quod erat demonstrandumint.n.

Brit.

/kwɒd ˌɛrat dɛmənˈstrandəm/, U.S.

/ˌkwɑd ˌɛrət ˌdɛmənˈstrɑndəm/

Origin: A borrowing from Latin. Etymon: Latin quod erat demonstrandum.

Etymology: < post-classical Latin quod erat demonstrandum, literally ‘which was to be demonstrated’ (1516 or earlier) < classical Latin quod what (see what pron.) + erat , third person singular imperfect indicative of esse to be (see be v.) + demonstrandum , gerundive of demonstrāre demonstrate v., after Hellenistic Greek ὅπερ ἔδει δεῖξαι , literally ‘what needed to be [shown] has been shown’ (Euclid). Compare (in less formulaic use) post-classical Latin quod demonstrandum est , quod demonstrandum fuit , etc. (4th cent. in Augustine). Compare Q.E.D. int.The earliest post-classical Latin translation of Euclid uses the phrases hoc est quod demonstrare intendimus, literally ‘this is what we intended to demonstrate’, hoc est quod demonstrare proposimus, literally ‘this is what we proposed to demonstrate’ , or occasionally quod demonstrare intendimus, literally ‘what we intended to demonstrate’ (11th cent., translated from Arabic). The Latin translation of 1509 used by Billingsley as the basis for the earliest English version has quod fuit propositum, literally ‘which was proposed’, and similar phrases. Compare:1570 H. Billingsley tr. Euclid Elements Geom. i. xlvii. f. 58 Wherefore in rectangle triangles, the square whiche is made of the side that subtendeth the right angle, is equal to the squares which are made of the sides contayning the right angle: which was required to be demonstrated [L. quare patet propositum].

A. int.

‘Which was to be demonstrated’: placed at the end of a mathematical proof (originally, one in Euclid) to indicate that a previously stated theorem is thereby proved; (in extended use) used to convey that a fact or situation demonstrates the truth of a person’s theory or claim. Abbreviated Q.E.D. int.

ΚΠ

1614 W. Bedwell De Numeris Geometricis iv. 54 Therefore d b, and b e, are continually proportionall betweene c b, and b g, the two lines giuen. That is, as c b, is to d b; so is d b, vnto b e: And as b d, is vnto b c; so is b c, vnto b g. quod erat demonstrandum.

1749 W. King Poet. Abridgem. Bentham's Let. to Young Gentleman Oxf. 51 And if there be two Jacobites in Oxford, there may be twenty Jacobites in Oxford; and if there be twenty Jacobites in Oxford, all the People in Oxford may therefore be Jacobites. Quod erat demonstrandum.

1898 Amer. Math. Monthly May 128 So NF produced must fall wholly toward the convex parts, and so it will be tangent to this curve. Quod erat demonstrandum.

1982 R. Sheppard & M. Valpy National Deal viii. 165 In some cases that interest had been extinguished by treaties (which, quod erat demonstrandum, was evidence of the recognition of aboriginal title).

2000 Z. Bauman in D. Garland & R. Sparks Criminol. & Social Theory ii. 25 The excluded are unfit to be free agents, quod erat demonstrandum.

B. n.

A statement or use of the formula ‘quod erat demonstrandum’; a conclusive demonstration of something, a justification. Abbreviated Q.E.D. n.¹

ΚΠ

1669 E. Reynolds Annot. Ecclesiastes xii. 402 Mathematicians having made their demonstration, do then resume their principal conclusion with a quod erat demonstrandum.

1740 T. Morgan Moral Philosopher III. iii. 221 The learned Reasoners in this Way have nothing to do, but to quote a Text of Scripture, in some Sense or other, right or wrong, and then come off triumphantly, with a quod erat demonstrandum.

1865 Med. & Surg. Reporter 19 Aug. 131/2 The Registrar's quod erat demonstrandums are upset just like a child's row of blocks.

1927 H. T. Lowe-Porter tr. T. Mann Magic Mountain II. vi. 503 A belief..is always in existence; which it is the task of the intellect to expound and demonstrate. It comes down every time to the quod erat demonstrandum.

2009 T. Buckley Bad Things Happen xix. 189 You can be messed up for lots of reasons. But my daughter was struggling and my daughter was adopted—the quod erat demonstrandum glared like a beacon.

This is a new entry (OED Third Edition, December 2012; most recently modified version published online March 2022).

单词	quod erat demonstrandum
释义	quod erat demonstrandumint.n. Brit. /kwɒd ˌɛrat dɛmənˈstrandəm/, U.S. /ˌkwɑd ˌɛrət ˌdɛmənˈstrɑndəm/ Origin: A borrowing from Latin. Etymon: Latin quod erat demonstrandum. Etymology: < post-classical Latin quod erat demonstrandum, literally ‘which was to be demonstrated’ (1516 or earlier) < classical Latin quod what (see what pron.) + erat , third person singular imperfect indicative of esse to be (see be v.) + demonstrandum , gerundive of demonstrāre demonstrate v., after Hellenistic Greek ὅπερ ἔδει δεῖξαι , literally ‘what needed to be [shown] has been shown’ (Euclid). Compare (in less formulaic use) post-classical Latin quod demonstrandum est , quod demonstrandum fuit , etc. (4th cent. in Augustine). Compare Q.E.D. int.The earliest post-classical Latin translation of Euclid uses the phrases hoc est quod demonstrare intendimus, literally ‘this is what we intended to demonstrate’, hoc est quod demonstrare proposimus, literally ‘this is what we proposed to demonstrate’ , or occasionally quod demonstrare intendimus, literally ‘what we intended to demonstrate’ (11th cent., translated from Arabic). The Latin translation of 1509 used by Billingsley as the basis for the earliest English version has quod fuit propositum, literally ‘which was proposed’, and similar phrases. Compare:1570 H. Billingsley tr. Euclid Elements Geom. i. xlvii. f. 58 Wherefore in rectangle triangles, the square whiche is made of the side that subtendeth the right angle, is equal to the squares which are made of the sides contayning the right angle: which was required to be demonstrated [L. quare patet propositum]. A. int. ‘Which was to be demonstrated’: placed at the end of a mathematical proof (originally, one in Euclid) to indicate that a previously stated theorem is thereby proved; (in extended use) used to convey that a fact or situation demonstrates the truth of a person’s theory or claim. Abbreviated Q.E.D. int. ΚΠ 1614 W. Bedwell De Numeris Geometricis iv. 54 Therefore d b, and b e, are continually proportionall betweene c b, and b g, the two lines giuen. That is, as c b, is to d b; so is d b, vnto b e: And as b d, is vnto b c; so is b c, vnto b g. quod erat demonstrandum. 1749 W. King Poet. Abridgem. Bentham's Let. to Young Gentleman Oxf. 51 And if there be two Jacobites in Oxford, there may be twenty Jacobites in Oxford; and if there be twenty Jacobites in Oxford, all the People in Oxford may therefore be Jacobites. Quod erat demonstrandum. 1898 Amer. Math. Monthly May 128 So NF produced must fall wholly toward the convex parts, and so it will be tangent to this curve. Quod erat demonstrandum. 1982 R. Sheppard & M. Valpy National Deal viii. 165 In some cases that interest had been extinguished by treaties (which, quod erat demonstrandum, was evidence of the recognition of aboriginal title). 2000 Z. Bauman in D. Garland & R. Sparks Criminol. & Social Theory ii. 25 The excluded are unfit to be free agents, quod erat demonstrandum. B. n. A statement or use of the formula ‘quod erat demonstrandum’; a conclusive demonstration of something, a justification. Abbreviated Q.E.D. n.¹ ΚΠ 1669 E. Reynolds Annot. Ecclesiastes xii. 402 Mathematicians having made their demonstration, do then resume their principal conclusion with a quod erat demonstrandum. 1740 T. Morgan Moral Philosopher III. iii. 221 The learned Reasoners in this Way have nothing to do, but to quote a Text of Scripture, in some Sense or other, right or wrong, and then come off triumphantly, with a quod erat demonstrandum. 1865 Med. & Surg. Reporter 19 Aug. 131/2 The Registrar's quod erat demonstrandums are upset just like a child's row of blocks. 1927 H. T. Lowe-Porter tr. T. Mann Magic Mountain II. vi. 503 A belief..is always in existence; which it is the task of the intellect to expound and demonstrate. It comes down every time to the quod erat demonstrandum. 2009 T. Buckley Bad Things Happen xix. 189 You can be messed up for lots of reasons. But my daughter was struggling and my daughter was adopted—the quod erat demonstrandum glared like a beacon. This is a new entry (OED Third Edition, December 2012; most recently modified version published online March 2022). < int.n.1614
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