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. 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. 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. & Magn., I. 137. 2β is the angle of the cone subtended by the disc at M′.
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. 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. N. 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 semicircular 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 background 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 Subtended 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. trans. Lotze’s Logic, 248. The formula we are seeking must mention the subtended angle.
