subtend, v.
(səbˈtɛnd)
[ad. L. subtendĕre, f. sub- sub- 2 + tendĕre to stretch, tend. Cf. Sp., Pg. subtender.]
1. trans. (Geom.) To stretch or extend under, or be opposite to: said esp. of a line or side of a figure opposite an angle; also, of a chord or angle opposite an arc.
| 1570 Billingsley Euclid i. iv. 14 That angle is said to subtend a side of a triangle, which is placed directly opposite, and against that side. 1571 Digges Pantom. i. xviii. F j, This done conioyne their endes togither and the angle subtended of the longest staffe is a right. 1646 Sir T. Browne Pseud. Ep. i. vii. 25 In rectangle triangles the square which is made of the side that subtendeth the right angle, is equall to the squares which are made of the sides containing the right angle. 1681 S. Colvil Whigs Suppl. (1710) 13 The truth is, they [sc. a man's legs] in every thing Resemble do a Bow and String. The one strait to the other bending, Is like a Chord an Arch subtending. c 1791 Encycl. Brit. (1797) VII. 666/2 An angle at the circumference is measured by half the arc it subtends. 1798 Hutton Course Math. I. 292 In any Triangle, the square of the Side subtending an Acute Angle, is Less than the Squares of the Base and the other Side, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Acute Angle. 1862 Todhunter Euclid 19 The greater angle of every triangle is subtended by the greater side or has the greater side opposite to it. 1885 C. Leudesdorf Cremona's Proj. Geom. 227 The angle subtended at any point on the curve by a fixed diameter would be a right angle. 1885 Watson & Burbury Math. Th. Electr. I. 137, 2β is the angle of the cone subtended by the disc at M{p}. |
b. in Astron. and Optics.
| 1722 Wollaston Relig. Nat. iii. 54 He must be a brute..who does not know, that the same line (v.g. the diameter of the Sun) at different distances subtends different angles at the eye. c 1790 J. Imison Sch. Arts I. 196 The best eye can hardly distinguish a particle of matter that subtends at the eye an angle less than half a minute. 1821 Craig Lect. Drawing, etc. vi. 362 The same angle which the picture subtends with the eye. 1833 M. Arnott Physics (ed. 5) II. 241 The fly then would subtend a larger visual angle than he, that is to say, would be forming on the retina a larger image than the man. 1835 Poe Adv. Hans Pfaall Wks. 1864 I. 36 Whose apparent diameter subtended at the balloon an angle of about sixty-five seconds. 1907 Hodges Elem. Photogr. (ed. 6) 24 The visual angle subtended on the plate. |
c. transf. and gen.
| 1859 Murchison Siluria (ed. 3) iii. 53 The Llandeilo formation is subtended on the north, south, and west by younger Silurian deposits. 1860 Motley Netherl. (1868) I. 140 The river..subtends the arc into which the place [sc. Antwerp] arranges itself. 1867 Murchison Siluria (ed. 4) xx. 493 The chalk-cliffs which subtend the Wealden area. 1868 Kinglake Crimea III. vii. 117 Standing upon a semi⁓circular tract of ground, subtended by the great bay or roadstead. 1873 Symonds Grk. Poets ix. 282 This large arc was subtended by a long straight line—the σκηνή, or back⁓ground of the stage. 1880 Nature XXI. 212/2 Tracts such as the great deserts or prairies might subtend a sufficient angle to preserve their natural hue. |
d. fig.
| 1866 Felton Greece, Anc. & Mod. I. 33 It takes but a few moments to tell in outline this traveller's story; but how many ages does it subtend. 1869 Spencer Princ. Psychol. (1872) I. ii. iv. 217 The angle it subtends in consciousness when we are reminded of it a year after, is very small. 1898 P. Manson Trop. Dis. Introd. p. xiv, When this third animal happens to be a tropical species, the disease it subtends, so to speak, is in natural conditions, necessarily tropical also. |
† 2. pass. Of an angle, a side of a figure: To be extended under, to be opposite to. Obs.
| 1570 Billingsley Euclid i. iv. 14 Euery angle of a triangle is contayned of two sydes of the triangle, and is subtended to the third side. 1660 Barrow Euclid i. iv, The remaining angles B, C, shall be equal to the remaining angles E, F, each to each, under which the equal sides are subtended. |
3. trans. (Bot.) To extend under, so as to embrace or enfold.
| 1871 W. A. Leighton Lichen-flora 94 Apothecia..subtended by the very short deformed divaricate extremities of the laciniæ. 1872 Oliver Elem. Bot. ii. 237 A 3-lobed bract, subtending a single nut. |
Hence subˈtended ppl. a., (a) stretched underneath; (b) of an angle opposite a side.
| 1679 Evelyn Sylva (ed. 3) 56 To clip, and let the leaves fall upon a subtended sheet. 1824 Smyth in Duppa Trav. Italy, etc. (1828) 185 note, The subtended angles carefully corrected. 1884 tr. Lotze's Logic 248 The formula we are seeking must mention the subtended angle. |