to be written in the order of the Zodiac

(Show lexicon entry in LSJ) (search) στοιχειογραφέω verb 1st sg pres ind act epic doric ionic aeolic parad_form
στοιχειογραφέω verb 1st sg pres subj act epic doric ionic aeolic

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στοιχειο-γρα^φέω , in Pass.,
A. to be written in the order of the Zodiac, Vett.Val.162.34, 335.30.

who presided over the elements

(Show lexicon entry in LSJ) (search) στοιχειοκράτωρ noun sg masc nom

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στοιχειο-κράτωρ [α^], ορος, ὁ, pl. ς. θεοί gods
A. who presided over the elements, Simp. in Cael.107.15.

the shadow of the gnomon, the length of which in feet indicated the time of day

(Show lexicon entry in LSJ Middle Liddell) (search) στοιχεῖον noun sg neut acc
στοιχεῖον noun sg neut nom
στοιχεῖον noun sg neut voc

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στοιχεῖον , τό:
I. in a form of sun-dial, the shadow of the gnomon, the length of which in feet indicated the time of day, ὅταν ᾖ δεκάπουν τὸ ς. when the shadow is ten feet long, Ar.Ec.652, v. Sch.; “ὁπηνίκ᾽ ἂν εἴκοσι ποδῶν . . τὸ ς. ᾖ” Eub.119.7, cf. Philem.83.
II. element,
1. a simple sound of speech, as the first component of the syllable, Pl.Cra.424d; τὸ ῥῶ τὸ ς. ib.426d; “γραμμάτων ς. καὶ συλλαβάς” Id.Tht.202e; “ς. ἐστι φωνὴ ἀδιαίρετος” Arist.Po.1456b22; “φωνῆς ς. καὶ ἀρχαὶ δοκοῦσιν εἶναι ταῦτ᾽ ἐξ ὧν σύγκεινται αἱ φωναὶ πρώτων” Id.Metaph.998a23, cf.Gal.15.6:—στοιχεῖα therefore, strictly, were different from letters (γράμματα), Diog.Bab.Stoic.3.213, Sch.D.T.p.32, al., but are freq. not clearly distd. from them, as by Pl.Tht.l.c., Cra.426d; “τὰ ς. τῶν γραμμάτων τὰ τέτταρα καὶ εἴκοσι” Aen.Tact.31.21; ς. ε_ letter ε (in a filing-system), BGU959.2 (ii A.D.); ἀκουόμενα ς. letters which are pronounced, A.D.Adv.165.17; γράμματα and ς. are expressly identified by D.T.630.32; the ς. and its name are confused by A.D. Synt.29.1, but distd. by Hdn.Gr. ap. Theod.1.340, Sch.D.T. l.c.:—“κατὰ στοιχεῖον” in the order of the letters, alphabetically, AP11.15 (Ammian.); Plu.2.422e.
2. in Physics, στοιχεῖα were the components into which matter is ultimately divisible, elements, reduced to four by Empedocles, who called them ῥιζὤματα, the word στοιχεῖα being first used (acc. to Eudem. ap. Ph.7.13) by Pl., τὰ πρῶτα οἱονπερεὶ ς, ἐξ ὧν ἡμεῖς τε συγκείμεθα καὶ τἄλλα Tht.201e; τὰ τῶν πάντων ς. Plt.278d; “αὐτὰ τιθέμενοι ς. τοῦ παντός” Ti.48b, cf. Arist.GC314a29, Metaph.998a28, Thphr.Sens.3, al., D.L.3.24; “ς. σωματικά” Arist.Mete.338a22, Thphr.Fr.46; ἄτομα ς. Epicur.Ep.2p.36U.; equivalent to ἀρχαί, Thales ap.Plu.2.875c, Anaximand. ap. D.L.2.1, Anon. ap. Arist.Ph.188b28, Metaph.1059b23, al.; but Arist. also distinguishes ς. from ἀρχή as less comprehensive, ib.1070b23; τὰ ς. ὕλη τῆς οὐσίας ib.1088b27; τρία τὰ ς. Id.Ph.189b16; distd. from ἀρχή on other grounds by Stoic.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” Orph.H.5.4; ἀνηλεὲς ς., of the sea, Babr.71.4; τὸ ς., of the sea, Polem.Cyn.44; ἄμφω τὰ ς., i.e. land and sea, ib.11, cf. Hdn.3.1.5, Him.Ecl.2.18.
3. the elements of proof, e.g. in general reasoning the πρῶτοι συλλογισμοί, Arist.Metaph.1014b1; in Geometry, the propositions whose proof is involved in the proof of other propositions, ib.998a26, 1014a36; title of geometrical works by Hippocrates of Chios, Leon, Theudios, and Euclid, Procl. in Euc.pp.66,67,68F.: hence applied to whatever is one, small, and capable of many uses, Arist.Metaph.1014b3; to whatever is most universal, e.g. the unit and the point, ib.6; the line and the circle, Id.Top.158b35; the τόπος (argument applicable to a variety of subjects), ib.120b13, al., Rh.1358a35, al.; “στοιχεῖα τὰ γένη λέγουσί τινες” Id.Metaph.1014b10; τὸ νόμισμα ς. καὶ πέρας τῆς ἀλλαγῆς coin is the unit . . of exchange, Id.Pol.1257b23; in Grammar, ς. τῆς λέξεως parts of speech, D.H.Comp.2; but also, the letters composing a word, A.D.Synt.313.7; letters of the alphabet, Diog. Bab.Stoic.3.213; ς. τοῦ λόγου the elements of speech, viz. words, or the kinds of words, parts of speech, Thphr. ap. Simp. in Cat.10.24, Chrysipp.Stoic.2.45, A.D.Synt.7.1, 313.6.
4. generally, elementary or fundamental principle, ἀρξάμενοι ἀπὸ τῶν ς. X.Mem.2.1.1; “ς. χρηστῆς πολιτείας” Isoc.2.16; τὸ πολλάκις εἰρημένον μέγιστον ς. Arist.Pol.1309b16; “ς. τῆς ὅλης τέχνης” Nicol.Com.1.30, cf. Epicur. Ep.1p.10U., Ep.3p.59U., Phld.Rh.1.127S., Gal.6.306.
5. ἄστρων στοιχεῖα the stars, Man.4.624; “ς. καυσούμενα λυθήσεται” 2 Ep.Pet.3.10, cf. 12; esp. planets, “στοιχείῳ Διός” PLond.1.130.60 (i/ii A.D.); so perh. in Ep.Gal.4.3, Ep.Col.2.8; esp. a sign of the Zodiac, D.L.6.102; of the Great Bear, PMag.Par.1.1303.
6. ς. = ἀριθμός, as etym. of Στοιχαδεύς, Sch.D.T.p.192 H.

στοιχει-όω ,
A. instruct in the basic principles (στοιχεῖα), Chrysipp.Stoic.2.39, Phot.:—Pass., -ωθήσεται will be instructed, Ael.Tact. Prooem.5, cf. Ath.Mech.5.5.
Henry George Liddell. Robert Scott. A Greek-English Lexicon. revised and augmented throughout by. Sir Henry Stuart Jones. with the assistance of. Roderick McKenzie. Oxford. Clarendon Press. 1940.

The National Science Foundation provided support for entering this text.

As much as may be known about stoa and its relative stoekeioo is presented here. It seems that it was too elementary to research significantly its etymology and to point out the obvious connections.

The root idea is to sequence.

Sequence is such a fundamental idea that it often gets overlooked. I have discussed it before, and its companion series.

The notion of stoixeio oo is to actively sequence and to engage in sequencing. Thus stoa are not passive products and imply agency in their production. No matter where we start in Greek thought agency is apparent and therefore cause and effect, order and arrangement, system and scheme or plan in terms of running order.

We see here evidence of the cultural use of letters and alphabets to impart this customary notion and practice, We ought not to think that numbers are hereby excluded, but rather understand that numbering is n alternative form of the same programme and as such is a later addition to the scheme. This is not to say that accounting did not take place prior to alphabets, but that both develop from a single factor the notion of actively sequencing. The terminology and notation that is utilised is secondary and may have historical primacy issues in etymological terms.

This active sequencing is an inherent part of our knowledge apprehension and production and thus undelies all our knowledge and wisdom and philosophy and thinking. Euclid's stoikeia thus make a bold claim: they underpin all our knowledge and thinking!

We ought not to think of Arithmoi as straightline forms. or stoikeia as straight line forms. They are natural forms found everywhere. Pythagoras saw arithmoi everywhere especially in phusis. When Pythagoras found that even music was ordered by arithmoi and relations between arithmoi the simplest arithmoi to demonstrate this was a monochord, but his observation applied to the vibration of any form, the Chladni vibrations are an example.

Arithmoi and stoikeia are natural sequences from which euclid selects the "good" or "right" ones for deeper study.


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