Tuesday, March 23, 2010

antiquated math word of the day

Today's OED word of the day (subscribe here) is sagitta.

A doubly-antiquated word (an old term for the old term 'versed sine'), it exhibits some interesting etymological connections between arrows, arches, fish-ears, sponges, and geometric constructions. I haven't yet parsed through the mathematical descriptions offered - it might be interesting to see how they connect to each other. The most surprising thing I learned from this (so far) is that there used to be a name for the middle horizontal line in an epsilon (an application of the geometric description).

[L.,lit. an arrow.]
1. Astr. A northern constellation lying between Hercules and Delphinus: = ARROW n. 4. 1704 in J.HARRIS Lex. Techn. I. [And in mod. Dicts.]

2.  Geom. a. The versed sine of an arc: = ARROW n. 6. [1594: see ARROW n. 6.] 1704 in J.HARRIS Lex. Techn. I. 1726 LEONI Alberti's Archit. I. 9/2 The..Line..from the middle Point of the Chord up to the Arch, leaving equal Angles on each Side, is call'd the Sagitta. 1853 SIR H. DOUGLAS Milit. Bridges (ed. 3) 32 The sagitta, or versed sine, of the curvature being about one fifth of the side of the triangle.
{dag}b. In extended sense: The abscissa of a curve. Obs. rare{em}01727-41 in CHAMBERS Cycl.

3. Arch. The key-stone of an arch. 1703 R. NEVE Builder's Dict. (1736). 1823 P.NICHOLSON Pract. Build. 592. 1849-50 WEALE Dict. Terms.

4. The middle horizontal stroke in the Greek letter {epsilon}. [App. an application of sense 2.]
1864 ELLICOTT Pastoral Ep. (ed. 3) 103 The thickened extremity of the sagitta of {epsilon}.
1881 Dublin Rev. VI. 134 The disputed line is really the sagitta of an epsilon.

5. Anat. ‘The sagittal suture’ (Cent. Dict. 1891).

6. Zool. a. One of the otoliths of a fish's ear. 1888 ROLLESTON & JACKSON Anim. Life 86 There are [in the ear of the perch] generally two large otoliths, a sagitta in the sacculus, an asteriscus in the recessus cochleae 1897 PARKER & HASWELL Text-bk. Zool. II. 199. b. One of the components of certain sponge-spicules: see quot. 1898 SEDGWICK Text-bk. Zool. I. 83 The Tri├Žne consists of the rhabdome, or shaft, and the cladome, which consists of the three cladi, a straight line joining the ends of the two cladi is the chord. The sagitta is a perpendicular from the origin of the cladome to the chord.