a. [f. SYMMETRY + -ICAL, alter geometrical. Cf. prec. and next.] Characterized by or exhibiting symmetry.
1. Having the parts or elements regularly and harmoniously arranged; regular in form; well-proportioned; balanced. (Said of natural or artificial bodies or structures, or of abstract or immaterial things; cf. SYMMETRY 2.)
1751. Johnson, Rambler, No. 94, ¶ 4. Some of the lines of this description are … defective in harmony, and therefore by no means correspondent with that symmetrical elegance … which they are intended to exhibit.
1833. Lyell, Princ. Geol., III. 319. The oldest lavas of Etna were poured out many thousand … years before the newest, and yet they have produced a symmetrical mountain.
1841. Dickens, Barn. Rudge, viii. That I had but eyes!… to behold my captain’s symmetrical proportions.
1870. Rolleston, Anim. Life, p. xxiii. An increase in our knowledge … may … overthrow the most perfectly symmetrical of systems.
1886. Ruskin, Præterita, I. 272. The symmetrical clauses of Pope’s logical metre.
2. Geom., etc. Said of a figure or body whose points or parts are equably distributed about a dividing line, plane, or point, i.e., arranged in pairs or sets so that those of each pair or set are at equal distances on opposite sides of such line, plane, or point; consisting of, or capable of being divided into two or more exactly similar and equal parts. Also said of the form of such a figure or object, of its parts or their arrangement, or of any part in relation to the corresponding part.
1794. R. J. Sullivan, View Nat., xxix. I. 423. In the passing of a substance from a fluid into a solid state, it almost universally appears … to have its parts arranged in a symmetrical order.
1805–17. R. Jameson, Char. Min. (ed. 3), 146. When the nucleus has not what is called a symmetrical form, as when it is a parallelopiped, whose faces differ in the respective inclinations of their faces, or in the measure of their angles.
1850. Grove, Corr. Phys. Forces (ed. 2), 88. Those crystals which have one axis of figure, or a line around which the figure is symmetrical.
1885. Leudesdorf, Cremona’s Proj. Geom., 267. The point M (and the symmetrical point in which the parabolas intersect again) can then be constructed.
1889. Cockshott & Walters, Geometr. Conics, 40. The ellipse is symmetrical with respect to the minor axis.
1894. C. Smith, Geometr. Conics, 4. When … corresponding to any point of the curve there is another point such that the chord joining the two points is bisected perpendicularly by [a] straight line, then the curve is said to be symmetrical about the straight line, and the straight line is called an axis of the curve.
b. Alg. and Higher Math. Applied to an expression, function, or equation whose value is never altered by interchanging the values of any two of the variables or unknown quantities.
Symmetrical or symmetric determinant: a determinant in which the constituents in each row are the same respectively, and in the same order, as those in the corresponding column, and which is therefore symmetrical about its principal diagonal.
1816. trans. Lacroix’ Diff. & Int. Calc., 536. On the supposition that f (α, β, γ, &c.) is symmetrical with respect to all the roots, except α.
1854. Orr’s Circ. Sci., Math., 217. Thus x + y = a; x2 + 3xy + y2 = b;… are … symmetrical equations; because for every x you may put y, and for every y, x, without altering either of the equations.
1863. Frost & Wolstenholme, Solid Geom., 29. To find the symmetrical equations of a straight line.
1878. W. K. Clifford, Math. Papers (1882), 317. If n is odd,… the determinant is skew symmetrical, and being of odd order it necessarily vanishes.
c. Photogr. Applied to a lens of symmetrical form; also ellipt. as sb. = symmetrical lens.
1890. Anthony’s Photogr. Bull., III. 326. Rapid, and portable symmetrical lenses, and a whole plate rapid symmetrical for long distance work.
1892. Photogr. Ann., II. 355. The lens is a rapid symmetrical with revolving diaphragms.
3. a. Bot. Of a flower: Having the same number of parts in each whorl: = ISOMEROUS 1.
1849. Balfour, Man. Bot., § 644. In speaking of flowers, it is usual to call them symmetrical when the sepals, petals, and stamens follow the law mentioned, even although the pistil may be abnormal. Thus, many Solanaceæ are pentamerous, and have a dimerous ovary, yet they are called symmetrical…. In Papilionaceous flowers, the parts are usually symmetrical, there being five divisions of the calyx, five petals, and ten stamens in two rows.
b. Anat. and Zool. Having similar or corresponding parts or organs on opposite sides of a dividing plane, or regularly arranged around an axis or center; consisting of two or more similar or corresponding divisions. Also said of the parts. (b) Path. Of a disease: Affecting such corresponding parts or organs simultaneously. (Cf. SYMMETRY 3 c.)
1851. Richardson, Geol., viii. (1855), 230. Some have internal symmetrical bones, as the Sepia and Loligo.
1851. Woodward, Mollusca, I. (1856), 62. Unlike most of the mollusca, they are symmetrical animals, having their right and left sides equally developed.
a. 1883. Fagge, Princ. & Prac. Med. (1886), II. 669. Remarkable cases of symmetrical gangrene of the extremities.
1892. H. Lane, Differ. Rheum. Dis. (ed. 2), 46. Rheumatoid Arthritis … affection of joints often symmetrical.
Hence Symmetricality = SYMMETRICALNESS.
1893. Chamb. Jrnl., 21 Jan., 44/2. With regard to symmetricality, Nature, when she has a purpose to serve, is nowise loth to depart from it.
