| 释义 |
geometrical, a.|dʒiːəʊˈmɛtrɪkəl|
[f. as prec. + -al1.]
1. a. Belonging to geometry; determined or constructed according to the methods of geometry; spec. = geometric a. c. geometrical staircase (see quot. 1842–59). geometrical tracery, tracery in which the openings are of geometrical form (circles, trefoils, etc.).
The name of geometrical figures was formerly restricted to those whose construction involved only the straight line and circle, all other curves being called mechanical.
1552Huloet, Geometricall description, ichnographia. 1562Cooper Answ. Def. Truth 52 b, To apointe a geometricall measure of place..that may serue for all churches..is far aboue our reache. 1576Fleming Panopl. Epist. 225 He shall learne to be skilfull in the art Geometrical. 1638F. Junius Paint. Ancients 282 Geometricall lines; which are nothing else but a length without breadth. 1695W. Alingham Geom. Epit. 114 Upon a given right line as a d, to make a Geometrical square. 1772Nugent tr. Grosley's Lond. II. 43 This hospital [Greenwich] has a great staircase of that sort which the English call Geometrical. 1817T. Rickman Architecture 74 The figures..are all worked with the same moulding, and do not always regularly join each other, but touch only at points. This may be called geometrical tracery. 1838Thirlwall Greece III. xviii. 59 A new town was built, with geometrical regularity. 1842–59Gwilt Archit. §2184 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. 1848Rickman Archit. p. xxxvi, The heads of two windows..affording very good examples of geometrical tracery. 1848[see decorated ppl. a. b]. 1849E. Sharpe Treat. Decorated Window Tracery in Eng. i. ii. 8, I propose..to name these three styles of Window tracery, Geometrical, Curvilinear, and Rectilinear. Ibid. ii. i. 89 Towards the close of the Geometrical Period there occurred some singular attempts at originality in the designs of Window Tracery. 1850Parker Gloss. Archit. I. 230 Geometrical tracery: this epithet was applied by Rickman to distinguish the early forms of tracery, in which the figures, such as circles, trefoils, &c., do not always regularly join each other, but touch only at points. 1875Encycl. Brit. II. 425/2 Edward I, 1272 to 1307. Transition from Early Pointed to Complete, or Geometrical Pointed. 1879Lubbock Sci. Lect. v. 160 The ornamentation..consists of geometrical patterns—straight lines, circles, triangles, etc. 1942N. Pevsner Outl. Europ. Archit. iii. 51 The kind of tracery which is called flowing as against the geometrical tracery of 1230 to about 1275.
? quasi-adv.1593Rites & Mon. Ch. Durh. (Surtees) 2 A goodly faire round window..havinge in it twenty-four lights verye artificially made, as it is called geometricall.
fig.1790Burke Fr. Rev. 80 Is every land-mark of the country to be done away in favour of a geometrical and arithmetical constitution?
b. geometrical ratio (now usually ratio simply, as the expression arithmetical r. is obsolete): that kind of relation between two quantities which is expressed by dividing the first by the second; the quotient expressing this. (The term survives chiefly in the phrase at a geometrical ratio, loosely used for in geometrical progression.) geometrical proportion: a proportion which involves an equality of geometrical ratio in its two parts, as 1:3::4:12. geometrical progression: a series in which the ratio between the successive quantities is constant, as 1:3:9:27:81, etc.
arithmetical progression, † proportion, † ratio, etc. (see arithmetical a.) relate to differences instead of quotients. The term geometrical points to the fact that problems involving multiplication were originally dealt with by geometry and not by arithmetic.
1557Recorde Whetst. G ij, You can haue no progression Geometricalle, but it must be made either of square nombers, or els of like flattes. Ibid. K k ij, I knowe the propertie of those nombers in proportion Geometricall to bee soche, that the multiplication of bothe the extremes is equalle to the square of the middell terme. 1594Blundevil Exerc. i. xiii. (ed. 7) 39 What is Progression Geometricall? It is that wherein every number exceedeth his fellow by like Proportion, for as six contayneth three twice, so doth twelve contayne six twice, &c. 1690Leybourn Curs. Math. 144 Thus in..the following Table, the Numbers in Geometrical Proportion are 1, 2, 4, 8, 16, &c. 1806Hutton Course Math. I. 110 Of these two numbers 6 and 3, the difference, or arithmetical ratio, is 6-3 or 3, but the geometrical ratio is 6/3 or 2. 1859Darwin Orig. Spec. iii. (1873) 52 All plants and animals are tending to increase at a geometrical ratio. 1885Watson & Burbury Math. Th. Electr. & Magn. I. 121 The distances of the images from the common centre are in geometrical progression.
†c. geometrical cubit, geometrical foot, geometrical mile, geometrical pace: measures of length, some of which are app. fixed by geographical computation (1 degree = 60 miles, 1 mile = 1000 paces, 1 pace = 5 feet). Obs.
Originally perh. with reference to the literal sense of geometry = ‘land-measuring’.
1559W. Cuningham Cosmogr. Glasse 56 Table..A Geometricall Pase conteyninge in it 5 Five foote. 1620–55I. Jones Stone-Heng (1725) 23 In height one hundred twenty one Geometrical Feet (which of our Measure makes one hundred thirty six Feet). 1668Wilkins Real Char. 163 The ægyptian Geometrical cubit, each of which (say they) did contein six of the vulgar cubits, namely, nine foot. 1677Plot Oxfordsh. 10, 456 Geometrical paces, or 2280 feet. 1697W. Dampier Voy. (1729) I. 287 Italian or Geometrical miles (at the rate of 60 to a degree). 1727Pope, etc. Art of Sinking 122 A stage as large as the athenian, which was near ninety thousand geometrical paces square. 1843Penny Cycl. XXVII. 198 In the second work, he [Fernel] says that five of his own paces, or those of ordinary men, make six geometrical paces.
d. ellipt. as n. pl. Numbers or magnitudes which stand to each other in geometrical proportion. rare.
1807Hutton Course Math. II. 114 The reciprocals of geometricals are also geometricals, and in the same ratio.
e. geometrical optics: the branch of optics which deals with the geometrical analysis of the paths of light in refraction and reflection.
1838W. N. Griffin Treat. Optics i. 1 In Geometrical Optics the circumstances of the transmission and modification of light are computed on certain laws established by experiment; in Physical Optics these laws are accounted for on hypotheses of the structure of bodies. 1936Discovery Nov. 364/1 The Physical Society's report on the teaching of Geometrical Optics.
2. That works by the methods of geometry. rare. geometrical spider (cf. geometric b).
a1682Sir T. Browne Tracts 6 Geometrical and Architectonical Artists look narrowly upon the description of the Ark. 1815Kirby & Sp. Entomol. I. 413 The geometrical spiders. 1853Kane Grinnell Exp. xl. (1856) 366 You remember the geometrical artist of Laputa. 1879Jefferies Wild Life in S. Co. 317 Towards the latter part of September the geometrical spiders become conspicuous, spinning their webs on every bush. |