στοιχεῖον: Difference between revisions

|Definition=τό: <span class="sense">&nbsp;&nbsp;&nbsp;<span class="bld">I</span> in a form of sun-dial, <b class="b2">the shadow of the gnomon, the length of which in feet indicated the time of day</b>, <b class="b3">ὅταν ᾖ δεκάπουν τὸ σ</b>. when the [[shadow]] is ten feet long, <span class="bibl">Ar.<span class="title">Ec.</span>652</span>, v. Sch.; ὁπηνίκ' ἂν εἴκοσι ποδῶν . . τὸ σ. ᾖ <span class="bibl">Eub.119.7</span>, cf. <span class="bibl">Philem.83</span>. </span><span class="sense">&nbsp;&nbsp;&nbsp;<span class="bld">II</span> [[element]], </span><span class="sense">&nbsp;&nbsp;&nbsp;<span class="bld">1</span> a [[simple sound]] of speech, as the [[first component]] of the syllable, <span class="bibl">Pl.<span class="title">Cra.</span>424d</span>; <b class="b3">τὸ ῥῶ τὸ σ</b>. ib.<span class="bibl">426d</span>; γραμμάτων σ. καὶ συλλαβάς <span class="bibl">Id.<span class="title">Tht.</span>202e</span>; σ. ἐστι φωνὴ ἀδιαίρετος <span class="bibl">Arist.<span class="title">Po.</span>1456b22</span>; φωνῆς σ. καὶ ἀρχαὶ δοκοῦσιν εἶναι ταῦτ' ἐξ ὧν σύγκεινται αἱ φωναὶ πρώτων <span class="bibl">Id.<span class="title">Metaph.</span>998a23</span>, cf.Gal.15.6:—[[στοιχεῖα]] therefore, strictly, were different from [[letters]] (γράμματα), <span class="bibl">Diog.Bab.Stoic.3.213</span>, Sch.D.T.<span class="bibl">p.32</span>, al., but are freq. not clearly distd. from them, as by Pl.<span class="title">Tht.</span>l.c., <span class="bibl"><span class="title">Cra.</span>426d</span>; τὰ σ. τῶν γραμμάτων τὰ τέτταρα καὶ εἴκοσι <span class="bibl">Aen.Tact.31.21</span>; <b class="b3">σ. ε</b> [[letter]] ε (in a filing-system), <span class="bibl"><span class="title">BGU</span>959.2</span> (ii A.D.); <b class="b3">ἀκουόμενα σ</b>. [[letters]] which are pronounced, <span class="bibl">A.D.<span class="title">Adv.</span>165.17</span>; [[γράμματα]] and ς. are expressly identified by <span class="bibl">D.T.630.32</span>; the ς. and its name are confused by <span class="bibl">A.D. <span class="title">Synt.</span>29.1</span>, but distd. by Hdn.Gr. ap. <span class="bibl">Choerob.<span class="title">in Theod.</span>1.340</span>, Sch.D.T. l.c.:—κατὰ στοιχεῖον <b class="b2">in the order of the letters, alphabetically</b>, AP11.15 (Ammian.); dub.sens.in Plu.2.422e. </span><span class="sense">&nbsp;&nbsp;&nbsp;<span class="bld">2</span> in Physics, [[στοιχεῖα]] were the <b class="b2">components into which matter is ultimately divisible, elements</b>, reduced to four by Empedocles, who called them [[ῥιζὤματα]], the word [[στοιχεῖα]] being first used (acc. to Eudem. ap. <span class="bibl">Simp.<span class="title">in Ph.</span>7.13</span>) by Pl., <b class="b3">τὰ πρῶτα οἱονπερεὶ ς, e)c w(=n h(mei=s te sugkei/meqa kai\ ta)/lla</b> <span class="bibl"><span class="title">Tht.</span>201e</span>; <b class="b3">τὰ τῶν πάντων σ</b>. <span class="bibl"><span class="title">Plt.</span>278d</span>; αὐτὰ τιθέμενοι σ. τοῦ παντός <span class="bibl"><span class="title">Ti.</span>48b</span>, cf. <span class="bibl">Arist.<span class="title">GC</span>314a29</span>, <span class="bibl"><span class="title">Metaph.</span>998a28</span>, <span class="bibl">Thphr.<span class="title">Sens.</span>3</span>, al., <span class="bibl">D.L.3.24</span>; σ. σωματικά <span class="bibl">Arist.<span class="title">Mete.</span>338a22</span>, <span class="bibl">Thphr.<span class="title">Fr.</span>46</span>; <b class="b3">ἄτομα σ</b>. <span class="bibl">Epicur.<span class="title">Ep.</span>2p.36U.</span>; equivalent to [[ἀρχαί]], Thales ap.Plu.2.875c, Anaximand. ap. <span class="bibl">D.L.2.1</span>, Anon. ap. <span class="bibl">Arist.<span class="title">Ph.</span>188b28</span>, <span class="bibl"><span class="title">Metaph.</span>1059b23</span>, al.; but Arist. also distinguishes ς. from [[ἀρχή]] as less comprehensive, ib.1070b23; <b class="b3">τὰ σ. ὕλη τῆς οὐσίας</b> ib.1088b27; <b class="b3">τρία τὰ σ</b>. <span class="bibl">Id.<span class="title">Ph.</span>189b16</span>; distd. from [[ἀρχή]] on other grounds by <span class="title">Stoic.</span>2.111; ς. used in three senses by Chrysipp., ib.136, cf. Zeno ib.1.24, al.; in Medicine, Gal.6.3, 420, al., 15.7, al.; Αἰθέρ, κόσμου σ. ἄριστον <span class="bibl">Orph.<span class="title">H.</span>5.4</span>; <b class="b3">ἀνηλεὲς σ</b>., of the sea, <span class="bibl">Babr.71.4</span>; <b class="b3">τὸ σ</b>., of the sea, <span class="bibl">Polem.<span class="title">Cyn.</span>44</span>; <b class="b3">ἄμφω τὰ σ</b>., i.e. land and sea, ib.''ΙΙ'', cf. <span class="bibl">Hdn.3.1.5</span>, <span class="bibl">Him.<span class="title">Ecl.</span>2.18</span>. </span><span class="sense">&nbsp;&nbsp;&nbsp;<span class="bld">3</span> the [[elements of proof]], e.g. in general reasoning the <b class="b3">πρῶτοι συλλογισμοί</b>, <span class="bibl">Arist.<span class="title">Metaph.</span>1014b1</span>; in Geometry, the propositions whose proof is involved in the proof of other propositions, ib.<span class="bibl">998a26</span>, <span class="bibl">1014a36</span>; title of geometrical works by Hippocrates of Chios, Leon, Theudios, and Euclid, <span class="bibl">Procl. <span class="title">in Euc.</span>pp.66,67</span>,<span class="bibl">68F.</span>: hence applied to whatever is one, small, and capable of many uses, <span class="bibl">Arist.<span class="title">Metaph.</span>1014b3</span>; to whatever is most universal, e.g. the unit and the point, ib.<span class="bibl">6</span>; the line and the circle, <span class="bibl">Id.<span class="title">Top.</span>158b35</span>; the [[τόπος]] (argument applicable to a variety of subjects), ib.<span class="bibl">120b13</span>, al., <span class="bibl"><span class="title">Rh.</span>1358a35</span>, al.; στοιχεῖα τὰ γένη λέγουσί τινες <span class="bibl">Id.<span class="title">Metaph.</span>1014b10</span>; <b class="b3">τὸ νόμισμα σ. καὶ πέρας τῆς ἀλλαγῆς</b> coin is the <b class="b2">unit . .</b>of exchange, <span class="bibl">Id.<span class="title">Pol.</span>1257b23</span>; in Grammar, <b class="b3">σ. τῆς λέξεως</b> [[parts]] of speech, <span class="bibl">D.H.<span class="title">Comp.</span>2</span>; but also, the [[letters]] composing a word, <span class="bibl">A.D.<span class="title">Synt.</span>313.7</span>; [[letters]] of the alphabet, Diog. Bab.<span class="title">Stoic.</span>3.213; <b class="b3">σ. τοῦ λόγου</b> the [[elements]] of speech, viz. [[words]], or the [[kinds of words]], [[parts]] of speech, Thphr. ap. <span class="bibl">Simp. <span class="title">in Cat.</span>10.24</span>, <span class="bibl">Chrysipp.Stoic.2.45</span>, <span class="bibl">A.D.<span class="title">Synt.</span>7.1</span>, <span class="bibl">313.6</span>. </span><span class="sense">&nbsp;&nbsp;&nbsp;<span class="bld">4</span> generally, [[elementary]] or [[fundamental principle]], <b class="b3">ἀρξάμενοι ἀπὸ τῶν σ</b>. <span class="bibl">X.<span class="title">Mem.</span>2.1.1</span>; σ. χρηστῆς πολιτείας <span class="bibl">Isoc.2.16</span>; <b class="b3">τὸ πολλάκις εἰρημένον μέγιστον σ</b>. <span class="bibl">Arist.<span class="title">Pol.</span>1309b16</span>; σ. τῆς ὅλης τέχνης <span class="bibl">Nicol.Com.1.30</span>, cf. <span class="bibl">Epicur. <span class="title">Ep.</span>1p.10U.</span>, <span class="bibl"><span class="title">Ep.</span>3p.59U.</span>, Phld.<span class="title">Rh.</span>1.127S., Gal.6.306. </span><span class="sense">&nbsp;&nbsp;&nbsp;<span class="bld">5</span> <b class="b3">ἄστρων στοιχεῖα</b> the [[stars]], <span class="bibl">Man.4.624</span>; σ. καυσούμενα λυθήσεται <span class="bibl"><span class="title">2 Ep.Pet.</span>3.10</span>, cf. <span class="bibl">12</span>; esp. [[planets]], στοιχείῳ Διός <span class="bibl"><span class="title">PLond.</span>1.130.60</span> (i/ii A.D.); so perh. in <span class="bibl"><span class="title">Ep.Gal.</span>4.3</span>, <span class="bibl"><span class="title">Ep.Col.</span>2.8</span>; esp. a [[sign of the Zodiac]], <span class="bibl">D.L.6.102</span>; of the Great Bear, <span class="title">PMag.Par.</span>1.1303. </span><span class="sense">&nbsp;&nbsp;&nbsp;<span class="bld">6</span> [[σ]]. = [[ἀριθμός]], as etym. of [[Στοιχαδεύς]], Sch.D.T.p.192 H.</span>