. That we maye be as good accompters of our offyces and dutyes, and se bothe in addycion and subtraction what somme may surmounte of the remaynes.
1738. T. Birch, App. Life Milton, I. 72. By comparing it with his other Account, we shall perceive … that there is not an entire Agreement in any one of the Paragraphs, but there are either Alterations, or Additions, or Subtractions, or Contradictions.
1820. R. Jackson, Sk. Febrile Dis. (ed. 2), I. 227. Dr. Rush, and other American physicians carried subtraction of blood to great extent in the American epidemic.
1828. P. Cunningham, N. S. Wales (ed. 3), II. 325. The gift of a single million out of this vast amount is about as insignificant as the subtraction of a grain of wheat from a peck measure.
1857. Miller, Elem. Chem., Org., xiii. § 1. 723. From it all the varieties of organized products might be obtained, by the addition or subtraction of water, oxygen, and ammonia.
1864. Lowell, Fireside Trav. (1909), 25. The world can endure the subtraction of even a justice of the peace with provoking equanimity.
4. Detraction, depreciation. (Cf. SUBTRACTOR.) rare.
1890. C. J. Woodbury, in Century Mag., XXXIX. 634/2. Of Shakspere he [sc. Emerson] talked much, and always without a word of subtraction.
