geometricaladj.n.

Brit.

/ˌdʒiːəˈmɛtrᵻkl/,

/dʒɪəˈmɛtrᵻkl/, U.S.

/ˌdʒiəˈmɛtrək(ə)l/

Forms: Middle English–1500s geometricalle, Middle English– geometrical, 1500s–1600s geometricall, 1600s jeometricall.

Origin: Either (i) a borrowing from Latin. Or (ii) a borrowing from Latin, combined with an English element. Etymons: Latin geometricalis ; Latin geōmetricus , -al suffix¹.

Etymology: Either < post-classical Latin geometricalis (from 12th cent. in British sources; compare geometricalia (plural noun) geometry (from 1267 in British sources)); or directly < classical Latin geōmetricus geometric adj. + -al suffix¹. Compare Middle French geometrical (of a measuring rod) belonging to a land surveyor (1517 in an apparently isolated attestation). Compare later geometric adj. and the foreign-language parallels cited at that entry.In use designating measures of length (see sense A. 2a) after the corresponding post-classical Latin use of classical Latin geōmetricus (a1364 in the passage translated in quot. ?a1475). In sense A. 4 after the corresponding post-classical Latin use of classical Latin geomētricus geometric adj. (1527 in the passage translated in quot. 1676, or earlier).

A. adj.

a. Of or relating to geometry; determined, constructed, or formed according to the methods or laws of geometry. Also figurative.In former use often contrasted with mechanical (mechanical adj. 11b), with reference to figures constructed solely from straight lines and circles, and to procedures involving the use of a ruler and compasses only.

ΘΚΠ

the world > relative properties > number > geometry > [adjective]

geometricalc1392

geometrialc1550

geometric1609

mathematical1614

mathematica1680

c1392 Equatorie of Planetis 18 This lymbe shaltow deuyde in 4 quarters by 2 diametral lynes..& lok thy croys be trewe proued by geometrical conclusioun.

1562 T. Cooper Answere Def. Truth f. 52^v, in Apol. Priuate Masse To apointe a geometricall measure of place..that may serue for all churches..is far aboue our reache.

1576 A. Fleming tr. Apollonius in Panoplie Epist. 225 He shall learne to be skilfull in the art Geometrical.

1638 F. Junius Painting of Ancients 282 Geometricall lines; which are nothing else but a length without breadth.

1695 W. Alingham Geom. Epitomiz'd 114 Upon a given right line as a d, to make a Geometrical square.

1737 S. Ashby Young Analyst's Exercise 55 The same Geometrical Problems may be solved by different Principals of Geometry.

1790 E. Burke Refl. Revol. in France 80 Is every land-mark of the country to be done away in favour of a geometrical and arithmetical constitution?

1838 C. Thirlwall Hist. Greece (new ed.) III. xviii. 59 A new town was built, with geometrical regularity.

1838 Penny Cycl. XI. 151/1 Every construction which can be made by the ruler and compasses, that is, which demands no points except such as can be found by the intersections of straight lines and circles, is geometrical.

1879 Fun 2 July 3/2 Bees are said to build their cells on geometrical principles, but, surely, they cannot like to learn Euclid.

1922 T. M. Lowry Inorg. Chem. xix. 211 The geometrical form of crystals is usually described by means of the intersections of the faces on three or more crystallographic axes.

1972 M. Kline Math. Thought ix. 193 The Arabs solved some cubics algebraically and gave a geometrical explanation..for quadratics.

2008 N.Y. Rev. Bks. 6 Mar. 34/4 Unable to draw simple geometrical figures or even tie their own shoelaces.

b. Of a design: characterized by or decorated with regular shapes or patterns.

ΘΚΠ

society > leisure > the arts > visual arts > ornamental art and craft > pattern or design > [adjective] > geometric

diapered?a1400

frettedc1420

checkeryc1440

checkeda1475

diaper1480

chequered1486

lozenged1523

diapery1605

fret1663

lozengy1686

reticulated1753

geometrical1777

reticular1783

geometric1842

Z-shaped1858

chessboard1889

1777 Archaeologia 4 91 The only remains of British masonry in England is the temple of the Druids on Salisbury plain; but in that we may observe the marks of the chisel, and the traces of a geometrical design.

1861 J. H. Parker Introd. Study Gothic Archit. (ed. 2) v. 142 Windows with flowing tracery, and those with reticulated, or net-like forms,..are in general somewhat later than the geometrical patterns.

1879 J. Lubbock Sci. Lect. v. 160 The ornamentation..consists of geometrical patterns—straight lines, circles, triangles, etc.

1909 A. C. Fox-Davies Compl. Guide Heraldry vii. 79 A fixed geometrical pattern, formed of rows of ear-shaped shields of alternate colours and alternately reversed.

2005 Archaeol. Rep. for 2004–5 (Soc. for Promotion Hellenic Stud.) No. 51. 84/2 The panels could have been decorated with very fine geometrical motifs.

2. Designating measures of length.

a. Designating a cubit six times as long as the ordinary or common cubit, and usually taken as equal to nine feet (approx. 2.74 m). Now historical.

ΘΚΠ

the world > relative properties > measurement > measurement of length > [adjective] > of a unit: greater than usual length

longa1300

geometrical?a1475

a1387 J. Trevisa tr. R. Higden Polychron. (St. John's Cambr.) (1869) II. 235 Þe cubites were cubites of gemetrie. For þe comoun cubite þat me vseþ conteyneþ but a foot and an half..But a cubite of gemetrie [L. cubitus..geometricus] conteyneþ sixe comoun cubites.]

?a1475 (?a1425) tr. R. Higden Polychron. (Harl. 2261) (1869) II. 235 A geometricalle cubite [L. cubitus geometricus] conteynethe vj commune cubites, whiche make ix footes.

1617 W. Raleigh Hist. World (new ed.) i. vii. 112 To make it manifest, that the Geometricall Cubit is not vsed in the Scripture, the stature of the Giants therein named may suffice.

1668 Bp. J. Wilkins Ess. Real Char. 163 The Ægyptian Geometrical cubit, each of which (say they) did contein six of the vulgar cubits, namely, nine foot.

1795 T. Maurice Hist. Hindostan I. xiii. 558 The magnitude of the ark..depended upon the sort of cubit supposed to be made use of; whether admitted to have been the geometrical cubit, containing six ordinary cubits, or what is called the sacred cubit.

1869 J. Kitto Illustr. Hist. Holy Bible i. ii. 81/1 The probability is, that there were two cubit measures beside the common; one being of twenty-one inches, and the. other of three feet. Some writers add the geometrical cubit of nine feet.

1996 N. Cohn Noah's Flood iv. 38 Origen could counter that argument by pointing out that Moses grew up in Egypt, where ‘cubit’ meant the geometrical cubit, which is six times larger.

b. geometrical pace n. a length of five feet (approx. 1.52 m); the distance between successive stationary positions of the same foot when walking; cf. pace n.¹ 8.

ΘΚΠ

the world > relative properties > measurement > measurement of length > [noun] > units of length or distance > fixed by geographical computation

geometrical pace1559

1559 W. Cuningham Cosmogr. Glasse 56 Table..A Geometricall Pase conteyninge in it 5 Five foote.

1702 Mil. Dict. at Pace There is a Common and a Geometrical Pace. The Common Pace is generally counted a Yard, the Geometrical a Foot.

1727 A. Pope et al. Περι Βαθους: Art of Sinking 87 in J. Swift et al. Misc.: Last Vol. A Stage as large as the Athenian, which was near ninety thousand Geometrical Paces square.

1828 J. M. Spearman Brit. Gunner 268 A league at sea..contains 3000 geometrical paces, or 3 English miles.

1876 G. E. Voyle & G. de Saint-Clair-Stevenson Mil. Dict. (ed. 3) 255/1 A geometrical mile consists of 1000 geometrical paces.

1920 A. J. F. Van Laer tr. Minutes Court of Fort Orange & Beverwyck, 1652–1656 8 The jurisdiction of the fort included all territory within range of cannon shot, reckoned at 600 geometrical paces of 5 feet to the pace.

2008 D. A. Wilson Forensic Procedures for Boundary & Title Investig. 387 The geometrical pace is five feet long, being the length of two steps, or the whole space passed over by the same foot from one step to another.

c. Designating imperial units of length ( geometrical foot, geometrical mile, etc.) variously explained, but in later use based on the degree of longitude (the nautical mile, formerly 6080 feet, giving a length for the geometrical foot of 1 foot 1.8 inches, approx. 35.1 cm). Now historical.

ΘΚΠ

the world > relative properties > measurement > measurement of length > [noun] > units of length or distance > mile > nautical mile

geometrical1597

maritime mile1632

geometric1670

nautical mile1730

knot1748

nautic mile1762

sea-mile1796

air mile1919

1597 E. Hoby tr. B. de Mendoza Theorique & Practise Warre 59 The bridge being fiue geometrical feete in depth.

1622 G. de Malynes Consuetudo 52 Gradus Geometrorum, wherewith the world is measured round about, is 15 miles, so the world is 360 Gradus, in toto 5400 miles, or at 4 miles for one Geometricall mile, is 21600 miles.

a1652 I. Jones Most Notable Antiq. called Stone-Heng (1655) 34 In height one hundred twenty one Geometrical feet (which of our measure makes one hundred thirty six feet).

1697 W. Dampier New Voy. around World x. 287 Italian or Geometrical miles, (at the rate of 60 to a degree).

1769 B. Alexander tr. G. B. Morgagni Seats & Causes Dis. II. xxxiv. 158 Widmann..found also a much longer portion of the intestinum jejunum, that is more than a geometrical foot, fallen within the part next to it.

1799 E. Little Usher 26 Long Measure... 8 Furlongs 1 Mile. 60 Geometrical miles 1 Degree.

1904 E. H. Blair et al. tr. Philippine Islands 1493–1898 XVI. 66 These walls were twelve thousand eight hundred and forty-three geometrical feet in extent.

1995 P. Sheingorn tr. Bk. Sainte Foy i. 82 There remains the golden frontal of the high altar, which is not less than seven feet and two fingers in length—not in geometrical feet, but as the peasants are accustomed to measure, with both hands spread out and the thumbs linked.

1998 J. J. Roche Math. Measurem. iv. 53 The geometrical foot seems to have won more approval than application from mathematical philosophers.

3. Mathematics. = geometric adj. 3.Chiefly in set compounds: cf. geometrical series n. at Compounds, geometrical progression n., geometrical proportion n., geometrical ratio n. 1.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [adjective] > of sets > of sequences > progression

geometrical1543

harmonical1569

progressional1570

musical1589

equidifferent1696

harmonic1706

synharmonic1850

preferred1922

1543 R. Record Ground of Artes f. 97^v There is another maner of Progression called Geometricall, when the nombres encrease by a lyke proportion.

1734 J. Harris's tr. Pardies's Short Plain Elements Geom. (new ed.) iii. 145 When the Terms of the Progression are continual Proportionals..then the Progression is call'd Geometrical, as 1, 2, 4, 8, 16, 32.

1816 T. Taylor Theoretic Arithm. 104 In continued geometrical proportionality also, the rectangle under the extremes is equal to the square of the mean.

1909 A. D. Jones Logic Inductive & Deductive ii. ii. 204 When we only have two quantities to deal with, the geometrical average is easily found.

1949 H. Hoover in Changing Times Nov. 21/1 The geometrical increase of spending by our governments—federal, state and local.

2003 M. Mayor & P.-Y. Frei New Worlds in Cosmos iii. 56 There is clearly a geometrical sequence in which each term is the double of the preceding one.

†4. Of an architect or draughtsman: making use of geometrical methods. Obsolete. rare.

ΚΠ

1676 tr. H. C. Agrippa Vanity Arts & Sci. lxiv. 200 Neither is the Geometrical Artist [L. geometricus architectus] wanting to give his assistance, by whose contrivance fine convenient Ladders are made for the scaling of Windows.

a1682 Sir T. Browne Certain Misc. Tracts (1683) i. 6 Geometrical and Architectonical Artists look narrowly upon the description of the Ark.

1853 E. K. Kane U.S. Grinnell Exped. (1856) xl. 366 You remember the geometrical artist of Laputa.

5. Architecture. = geometric adj. 5.

ΘΚΠ

society > leisure > the arts > visual arts > architecture > style of architecture > [adjective] > decorated

decorated1812

geometrical1838

geometric1845

Middle Pointed1846

1838 B. Winkles Archit. & Picturesque Illustr. Cathedral Churches II. 11 The windows which were before of single lights, are here divided into several, by mullions, and tracery of geometrical form, an invention peculiar to pointed architecture.

1849 E. Sharpe Treat. Decorated Window Tracery i. ii. 8 I propose..to name these three styles of Window tracery, Geometrical, Curvilinear, and Rectilinear.

1875 Encycl. Brit. II. 425/2 Edward I, 1272 to 1307. Transition from Early Pointed to Complete, or Geometrical Pointed.

1906 Musical Times 1 Mar. 158 The unusual shape of the arches and the fine effective windows of this north transept cause it to be one of the most distinguished English specimens of middle geometrical style.

2002 R. Bork in N. Y. Wu Ad Quadratum xi. 255 All of these Late Gothic projects share an emphatically rigid polygonality that seems to contrast with the more fluid geometrical approach seen in choir designs like that of Amiens.

B. n.

†1. Mathematics. A number in a geometrical progression. Obsolete.

ΚΠ

1706 H. Ditton Inst. Fluxions 64 y¹, y², y³, y⁴, y⁵, &c. Now, that these are a Series of continued Geometricals, is most evident.

1807 C. Hutton Course Math. (ed. 5) II. 114 The reciprocals of geometricals are also geometricals, and in the same ratio.

1895 Physical Rev. 2 149 Napier..proceeded to calculate the successive ordinates (geometricals) and the corresponding arithmeticals.

2. A geometrical figure or pattern.

ΚΠ

1866 York Herald 13 Oct. 11/4 Amongst the subjects of their [sc. stained glass windows] manufacture are..a number of beautiful samples of geometricals.

1908 Newark (Ohio) Advocate 11 July 8/2 (advt.) In blue florals—red scrolls, green geometricals and solid red carpet with borders—all reduced to 70c a yard.

2006 R. B. Schwartz Last Voice you Hear 300 He had set aside his dual-breast brown Armani with the soft lapels and the tie with subdued blue geometricals.

Compounds

geometrical isomer n. [after German geometrisches Isomer (1888 or earlier)] Chemistry each of two or more compounds which differ from each other only in the spatial arrangement of atoms relative to a rigid structure such as a double bond or ring; cf. cis-trans isomer.

ΚΠ

1888 London, Edinb. & Dublin Philos. Mag. 5th Ser. 26 429 Mesotartaric acid for example is to be regarded as a geometrical isomer of dextro- and lævotartaric acids, which two are optical isomers of one another.

1936 H. G. Rule tr. J. Schmidt Text-bk. Org. Chem. (ed. 3) 51 Under certain conditions the geometrical isomers of the ethylene series are interconvertible.

2007 J. L. Rosenberg et al. Schaum's Outl. Theory & Probl. College Chem. ix. 143 An important set of geometrical isomers occurs in compounds containing a carbon–carbon double bond.

geometrical isomerism n. [after German geometrische Isomerie (J. Wislicenus 1873, in Ann. der Chemie u. Pharmacie 157 345)] Chemistry isomerism involving geometrical isomers.

ΚΠ

1887 Amer. Chem. Jrnl. 9 268 The isomerism of fumaric and maleic acids descends, to be sure, from the region of geometrical isomerism to that of ordinary isomerism.

1964 N. G. Clark Mod. Org. Chem. iii. 40 About the double bond, the molecule is flat and therefore it possesses a plane of symmetry..and is identical with its mirror image. This style of stereoisomerism is an example of geometrical isomerism.

2003 Independent (Nexis) 27 Oct. 17 The well-known food pigment ‘bixin’ found in the seeds of Bixa orellana (‘annatto’), which was the first carotenoid to exhibit geometrical isomerism.

geometrical optics n. Physics the branch of optics that deals with light as rays (as opposed to its physical nature), esp. in reflection and refraction; contrasted with physical optics.

ΘΚΠ

the world > matter > physics > electromagnetic radiation > light > refraction > [noun] > study of

dioptrics1644

dioptic1665

catadioptrics1755

geometrical optics1835

the world > matter > physics > electromagnetic radiation > light > reflection > [noun] > study of

catoptrics1570

anacamptics1696

catadioptrics1755

geometrical optics1835

fibre optics1956

1835 R. Phelps Elem. Treat. Optics i. 5 As far as the subject of geometrical optics is concerned, it matters not which of these theories be adopted.

1918 F. R. Fraprie tr. H. Harting Optics for Photographers iii. 17 The laws, in accordance with which the reflection and refraction of a ray take place.., together with those of the rectilinear and independent propagation of all light rays, form the foundations on which the structure of geometrical optics is erected.

2001 R. W. Cahn Coming of Materials Sci. vii. 289 Design of the objectives—the province of geometrical optics.

geometrical series n. Mathematics = geometric series n. at geometric n. and adj. Compounds.

ΚΠ

1704 C. Hayes Treat. Fluxions 11 'Tis evident, that Double, Triple, Quadruple, &c. the Exponent of any Term in a Geometrical Series, is the Index or Exponent of the Square, Cube, Biquadrate, &c. of the said Term.

1875 W. S. Jevons Money (1878) 123 A geometrical series with the common ratio 3.

1917 T. R. Running Empirical Formulas iii. 49 If the values of x form a geometrical series the first differences of the corresponding values of log y also form a geometrical series.

1998 M. Black in P. van Inwagen & D. W. Zimmerman Metaphysics xiv. 121 This is a convergent geometrical series whose sum can be expressed in decimal notation as 111.1.

geometrical spider n. now rare = geometric spider n. at geometric n. and adj. Compounds.

ΘΚΠ

the world > animals > invertebrates > phylum Arthropoda > class Arachnida > [noun] > order Aranea > suborder Labidognatha or Dipneumones > member of family Argiopidae

retiary spider1658

geometrical spider1815

geometric spider1815

retiary1835

Epeirid1881

orb-weaver1883

magnificent spider1936

orb-web spider1945

orb spider1983

1815 W. Kirby & W. Spence Introd. Entomol. I. 413 The geometrical spiders.

1879 R. Jefferies Wild Life 317 Towards the latter part of September the geometrical spiders become conspicuous, spinning their webs on every bush.

1924 Wilson Bull. 36 194 Egg cases of the geometrical spider.

geometrical staircase n. a staircase, esp. one that is spiral or curved, in which each step is supported at the wall end only.

ΚΠ

1756 J. Hanway Jrnl. Eight Days Journey xiii. 41 The geometrical staircase is said to be the first erected in this island.

1842 J. Gwilt Encycl. Archit. ii. iii. 576 A Geometrical Staircase is one whose opening is down its centre..in which each step is supported by one end being fixed in the wall or partition.

1915 E. Singleton Daughter of Revol. xxiv. 300 Did you see the Whispering Gallery and the Geometrical Staircase?

2002 Newcastle (Australia) Herald (Nexis) 6 Apr. 16 A wide church pew spans a sunlit area and is an eye-catching piece for anyone descending the geometrical staircase.

geometrical tracery n. Architecture tracery with openings of geometric form, such as circles, trefoils, etc.; cf. sense A. 5.

ΚΠ

1807 Gentleman's Mag. Sept. 819/2 Geometrical tracery was made the standard, and with small variations continued in practice until our ancient Architecture became extinct.

1848 J. H. Parker Rickman's Styles Archit. Eng. (ed. 5) p. xxxvi The heads of two windows..affording very good examples of geometrical tracery.

1903 G. W. Forrest Cities of India vii. 174 The Hindu mason has impressed his originality on Saracenic geometrical tracery.

2002 N.Y. Times (Nexis) 17 May f1 The large polychrome entrance has a fanlight with geometrical tracery and a rusticated stone arch.

This entry has been updated (OED Third Edition, March 2012; most recently modified version published online March 2022).

单词	geometrical
释义	geometricaladj.n. Brit. /ˌdʒiːəˈmɛtrᵻkl/, /dʒɪəˈmɛtrᵻkl/, U.S. /ˌdʒiəˈmɛtrək(ə)l/ Forms: Middle English–1500s geometricalle, Middle English– geometrical, 1500s–1600s geometricall, 1600s jeometricall. Origin: Either (i) a borrowing from Latin. Or (ii) a borrowing from Latin, combined with an English element. Etymons: Latin geometricalis ; Latin geōmetricus , -al suffix¹. Etymology: Either < post-classical Latin geometricalis (from 12th cent. in British sources; compare geometricalia (plural noun) geometry (from 1267 in British sources)); or directly < classical Latin geōmetricus geometric adj. + -al suffix¹. Compare Middle French geometrical (of a measuring rod) belonging to a land surveyor (1517 in an apparently isolated attestation). Compare later geometric adj. and the foreign-language parallels cited at that entry.In use designating measures of length (see sense A. 2a) after the corresponding post-classical Latin use of classical Latin geōmetricus (a1364 in the passage translated in quot. ?a1475). In sense A. 4 after the corresponding post-classical Latin use of classical Latin geomētricus geometric adj. (1527 in the passage translated in quot. 1676, or earlier). A. adj. 1. a. Of or relating to geometry; determined, constructed, or formed according to the methods or laws of geometry. Also figurative.In former use often contrasted with mechanical (mechanical adj. 11b), with reference to figures constructed solely from straight lines and circles, and to procedures involving the use of a ruler and compasses only. ΘΚΠ the world > relative properties > number > geometry > [adjective] geometricalc1392 geometrialc1550 geometric1609 mathematical1614 mathematica1680 c1392 Equatorie of Planetis 18 This lymbe shaltow deuyde in 4 quarters by 2 diametral lynes..& lok thy croys be trewe proued by geometrical conclusioun. 1562 T. Cooper Answere Def. Truth f. 52^v, in Apol. Priuate Masse To apointe a geometricall measure of place..that may serue for all churches..is far aboue our reache. 1576 A. Fleming tr. Apollonius in Panoplie Epist. 225 He shall learne to be skilfull in the art Geometrical. 1638 F. Junius Painting of Ancients 282 Geometricall lines; which are nothing else but a length without breadth. 1695 W. Alingham Geom. Epitomiz'd 114 Upon a given right line as a d, to make a Geometrical square. 1737 S. Ashby Young Analyst's Exercise 55 The same Geometrical Problems may be solved by different Principals of Geometry. 1790 E. Burke Refl. Revol. in France 80 Is every land-mark of the country to be done away in favour of a geometrical and arithmetical constitution? View more context for this quotation 1838 C. Thirlwall Hist. Greece (new ed.) III. xviii. 59 A new town was built, with geometrical regularity. 1838 Penny Cycl. XI. 151/1 Every construction which can be made by the ruler and compasses, that is, which demands no points except such as can be found by the intersections of straight lines and circles, is geometrical. 1879 Fun 2 July 3/2 Bees are said to build their cells on geometrical principles, but, surely, they cannot like to learn Euclid. 1922 T. M. Lowry Inorg. Chem. xix. 211 The geometrical form of crystals is usually described by means of the intersections of the faces on three or more crystallographic axes. 1972 M. Kline Math. Thought ix. 193 The Arabs solved some cubics algebraically and gave a geometrical explanation..for quadratics. 2008 N.Y. Rev. Bks. 6 Mar. 34/4 Unable to draw simple geometrical figures or even tie their own shoelaces. b. Of a design: characterized by or decorated with regular shapes or patterns. ΘΚΠ society > leisure > the arts > visual arts > ornamental art and craft > pattern or design > [adjective] > geometric diapered?a1400 frettedc1420 checkeryc1440 checkeda1475 diaper1480 chequered1486 lozenged1523 diapery1605 fret1663 lozengy1686 reticulated1753 geometrical1777 reticular1783 geometric1842 Z-shaped1858 chessboard1889 1777 Archaeologia 4 91 The only remains of British masonry in England is the temple of the Druids on Salisbury plain; but in that we may observe the marks of the chisel, and the traces of a geometrical design. 1861 J. H. Parker Introd. Study Gothic Archit. (ed. 2) v. 142 Windows with flowing tracery, and those with reticulated, or net-like forms,..are in general somewhat later than the geometrical patterns. 1879 J. Lubbock Sci. Lect. v. 160 The ornamentation..consists of geometrical patterns—straight lines, circles, triangles, etc. 1909 A. C. Fox-Davies Compl. Guide Heraldry vii. 79 A fixed geometrical pattern, formed of rows of ear-shaped shields of alternate colours and alternately reversed. 2005 Archaeol. Rep. for 2004–5 (Soc. for Promotion Hellenic Stud.) No. 51. 84/2 The panels could have been decorated with very fine geometrical motifs. 2. Designating measures of length. a. Designating a cubit six times as long as the ordinary or common cubit, and usually taken as equal to nine feet (approx. 2.74 m). Now historical. ΘΚΠ the world > relative properties > measurement > measurement of length > [adjective] > of a unit: greater than usual length longa1300 geometrical?a1475 a1387 J. Trevisa tr. R. Higden Polychron. (St. John's Cambr.) (1869) II. 235 Þe cubites were cubites of gemetrie. For þe comoun cubite þat me vseþ conteyneþ but a foot and an half..But a cubite of gemetrie [L. cubitus..geometricus] conteyneþ sixe comoun cubites.] ?a1475 (?a1425) tr. R. Higden Polychron. (Harl. 2261) (1869) II. 235 A geometricalle cubite [L. cubitus geometricus] conteynethe vj commune cubites, whiche make ix footes. 1617 W. Raleigh Hist. World (new ed.) i. vii. 112 To make it manifest, that the Geometricall Cubit is not vsed in the Scripture, the stature of the Giants therein named may suffice. 1668 Bp. J. Wilkins Ess. Real Char. 163 The Ægyptian Geometrical cubit, each of which (say they) did contein six of the vulgar cubits, namely, nine foot. 1795 T. Maurice Hist. Hindostan I. xiii. 558 The magnitude of the ark..depended upon the sort of cubit supposed to be made use of; whether admitted to have been the geometrical cubit, containing six ordinary cubits, or what is called the sacred cubit. 1869 J. Kitto Illustr. Hist. Holy Bible i. ii. 81/1 The probability is, that there were two cubit measures beside the common; one being of twenty-one inches, and the. other of three feet. Some writers add the geometrical cubit of nine feet. 1996 N. Cohn Noah's Flood iv. 38 Origen could counter that argument by pointing out that Moses grew up in Egypt, where ‘cubit’ meant the geometrical cubit, which is six times larger. b. geometrical pace n. a length of five feet (approx. 1.52 m); the distance between successive stationary positions of the same foot when walking; cf. pace n.¹ 8. ΘΚΠ the world > relative properties > measurement > measurement of length > [noun] > units of length or distance > fixed by geographical computation geometrical pace1559 1559 W. Cuningham Cosmogr. Glasse 56 Table..A Geometricall Pase conteyninge in it 5 Five foote. 1702 Mil. Dict. at Pace There is a Common and a Geometrical Pace. The Common Pace is generally counted a Yard, the Geometrical a Foot. 1727 A. Pope et al. Περι Βαθους: Art of Sinking 87 in J. Swift et al. Misc.: Last Vol. A Stage as large as the Athenian, which was near ninety thousand Geometrical Paces square. 1828 J. M. Spearman Brit. Gunner 268 A league at sea..contains 3000 geometrical paces, or 3 English miles. 1876 G. E. Voyle & G. de Saint-Clair-Stevenson Mil. Dict. (ed. 3) 255/1 A geometrical mile consists of 1000 geometrical paces. 1920 A. J. F. Van Laer tr. Minutes Court of Fort Orange & Beverwyck, 1652–1656 8 The jurisdiction of the fort included all territory within range of cannon shot, reckoned at 600 geometrical paces of 5 feet to the pace. 2008 D. A. Wilson Forensic Procedures for Boundary & Title Investig. 387 The geometrical pace is five feet long, being the length of two steps, or the whole space passed over by the same foot from one step to another. c. Designating imperial units of length ( geometrical foot, geometrical mile, etc.) variously explained, but in later use based on the degree of longitude (the nautical mile, formerly 6080 feet, giving a length for the geometrical foot of 1 foot 1.8 inches, approx. 35.1 cm). Now historical. ΘΚΠ the world > relative properties > measurement > measurement of length > [noun] > units of length or distance > mile > nautical mile geometrical1597 maritime mile1632 geometric1670 nautical mile1730 knot1748 nautic mile1762 sea-mile1796 air mile1919 1597 E. Hoby tr. B. de Mendoza Theorique & Practise Warre 59 The bridge being fiue geometrical feete in depth. 1622 G. de Malynes Consuetudo 52 Gradus Geometrorum, wherewith the world is measured round about, is 15 miles, so the world is 360 Gradus, in toto 5400 miles, or at 4 miles for one Geometricall mile, is 21600 miles. a1652 I. Jones Most Notable Antiq. called Stone-Heng (1655) 34 In height one hundred twenty one Geometrical feet (which of our measure makes one hundred thirty six feet). 1697 W. Dampier New Voy. around World x. 287 Italian or Geometrical miles, (at the rate of 60 to a degree). 1769 B. Alexander tr. G. B. Morgagni Seats & Causes Dis. II. xxxiv. 158 Widmann..found also a much longer portion of the intestinum jejunum, that is more than a geometrical foot, fallen within the part next to it. 1799 E. Little Usher 26 Long Measure... 8 Furlongs 1 Mile. 60 Geometrical miles 1 Degree. 1904 E. H. Blair et al. tr. Philippine Islands 1493–1898 XVI. 66 These walls were twelve thousand eight hundred and forty-three geometrical feet in extent. 1995 P. Sheingorn tr. Bk. Sainte Foy i. 82 There remains the golden frontal of the high altar, which is not less than seven feet and two fingers in length—not in geometrical feet, but as the peasants are accustomed to measure, with both hands spread out and the thumbs linked. 1998 J. J. Roche Math. Measurem. iv. 53 The geometrical foot seems to have won more approval than application from mathematical philosophers. 3. Mathematics. = geometric adj. 3.Chiefly in set compounds: cf. geometrical series n. at Compounds, geometrical progression n., geometrical proportion n., geometrical ratio n. 1. ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [adjective] > of sets > of sequences > progression geometrical1543 harmonical1569 progressional1570 musical1589 equidifferent1696 harmonic1706 synharmonic1850 preferred1922 1543 R. Record Ground of Artes f. 97^v There is another maner of Progression called Geometricall, when the nombres encrease by a lyke proportion. 1734 J. Harris's tr. Pardies's Short Plain Elements Geom. (new ed.) iii. 145 When the Terms of the Progression are continual Proportionals..then the Progression is call'd Geometrical, as 1, 2, 4, 8, 16, 32. 1816 T. Taylor Theoretic Arithm. 104 In continued geometrical proportionality also, the rectangle under the extremes is equal to the square of the mean. 1909 A. D. Jones Logic Inductive & Deductive ii. ii. 204 When we only have two quantities to deal with, the geometrical average is easily found. 1949 H. Hoover in Changing Times Nov. 21/1 The geometrical increase of spending by our governments—federal, state and local. 2003 M. Mayor & P.-Y. Frei New Worlds in Cosmos iii. 56 There is clearly a geometrical sequence in which each term is the double of the preceding one. †4. Of an architect or draughtsman: making use of geometrical methods. Obsolete. rare. ΚΠ 1676 tr. H. C. Agrippa Vanity Arts & Sci. lxiv. 200 Neither is the Geometrical Artist [L. geometricus architectus] wanting to give his assistance, by whose contrivance fine convenient Ladders are made for the scaling of Windows. a1682 Sir T. Browne Certain Misc. Tracts (1683) i. 6 Geometrical and Architectonical Artists look narrowly upon the description of the Ark. 1853 E. K. Kane U.S. Grinnell Exped. (1856) xl. 366 You remember the geometrical artist of Laputa. 5. Architecture. = geometric adj. 5. ΘΚΠ society > leisure > the arts > visual arts > architecture > style of architecture > [adjective] > decorated decorated1812 geometrical1838 geometric1845 Middle Pointed1846 1838 B. Winkles Archit. & Picturesque Illustr. Cathedral Churches II. 11 The windows which were before of single lights, are here divided into several, by mullions, and tracery of geometrical form, an invention peculiar to pointed architecture. 1849 E. Sharpe Treat. Decorated Window Tracery i. ii. 8 I propose..to name these three styles of Window tracery, Geometrical, Curvilinear, and Rectilinear. 1875 Encycl. Brit. II. 425/2 Edward I, 1272 to 1307. Transition from Early Pointed to Complete, or Geometrical Pointed. 1906 Musical Times 1 Mar. 158 The unusual shape of the arches and the fine effective windows of this north transept cause it to be one of the most distinguished English specimens of middle geometrical style. 2002 R. Bork in N. Y. Wu Ad Quadratum xi. 255 All of these Late Gothic projects share an emphatically rigid polygonality that seems to contrast with the more fluid geometrical approach seen in choir designs like that of Amiens. B. n. †1. Mathematics. A number in a geometrical progression. Obsolete. ΚΠ 1706 H. Ditton Inst. Fluxions 64 y¹, y², y³, y⁴, y⁵, &c. Now, that these are a Series of continued Geometricals, is most evident. 1807 C. Hutton Course Math. (ed. 5) II. 114 The reciprocals of geometricals are also geometricals, and in the same ratio. 1895 Physical Rev. 2 149 Napier..proceeded to calculate the successive ordinates (geometricals) and the corresponding arithmeticals. 2. A geometrical figure or pattern. ΚΠ 1866 York Herald 13 Oct. 11/4 Amongst the subjects of their [sc. stained glass windows] manufacture are..a number of beautiful samples of geometricals. 1908 Newark (Ohio) Advocate 11 July 8/2 (advt.) In blue florals—red scrolls, green geometricals and solid red carpet with borders—all reduced to 70c a yard. 2006 R. B. Schwartz Last Voice you Hear 300 He had set aside his dual-breast brown Armani with the soft lapels and the tie with subdued blue geometricals. Compounds geometrical isomer n. [after German geometrisches Isomer (1888 or earlier)] Chemistry each of two or more compounds which differ from each other only in the spatial arrangement of atoms relative to a rigid structure such as a double bond or ring; cf. cis-trans isomer. ΚΠ 1888 London, Edinb. & Dublin Philos. Mag. 5th Ser. 26 429 Mesotartaric acid for example is to be regarded as a geometrical isomer of dextro- and lævotartaric acids, which two are optical isomers of one another. 1936 H. G. Rule tr. J. Schmidt Text-bk. Org. Chem. (ed. 3) 51 Under certain conditions the geometrical isomers of the ethylene series are interconvertible. 2007 J. L. Rosenberg et al. Schaum's Outl. Theory & Probl. College Chem. ix. 143 An important set of geometrical isomers occurs in compounds containing a carbon–carbon double bond. geometrical isomerism n. [after German geometrische Isomerie (J. Wislicenus 1873, in Ann. der Chemie u. Pharmacie 157 345)] Chemistry isomerism involving geometrical isomers. ΚΠ 1887 Amer. Chem. Jrnl. 9 268 The isomerism of fumaric and maleic acids descends, to be sure, from the region of geometrical isomerism to that of ordinary isomerism. 1964 N. G. Clark Mod. Org. Chem. iii. 40 About the double bond, the molecule is flat and therefore it possesses a plane of symmetry..and is identical with its mirror image. This style of stereoisomerism is an example of geometrical isomerism. 2003 Independent (Nexis) 27 Oct. 17 The well-known food pigment ‘bixin’ found in the seeds of Bixa orellana (‘annatto’), which was the first carotenoid to exhibit geometrical isomerism. geometrical optics n. Physics the branch of optics that deals with light as rays (as opposed to its physical nature), esp. in reflection and refraction; contrasted with physical optics. ΘΚΠ the world > matter > physics > electromagnetic radiation > light > refraction > [noun] > study of dioptrics1644 dioptic1665 catadioptrics1755 geometrical optics1835 the world > matter > physics > electromagnetic radiation > light > reflection > [noun] > study of catoptrics1570 anacamptics1696 catadioptrics1755 geometrical optics1835 fibre optics1956 1835 R. Phelps Elem. Treat. Optics i. 5 As far as the subject of geometrical optics is concerned, it matters not which of these theories be adopted. 1918 F. R. Fraprie tr. H. Harting Optics for Photographers iii. 17 The laws, in accordance with which the reflection and refraction of a ray take place.., together with those of the rectilinear and independent propagation of all light rays, form the foundations on which the structure of geometrical optics is erected. 2001 R. W. Cahn Coming of Materials Sci. vii. 289 Design of the objectives—the province of geometrical optics. geometrical series n. Mathematics = geometric series n. at geometric n. and adj. Compounds. ΚΠ 1704 C. Hayes Treat. Fluxions 11 'Tis evident, that Double, Triple, Quadruple, &c. the Exponent of any Term in a Geometrical Series, is the Index or Exponent of the Square, Cube, Biquadrate, &c. of the said Term. 1875 W. S. Jevons Money (1878) 123 A geometrical series with the common ratio 3. 1917 T. R. Running Empirical Formulas iii. 49 If the values of x form a geometrical series the first differences of the corresponding values of log y also form a geometrical series. 1998 M. Black in P. van Inwagen & D. W. Zimmerman Metaphysics xiv. 121 This is a convergent geometrical series whose sum can be expressed in decimal notation as 111.1. geometrical spider n. now rare = geometric spider n. at geometric n. and adj. Compounds. ΘΚΠ the world > animals > invertebrates > phylum Arthropoda > class Arachnida > [noun] > order Aranea > suborder Labidognatha or Dipneumones > member of family Argiopidae retiary spider1658 geometrical spider1815 geometric spider1815 retiary1835 Epeirid1881 orb-weaver1883 magnificent spider1936 orb-web spider1945 orb spider1983 1815 W. Kirby & W. Spence Introd. Entomol. I. 413 The geometrical spiders. 1879 R. Jefferies Wild Life 317 Towards the latter part of September the geometrical spiders become conspicuous, spinning their webs on every bush. 1924 Wilson Bull. 36 194 Egg cases of the geometrical spider. geometrical staircase n. a staircase, esp. one that is spiral or curved, in which each step is supported at the wall end only. ΚΠ 1756 J. Hanway Jrnl. Eight Days Journey xiii. 41 The geometrical staircase is said to be the first erected in this island. 1842 J. Gwilt Encycl. Archit. ii. iii. 576 A Geometrical Staircase is one whose opening is down its centre..in which each step is supported by one end being fixed in the wall or partition. 1915 E. Singleton Daughter of Revol. xxiv. 300 Did you see the Whispering Gallery and the Geometrical Staircase? 2002 Newcastle (Australia) Herald (Nexis) 6 Apr. 16 A wide church pew spans a sunlit area and is an eye-catching piece for anyone descending the geometrical staircase. geometrical tracery n. Architecture tracery with openings of geometric form, such as circles, trefoils, etc.; cf. sense A. 5. ΚΠ 1807 Gentleman's Mag. Sept. 819/2 Geometrical tracery was made the standard, and with small variations continued in practice until our ancient Architecture became extinct. 1848 J. H. Parker Rickman's Styles Archit. Eng. (ed. 5) p. xxxvi The heads of two windows..affording very good examples of geometrical tracery. 1903 G. W. Forrest Cities of India vii. 174 The Hindu mason has impressed his originality on Saracenic geometrical tracery. 2002 N.Y. Times (Nexis) 17 May f1 The large polychrome entrance has a fanlight with geometrical tracery and a rusticated stone arch. This entry has been updated (OED Third Edition, March 2012; most recently modified version published online March 2022). < adj.n.c1392
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