Gonu – Corner, knee


(Show lexicon entry in LSJ Middle Liddell Slater Autenrieth) (search) γόνυ noun sg neut nom indeclform
γόνυ noun sg neut voc indeclform
γόνυ noun sg neut acc indeclform

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γόνυ^ , τό, gen. γόνατος, Ep. and Ion. γούνατος (for γόνϝατος) Il.21.591, Hdt.2.80: pl. nom.
A. “γούνατα” Il.5.176, Hes.Op.587, Hdt.1.199, Schwyzer694.7 (Chios, iv B. C.), gen. “γουνάτων” Hdt.9.76, dat. “γούνασι” Il.9.455, Hdt.4.152 (also Pi.I.2.26), “γονάτεσσι” Theoc.16.11, Epigr.Gr. 782 (Halic.); also Ep. gen. γουνός (expl. as for γόνυος by Hdn.Gr.2.768, A.D.Synt.342.9) Il.11.547: pl. “γοῦνα” 6.511; “γούνων” 1.407, al.: dat. “γούνεσσι” 9.488, al. (v.l. γούνασσι):—Aeol. acc. pl. “γόνα” Alc.39.7 (prob.), but γόννα acc. to St.Byz. s.v. Γόννοι, Eust.335.39: gen. pl. “γόνων” Alc.Supp.10:
E. has “γουνάτων” Hec.752, 839, “γούνασι” Supp.285 (lyr.), Andr.529 (lyr.), but not γουνός (γοῦν᾽ acc. pl. was read by Sch. in Ph.852): gen. pl. γεύνων, Hsch.:—knee, “γόνυ γουνὸς ἀμείβων” Il.11.547, etc.: freq. of clasping the knees in earnest supplication, “ἥψατο γούνων” 1.512; “ἑλεῖν, λαβεῖν γούνων” 21.71, 1.407, etc.; “τῶν γουνάτων λαβέσθαι” Hdt.9.76; ποτὶ (v.l. περὶ) or “ἀμφὶ γούνασί τινος χεῖρας βαλεῖν” Od.6.310, 7.142; “περὶ γόνυ χέρας ἱκεσίους ἔβαλον” E.Or.1414, cf. Ph.1622, etc.; “τὰ σὰ γούναθ᾽ ἱκάνομαι” Il.18.457, cf. Od.7.147, etc.; “κιχανόμενοι τὰ σὰ γοῦνα ἱκόμεθ᾽” 9.266; “ἀντίος ἤλυθε γούνων” Il.20.463; “γόνυ σὸν ἀμπίσχειν χερί” E.Supp.165; “σοῖς προστίθημι γόνασιν ὠλένας” Id.Andr.895; ἐς γούνατά τινι or “τινος πεσεῖν” Hdt.5.86, S.OC1607; “ἀμφὶ γόνυ τινὸς πίπτειν” E.Hec.787; γόνυ τινός or πρὸς γόνυ προσπίπτειν ib.339, HF79; “γόνασί τινος προσπίπτειν” Id.Or.1332 (but προσπίτνω σε γόνασιν on my knees, S.Ph.485); πίπτειν πρὸς τὰ γ. τινος, τινι, Lys.1.19, D.19.198; also “γούνων λίσσεσθαι” Il.9.451; “ἐλλιτανεύειν” Od.10.481; “γουνάζεσθαι” Il.22.345; “ἄντεσθαι πρὸς τῶν γονάτων” E.Med.710; “ἱκετεῦσαι πρὸς τ. γ.” D.58.70.
2. of a sitting posture, φημί μιν ἀσπασίως γ. κάμψειν will be glad to bend the knee so as to sit down and rest, Il.7.118, cf. 19.72; but also, bow the knee in submission, ἐμοὶ κάμψει (intr.) “πᾶν γ.” LXX Is.45.23; γ. ὀκλάζειν τινί ib.3 Ki.19.18, v. sub κάμπτω: ἐπὶ γούνασι on one's knees, “ἐπὶ γούνασι πατρός” Il.22.500; “ποτὶ γ.” 5.408; “γούνασιν ἐφέσσεσθαι φίλον υἱόν” 9.455; “σ᾽ ἐπ᾽ ἐμοῖσι . . γούνεσσι καθίσσας” 9.488; “τόν ῥά οἱ . . ἐπὶ γούνασι θῆκεν” Od.19.401; “ἐν τοῖς γόνασί τινος στρέφεσθαι” Pl.R. 617b; πέπλον . . θεῖναι Ἀθηναίης ἐπὶ γούνασιν to lay it on her lap (as an offering), Il.6.92, cf. Schwyzer l.c.: hence metaph., θεῶν ἐν γούνασι κεῖται it rests in the lap of . . , Il.17.514, Od.1.267, etc.; but ἐν γούνασιν πίτνοντα Νίκας victorious, Pi.I.2.26.
3. of the knees as the seat of strength, “ἐν δὲ βίην ὤμοισι καὶ ἐν γούνεσσιν ἔθηκε” Il.17.569; of swiftness, “λαιψηρά γ.” 22.204, etc.; γούνατά τινος λύειν disable, kill him, 5.176, etc.; “ὑπὸ γούνατ᾽ ἔλυσεν” 11.579; βλάπτειν γ. τινι, κάματος δ᾽ ὑπὸ γ. ἐδάμνα, 7.271, 21.52:—Pass., “αὐτοῦ λύτο γούνατα” 21.114, etc.
4. metaph., ἐς γόνυ βάλλειν bring down upon the knee, i. e. humble, conquer, Hdt.6.27; ἐς γ. ῥίπτειν, κλίνειν, App.BC3.20,30; “ἐς γ. ἐλθεῖν” Procop.Arc.14, Pers.1.17; “Ἀσία δὲ χθὼν . . ἐπὶ γόνυ κέκλιται” A.Pers.931 (lyr.).
5. prov., ἀπωτέρω ἢ γόνυ κνάμα 'blood is thicker than water', 'charity begins at home', Theoc.16.18; “γ. κνήμης ἔγγιον” Arist.EN1168b8, Ath.9.383b.
II. joint of grasses or plants, Hdt.3.98, X.An.4.5.26, Thphr.HP8.2.4, Porph.Antr.19. (Cf. Skt. jā´nu, Lat. genu, etc.)

Man is the measure of all things

I believe i can attribute to space a ractal pattern of vortices, and such vortices as are akin to the shells of the molluscs of the sea

The bubbliness and springiness of space is explainable by the vorticular shell of space "density/ intensity" distribution. The fractal level at which an attribute is applied is the level at which it is explainable, thus extensive empirical knowledge is more explanatory than in depth analysis, which serves to distinguish the fractal levels more than to explain them.

corner, angle,

(Show lexicon entry in LSJ Middle Liddell) (search) γωνίᾳ noun pl fem voc
γωνίᾳ noun sg fem dat attic doric aeolic
γωνίᾳ noun pl fem nom
γωνία noun sg fem voc attic doric aeolic
γωνία noun dual fem voc
γωνία noun sg fem nom attic doric aeolic
γωνία noun dual fem nom
γωνία noun dual fem acc

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place at an angle,

(Show lexicon entry in LSJ) (search) γωνίᾳ verb 3rd sg fut ind act epic contr
γωνίᾳ verb 2nd sg fut ind mid epic contr
γωνία verb 1st sg fut ind act doric aeolic contr

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γωνία , ἡ,
A. corner, angle, Hdt.1.51, Pl.Men.84d, etc.; γ. ἐπίπεδος, στερεά, plane, solid angle, Euc.1 Def.8,11Def.11; αἱ πρὸς τῇ βάσει γ. the angles at the base, Id.1.5; ἡ ὑπὸ ΒΑΓ or ὑπὸ τῶν ΒΑΓ γ. the angle ΒΑΓ, Id.1.9,al.
2. metaph., corner, secluded spot, “ἐν γωνίᾳ ψιθυρίζειν” Pl.Grg.485d; “ἐν γ. πεπραγμένον” Act.Ap.26.26.
3. of the four quarters of the compass, Ptol.Tetr.29.
4. joint, Arist.PA 690a13.
II. joiner's square, Pl.Phlb.51c, Plu.Marc.19.
III. cutwater of a bridge, D.S.2.8.
IV. of persons, leader, chief, LXX 1 Ki.14.38. (Akin to γόνυ.)


(Show lexicon entry in LSJ Middle Liddell Slater) (search) ἀγωνία adj pl neut voc
ἀγωνία adj pl neut nom
ἀγωνία adj pl neut acc

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without angle

(Show lexicon entry in LSJ) (search) ἀγωνία adj pl neut voc
ἀγωνία adj pl neut nom
ἀγωνία adj pl neut acc

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contest, struggle for victory

(Show lexicon entry in LSJ Middle Liddell Slater) (search) ἀγωνίᾳ noun sg fem dat attic doric aeolic
ἀγωνίᾳ noun pl fem voc
ἀγωνίᾳ noun pl fem nom
ἀγωνία noun sg fem voc attic doric aeolic
ἀγωνία noun sg fem nom attic doric aeolic
ἀγωνία noun dual fem nom
ἀγωνία noun dual fem voc
ἀγωνία noun dual fem acc

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contend eagerly, struggle

(Show lexicon entry in LSJ Middle Liddell) (search) ἀγωνίᾳ verb 3rd sg pres subj act contr
ἀγωνίᾳ verb 3rd sg pres ind act epic doric aeolic contr
ἀγωνίᾳ verb 2nd sg pres subj mp contr
ἀγωνίᾳ verb 2nd sg pres ind mp epic doric aeolic contr
ἀγωνία verb 2nd sg pres imperat act contr
ἀγωνία verb 3rd sg imperf ind act homeric ionic contr unaugmented
ἀγωνία verb 1st sg pres ind act doric aeolic contr
ἀγωνία verb 1st sg pres subj act doric aeolic contr

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ἀγων-ία , ἡ,
A. contest, struggle for victory, “ἀγὼν διὰ πάσης ἀγωνίης ἔχων” Hdt.2.91; “πολεμίων ἀ.” E.Hec.314, cf. Tr.1003; esp. in games, Pi.O.2.52, P.5.113:—also in Prose, “ἐν δημοτικῇ ἀ.” X.Cyr.2.3.15; ἅπασαν ἀ. ἐκτεἶναι [D.]60.30, etc.
2. gymnastic exercise, Hp.Art. 11, Pl.Men.94b, Lg.765c, etc.: generally, exercise, Id.Grg.456d sq., R.618b.
3. of the mind, agony, anguish, “ἐν φόβῳ καὶ πολλῇ ἀ.” D.18.33, cf. Men.534.12 (pl.), Arist.Pr.869b6; “ἐν τοῖς τῆς ψυχῆς φόβοις, ἐλπίσιν, ἀγωνίαις” Id.Spir.483a5; cf. Chrysipp.Stoic.2.248, al., Phld.Ir.p 56 W. (pl.), Nic.Dam.Vit. Caes.9.

place at an angle,

(Show lexicon entry in LSJ) (search) γωνία verb 1st sg fut ind act doric aeolic contr

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γωνι-άζω ,
A. place at an angle, Porph. inCat.132.31.

three-cornered, triangular,

(Show lexicon entry in LSJ Middle Liddell) (search) τρίγωνον adj sg neut nom
τρίγωνον adj sg neut voc
τρίγωνον adj sg neut acc
τρίγωνον adj sg masc acc
τρίγωνον adj sg fem acc

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τρίγωνος 1 γωνία
I. three-cornered, triangular, Aesch.
II. as Subst., τρίγωνον, ου, a triangle, Plat.: name of a musical instrument, id=Plat.

1 τρί-γωνος, ον,

the ideal triangle, the Form of triangle,

(Show lexicon entry in LSJ) (search) αὐτο-τρίγωνον noun sg neut voc
αὐτο-τρίγωνον noun sg neut acc
αὐτο-τρίγωνον noun sg neut nom

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γνωμον-ικός , ή, όν, (
A. “γνώμων” 1) judging by rule, X.Mem.4.2.10; fit to judge of, skilled in a thing, “τινός” Pl.R.467c, Iamb.Myst. 3.27.
II. (“γνώμων” 11.2.a) of or concerning sun-dials, “θεωρήματα” Hipparch. 1.9.8, cf. Str.1.1.20: -κός, ὁ, expert in sun-dials, AP14.139, Gal.5.652, Procl.Hyp.5.54: ἡ -κή (sc. τέχνη), the art of making them, Vitr.1.3. Adv. “-κῶς” Str.2.1.35.
2. forming a γνώμων (11.2. c), “τρίγωνα” Iamb. in Nic.p.71 P. Adv. -κῶς ib.p.77 P.

γνώμων , ονος, ὁ, (γι-γνώ-σκω)
A. one that knows or examines, an interpreter, discerner, “θεσφάτων” A.Ag.1130; “τῶν παραχρῆμα” Th.1.138; γλῶττα γ. (sc. γλυκέων καὶ δριμέων) X.Mem.1.4.5: γνώμονες, οἱ, inspectors of the sacred olives at Athens, Lys.7.25.
2. expert witness or valuer, SIG169.52 (lasus, iv B. C.).
3. as Adj., discerning, “νόος” Hymn.Is.141.
II. carpenter's square, Polyaen.4.3.21; [“ὁ δημιουργὸς τῇ δεκάδι] ὥσπερ γνώμονι καὶ εὐθυντηρίῳ ἐχρήσατο” Theol.Ar.59.
2. pointer of the sun-dial, Hdt.2.109, Phld.Sign.30, Plu. Per.6 (pl.), D.L.2.1.
b. Geom., gnomon, Euc.2 Def.2, etc.
c. Arith., number added to a figurate number to obtain the next number of the same figure, Iamb.in Nic.p.58 P.; esp. of the odd integers, Arist.Ph.203a14, Theo Sm.p.32 H.; also of the original figurate number, Theol.Ar.9 (dub.l.).
3. = κλεψύδρα, Thphr.Fr. 159.
4. point of a drill, Apollod.Poliorc.149.4.
5. generally, index, “τινός” Plu.2.968f, Ael.NA6.34, al., Vett.Val.305.10; simply, mark, POxy.1409.18 (iii A. D.).
6. in pl., teeth that mark a horse's age, X.Eq.3.1.
7. metaph., rule of life, Thgn.543, cf. Luc.Herm. 76.
8. sens. obsc., “ὁ γ. ἀνίσταται” Diog.Ep.35.
V. tariff, OGI 674.5 (Coptos), BGU1118.45 (i B. C.), AB233.
2. code of regulations, PGnom.1, OGI669.44 (i A. D.).

νόος , νόου, ὁ, Att. contr. νοῦς , gen. νοῦ: Hom. uses the contr. form once, in nom., Od.10.240, cf. Hes.Fr.205 (Hdt. never): Trag. use contr. form, exc. in A.Ch.742 (iamb.), S.Ph.1209 (lyr.): Aeol. gen.
A. “νῶ” Alc.Supp.9.1; acc.νῶν Sapph.ib.25.2; νόον Ead.70 (s.v.l.): heterocl. forms are found in NT and later writers, gen. “νοός” Ep.Rom.7.23, LXX 4 Ma.1.35; dat. “νοΐ” 1 Ep.Cor.1.10, [Aristid.] Or.35(9).26; nom. pl. “νόες” Ph.1.86, Plot.6.7.17, Dam.Pr.96; acc. pl. “νόας” Plu. Fr.7.27, Iamb.Myst.1.15, Ammon.in Int.243.3 (v.l.), Dam.Pr.103: Att. pl. νοῖ, acc. νοῦς, gen. νόων ib.122, dat. νοῖς ibid., is rare in early writers, as Ar.Fr.471, but freq. in later philosophy:
1. mind, as employed in perceiving and thinking, sense, wit, “οὐ λῆθε Διὸς πυκινὸν ν.” Il.15.461; “ν. πολυκερδέα” Od.13.255; “ν. ὁρῇ καὶ ν. ἀκούει, τἄλλα κωφὰ καὶ τυφλά” Epich.249, cf. S.OT371; “νόῳ” prudently, Od.6.320; “παρὲκ νόον” senselessly, Il.20.133; “σὺν νόῳ” wisely, Hdt.8.86, 138; ξὺν νῷ with play on ξυνῷ, Heraclit.114 (νόῳ codd. Stob.); “ξὺν νῷ ἑλομένῳ” Pl. R.619b; “οὐδενὶ ξὺν νῷ” Id.Cri.48c; “μηδενὶ ξὺν νῷ” Ar.Nu.580; “τοῦ νοῦ χωρίς” S.OT550; “τοῦ ν. κενός” Id.OC931; νόῳ λαβεῖν τι to apprehend it, Hdt.3.51; νόῳ σχεῖν, ἔχειν, recall, remember, Id.5.92.ή, Pl.R.490a; “κοινὸς ν.” Phld.Rh.1.37 S., Arr.Epict.3.6.8; ἀγαθὸς ν., σπουδαῖος ν., Phld.Rh.2.61, 1.252 S.
2. νοῦν ἔχειν in two senses,
a. to have sense, be sensible, S.Tr.553, El.1013, 1465, Ar.Ra.535, etc.; “ὁ νοῦς ὅδ᾽ αὐτὸς ν. ἔχων οὐ τυγχάνει” E.IA1139; so ν. ὀλίγον κεκτημένος Ar.Ec.747; “σμικρὸν νοῦ κεκτῆσθαι” Pl.Lg.887e; impers., “τὸ γὰρ περισσὰ πράσσειν οὐκ ἔχει ν. οὐδένα” S.Ant.68, cf. Pl.Ti.68b; cf. νουνεχόντως.
b. νοῦν or τὸν ν. ἔχειν to have one's mind directed to something, “ἄλλοσ᾽ ὄμμα, θητέρᾳ δὲ ν. ἔχειν” S.Tr.272, cf. Sapph.Supp.25.2; “τὸν ν. πρὸς αὑτὸν οὐκ ἔχων, ἐκεῖσε δέ” E.Ph.1418; “δεῦρο ν. ἔχε” Id.Or. 1181; “οἴκοι τὸν ν. ἔχειν” Id.Ion 251; ποῦ τὸν ν. ἔχεις; Ar.Ec.156; τὸν ν. ἔχειν πρός τινα or τι (like προσέχειν τὸν ν.) Th.7.19, Pl.Grg.504d; “πρός τινι” Id.Prt.324a, etc.; “περί τινος” Id.R.534b; “ἐν πέρδιξιν” AP7.206 (Damoch.): conversely, ἐπὶ νοῦν ἐλθεῖν τινι to occur to one, D.H.3.15, Arr.An.7.24.3.
3. mind, more widely, as employed in feeling, deciding, etc., heart, “χαῖρε νόῳ” Od.8.78; “κεῦθε νόῳ” Il.1.363; “[χόλος] οἰδάνει νόον” 9.554; “ἐνὶ στήθεσσιν ἀτάρβητος ν. ἐστί” 3.63; ν. ἔμπεδος, ἀκήλητος, ἀπηνής, 11.813, Od.10.329, 18.381; ν. εὐμενής, ἄγναμπτος, etc., Pi.P.8.18, A.Pr.164 (lyr.), etc.; “πολλῶν ἀνθρώπων νόον ἔγνω” Od.1.3; ἐκ παντὸς νόου with all his heart and soul, Hdt.8.97; τῷ νῷ . . κἀπὸ τῆς γλώσσης in heart as well as tongue, S.OC 936: freq. in phrase κατὰ νόον according to one's mind, Hdt.1.117, 7.104; “εἰ τάδ᾽ ἔχει κατὰ νοῦν κείνῳ” S.OC1768 (anap.); “πράξειας κατὰ ν. τὸν ἐμόν” Id.Fr.469 (anap.); “κατὰ ν. πράξας” Ar.Eq.549; “χωρεῖ κατὰ ν.” Id.Pax940, cf. Pl.Euthphr.3e.
4. mind, resolve, purpose, ἀγαθῷ νόῳ, i.e. kindly, Hdt.1.60; τί σοι ἐν νόῳ ἐστὶ ποιέειν; what do you intend to do? ib.109; “ἡμῖν ἐν ν. ἐγένετο εἰπεῖν” Id.9.46; ἐν ν. ἔχειν c. fut. inf., to intend . . , Id.1.10 (v.l.): c. pres. inf., ib. 27, Pl.R.344d; ποιέειν τι ἐπὶ νόον τινί to put into his mind to do . . , Hdt.1.27; ἐπὶ νόον τρέπειν τινί . . Id.3.21; “ταύτῃ <ὁ> ν. ἔφερε” Id.9.120.
5. reason, intellect, “νόου φρενί” Xenoph.25, cf. Parm.16.2, etc.; “θεῖος ν.” Democr.112, cf. Id. ap. Arist. de An.404a28; opp. δόξα, Pl.Ti.51d, cf. Arist. de An.428a5.
b. Mind as the active principle of the Universe, Anaxag. 12, etc.; “Θαλῆς νοῦν τοῦ κόσμου τὸν θεόν” Placit.1.7.11; “ἡ τοῦ κόσμου γένεσις ἐξ ἀνάγκης καὶ νοῦ συστάσεως” Pl. Ti.48a, cf. Sph.249a, Phlb.30c, Arist.Metaph.1072b20, de An.430a17, Zeno Stoic.1.28, Plot.5.1.4.
II. act of mind, thought, “ἡμῖν δ᾽ οὔ τις τοῦδε νόος καὶ μῆτις ἀμείνων” Il.15.509; “οὐ γάρ τις νόον ἄλλος ἀμείνονα τοῦδε νοήσει” 9.104; “οὐ γὰρ δὴ τοῦτον μὲν ἐβούλευσας νόον αὐτή” Od.5.23.
2. purpose, design, “νόον τελεῖν τινι” Il.23.149; “σάφα οἶσθ᾽ οἷος ν. Ἀτρεΐωνος” 2.192.
III. sense, meaning of a word, etc., “οὗτος ὁ νόος τοῦ ῥήματος” Hdt.7.162, cf. Ar.Ra.1439, Plb.5.83.4, Phld.Rh. 1.106 S., etc.; ὁ νόος τῆς θυσίης cj. for νόμος in Hdt.1.216; meaning of a work of art, Philostr.VA4.28; “πολὺς ν. ἐν ὀλίγῃ λέξει συνέσταλται” Plu.2.510e; πρὸς τὸν αὐτὸν νοῦν to the same effect, Str.15.3.7; πρὸς νοῦν οὐδὲν λέγοντες to the point, Phld.Mus.p.96K.; “οὐδὲ νοῦν ἔχον” senseless, Id.Po.5.29.
IV. Pythag. name for μονάς, Theol.Ar.6. (Etym. dub.; the pr.n. “Πολυνόϝα” IG9(1).870 hardly proves νόϝος.)

Entirely phonetically the gonia through the gnomon is linked to the noos, that is the knee through a symbol of a knee is linked to the perceiving senses.

The idea of an angle is such a poor substitute for the gonia notion, as you can see. The "knee of the mind" is a notion which draws on the discernment of the carpenter who uses a symbolic tool to discern or judge or perceive, Thus when a circle shows no "knee" it is effectively indiscernible.

The notion of rotation is inherent in gonia as a knee joint that bends and flexes, and agonia emphasises this jerky collection of motions.

ἴς (A) [ι_], ἡ, gen. ἰνός, acc. ἶνα, nom.pl. ἶνες, dat.
A. “ἴνεσι” Il.23.191, also “ἰσίν” Sor. (v. infr.), Suid. s.v. ἶνες, cj. Nauck for εἰσίν in A.Fr.229:— sinew, tendon, sg. once in Hom., “ὡς δ᾽ ὅτ᾽ ἂν . . ἀνὴρ . . ἶνα τάμῃ διὰ πᾶσαν” Il.17.522: usu. in pl., sinews, “οὐ γὰρ ἔτι σάρκας τε καὶ ὀστέα ἲνες ἔχουσιν” Od.11.219, cf. Il.23.191; “ἶνες ἄρθρων” Ar.Pax86, cf. Archil.138; ἶνες αὐτὸ μόνον καὶ λεπτὴ δορά, of a person wasted by disease, Ph.2.432; δοράς, σάρκας, ἶνας ib.527: metaph., “Τρωίας ἶνας ἐκταμὼν δορί” Pi.I.8(7).57.
2. later, the fibrous vessels in the muscles, Pl.Ti.84a, Arist.HA515b27, al.; in blood, fibrine, Id.PA650b14, cf. Pl.Ti.82c, Meno Iatr.17.34: metaph., of metals, Plu.2.434b.
3. rib in the leaves of plants, Thphr.HP3.12.7 (sg.).
4. strip of papyrus, “ταῖς τῶν χαρτῶν ἰσίν” Sor.1.13: sg., Gal.10.1000.
b. λεπτὴ ἴς a small fibre of papyrus, Id.17(1).795.

ἴς (B) [ι_], ἡ, three times in acc. sg. ἶνα (elided ἶν᾽) Il.5.245,7.269, Od.9.538, freq. in instr. ἶφι (q.v.), elsewh. only nom. sg.:—
A. strength, force, of persons, “ἀλλ᾽ ἄρα καὶ ἲς ἐσθλή” Il.12.320; “ἐπέρεισε δὲ ἶν᾽ ἀπέλεθρον” 7.269; “ἤ μοι ἔτ᾽ ἐστὶν ἴς, οἵη πάρος . . ” Od.21.283, cf. 11.393, 18.3: freq. in periphr., ἱερὴ ἲς Τηλεμάχοιο the strong Telemachus, 2.409; “κρατερὴ ἲς Ὀδυσῆος” Il.23.720; “ἲς Ἡρακλῆος” Hes.Th.951; and in twofold periphr., ἲς βίης Ἡρακληείης ib.332; also of things, ἲς ἀνέμου or ἀνέμοιο, Il.15.383, 17.739, Od.9.71; “ἲς ποταμοῖο” Il.21.356; κράται᾽ ἴς was read by Ptol.Asc.in Od.11.597; v. κρατύς. (ϝι_-, cf. γίς: ἰσχύς, Hsch., pr. n. “ϝιφιάδας” IG7.3172.70, Lat. vis, vim; prob. cogn. with ἵεμαι but not with ἴς (A).)

ἰσ-άζω :—Pass., fut.
A. “ἰσασθήσομαι” Arist.EE 1243b31: aor. 1 “ἰσάσθην” Id.EN1133a14: pf. ἴσασμαι ib.b5: (ἴσος):— make equal, balance, of a person holding scales, “σταθμὸν . . καὶ εἴριον . . ἀνέλκει ἰσάζουσ᾽” Il.12.435; ἰ. τὰς κτήσεις to equalize them, Arist.Pol. 1265a38; “ἰ. τὸ ἄνισον” Id.EN1132a7; τὴν φιλίαν ib.1163b33:—Med., make oneself equal to another, οὕνεκ᾽ ἄρα Λητοῖ ἰσάσκετο (sc. Νιόβη) Il. 24.607:—Pass., to be made or to be equal, “θεοῖς” Pl.Ti.41c: abs., Arist. EN1133a14, al.; “μήκει ποδὸς ἴχνος ἰσάζεται” Nic.Th.286; “δίστιχα ψήφοισιν ἰσάζεται” AP9.356 (Leon.).
II. intr. in Act., to be equal, Pl.Lg.773a, Arist.EN1154b24; “ἀλλήλοις” Id.Pol.1304a39.
2. to be even, normal, Hp.Morb.4.49. [ι_ in Hom.; ι^ in Nic.Th.286, 886.]

ἴσος , η, ον, Ep. ἶσος and ἔϊσος (v. infr.); Cret., Arc. ϝίσϝος GDI 4998ii2, 4982.2, Schwyzer665, cf. γισγόν: ἴσον, Hsch.; later ἵσος Schwyzer 708a(1) (Ephesus, iv B.C.), Tab.Heracl.1.175, etc.:—
A. equal in size, strength, or number, c. dat., “κύματα ἶσα ὄρεσσιν” Od.3.290, etc.; freq. of appearance, like, “ἶσος ἀναύδῳ” 10.378; “ἶσος Ἄρευι” Sapph.91 (dub.); ἴσος θεοῖσιν Ead.2.1: freq.abs., “ἴσην . . βίην καὶ κῦδος” Il.7.205; ἶσον θυμὸν ἔχειν to be of like mind, 13.704, 17.720: neut. as Adv., “ἶσον ἐμοὶ φρονέουσα” 15.50; “θεοῖσιν ἶσ᾽ ἔθελε φρονέειν” 5.441, cf. 21.315, etc.; ἴσος τινὶ τὸ μέγαθος, ὕψος, Hdt.2.32, 124; τὸ μῆκος, τὸ πλάτος, X.An. 5.4.32; “ἀριθμόν” E.Supp.662; ἴσα τὸν ἀ. Pl.R.441c; ποτὴν ἴσον equal in flight of song, Alex.Aet.5.5; ἴσον, τό, copy of a document, PLond. 3.1222.5 (ii A.D.), etc.: with dat. pers. in place of an object of comparison, οὐ μὲν σοί ποτε ἶσον ἔχω γέρας (i.e. τῷ σῷ γέραϊ) Il.1.163; τοῖσδ᾽ ἴσας ναῦς (i.e. ταῖς τῶνδε) E.IA262(lyr.); “ἴσα τοῖς νῦν στρατηγοῖς ἀγάθ᾽ εἰργασμένους” D.13.21: folld. by a relative word, ἐμοὶ ἴσον . . , ὅσονπερ ὑμῖν the same to me as to you, Ar.Ec.173; “τὰ ἐκεῖ ἴσα, ὥσπερ τὰ ἐνθάδε” Lys.19.36 codd. (fort. σᾶ); τὰ ἴσα ὅσαπερ . . Lex ap.D.23.44; “ἴσον . . ὅπερ” Pl.Erx.405b.
2. repeated to denote equal relations, ἴσα πρὸς ἴσα tit for tat, Hdt.1.2; “ταχθέντες ἴσοι πρὸς ἴσους” S. Ant.142 (anap.); “ἴσους ἴσοισι . . ἀντιθείς” E.Ph.750; “ἴσα ἀντὶ ἴσων λαμβάνειν, ἐκδοῦναι” Pl.Lg.774c; ἴσος ἴσῳ (sc. οἶνος ὕδατι) Cratin.184, Com.Adesp.107, etc.; κύλικος ἴσον ἴσῳ κεκραμένης (where ἴσον is adverbial) Ar.Pl.1132; “διδόναι γάλα καὶ οἶνον πίνειν ἴσον ἴσῳ” Hp. Epid.2.5.1: metaph., 'fairly blended', “μηδὲν ἴσον ἴσῳ φέρων” Ar.Ach. 354.
3. of persons, equal in rights, “βούλεται ἡ πόλις ἐξ ἴσων εἶναι καὶ ὁμοίων” Arist.Pol.1295b25; ἡ πολιτικὴ ἐλευθέρων καὶ ἴσων ἀρχή ib. 1255b20; τὸ κατ᾽ ἀξίαν ἴ. ib.1307a26, al.
II. equally divided or distributed, “ἴση μοῖρα” Il.9.318; ἴση alone, one's equal share, “μή τίς μοι ἀτεμβόμενος κίοι ἴσης” Od.9.42 (ἴσσης cj. Fick, cf. ἴσσασθαι)“; τὴν ἴ. ἔχων” Cratin.250; οὐ μὴν ἴ. ἔτεισεν (sc. τίσιν) S.OT810; ἄχρι τῆς ἴ. up to the point of equality, D.5.17: neut., “μὴ ἴσον νεῖμαι ἑκατέρῳ” Pl.Prt.337a; “οὐ μόνον ἴσον, ἀλλὰ καὶ πλέον ἔχειν” Isoc.17.57; οὐκ ἀνέξῃ δωμάτων ἔχων ἴσον καὶ τῷδε νεῖμαι; E.Ph.547; τὰ ἴσα fair measure, “τὰ ἴ. νέμειν” Hdt. 6.11; μὴ ἴσων ἕκαστον τυγχάνειν ἀλλὰ πλεονεκτεῖν, X.Cyr.2.2.20; προστυχεῖν τῶν ἴ. to obtain fair terms, S.Ph.552; κἂν ἴσαι (sc. ψῆφοι) γένωνται equally divided, Ar.Ra.685.
2. based on equality of rights, “ἴ. καὶ ἔννομος πολιτ εία” Aeschin.1.5; “τὴν πολιτείαν ἰσαιτέραν καθιστάναι” Th.8.89; τὰ ἴ. equal rights, equality, freq. joined with τὰ ὅμοια or “τὰ δίκαια, ὡς τῆς πολιτείας ἐσομένης ἐν τοῖς ἴ. καὶ ὁμοίοις” X.HG7.1.45; “τῶν ἴ. καὶ τῶν δικαίων ἕκαστος ἡγεῖται ἑαυτῷ μετεῖναι ἐν τῇ δημοκρατίᾳ” D.21.67; οὐ μέτεστι τῶν ἴ. οὐδὲ τῶν ὁμοίων πρὸς τοὺς πλουσίους τοῖς λοιποῖς ib.112; τῶν ἴ. μετεῖχε τοῖς ἄλλοις ib.96; also ἡ ἴ. καὶ ὁμοία (sc. δίκη)“, τῆς ἴ. καὶ ὁμοίας μετέχειν” Th.4.105; ἐπ᾽ ἴ. τε καὶ ὁμοίῃ on fair and equal terms, Hdt.9.7, ά, cf. Th.1.145; ἐπὶ τῇ ἴ. καὶ ὁμοίᾳ ib.27, cf. SIG312.27 (Samos, iv B.C.), OGI229.44 (Smyrna, iii B.C.), etc.: generally, just, fair, ἐκ ποίας ἴ. καὶ δικαίας προφάς εως; D.18.284.
3. of persons, fair, impartial, S.Ph.684(lyr.), OT677; “ἴ. δικαστής” Pl.Lg. 957c; “ἴ. καὶ κοινοὶ ἀκροαταί” D.29.1, cf. 18.7; “ἴ. καὶ κοινὸν δικαστήριον” Id.7.36; “κοινοὺς μὲν . . , ἴ. δὲ μή” Pl.Prt.337a; “ἴ. ἴσθι κρινων” Men.Mon. 266, cf. 257; “κριταὶ ἴ. καὶ δίκαιοι” Plb.24.15.3, etc.
4. adequate, “ἡ ἴ. φρουρά” Th.7.27 (expld. by Sch. as regular, τεταγμένη); ἴσος τοῖς “παροῦσι” Id.1.132.
III. of ground, even, flat, εἰς τὸ ἴ. καταβαίνειν, of an army, X.An.4.6.18 (but ἐν ἴσῳ προσιέναι to advance with even step, ib.1.8.11); λέουσιν εἰς τὸ ἴ. καθιστάμενοι μάχεσθαι, opp. μετὰ πλεονεξίας ἀγωνίζεσθαι, on even terms, Id.Cyr.1.6.28; ἴ. τοῖχος, opp. κεκλικώς, perpendicular, Phlp.in APo.2.27.
IV. Adv. ἴσως (v. sub voc.): but also,
1. neut. sg. and pl. from Hom. downwds. (v. sub init.), ἶσον . . ἀπήχθετο κηρὶ μελαίνῃ even as Death, Il.3.454; ἶσον ἐμοὶ βασίυε be king like me, 9.616; ἶσον γάρ σε θεῷ τίσουσιν Ἀχαιοί ib. 603; “ἶσον ἐμῇ κεφαλῇ” 18.82; “τὸν . . ἶσα θεῷ . . εἰσορόωσιν” Od.15.520; “ἶσα φίλοισι τέκεσσι” Il.5.71, cf. 13.176, Od.1.432, 11.304, etc.: later abs., alike, “δείλαιε τοῦ νοῦ τῆς τε συμφορᾶς ἴσον” S.OT1347; “τὴν Σάμον καὶ Ἡρακλέας στήλας ἴσον ἀπέχειν” Hdt.8.132: c. dat., “ἴσον ναοῖς θεῶν” E.Hel.801; ἴσον ἄπεσμεν τῷ πρίν equally as before, Id.Hipp.302 (v.l. τῶν πρίν)“; ἴσα τοῖς πάνυ” D.C.Fr.70.6; ἴσα καί . . like as, as if, S.OT 1187(lyr.), E.El.994 (anap.), Th.3.14; “ἴσον ὡς . . ” E.Ion1363; ὥσπερ . . S.El.532; “ὥστε . . ” E.Or.882; “ἅτε . . ” Id.HF667(lyr.); “ὅσονπερ . . ” D.15.1.
2. with Preps.: ἀπὸ τῆς ἴσης equally, Th.1.15; “ὁ ἀπὸ τῆς ἴ. ἐχθρός” Id.3.40; “ἀπ᾽ ἴσης εἶναι” D.14.6; “ἀφ᾽ ἵσου” SIG426.14 (Teos, iii B.C.); “δι᾽ ἴσου” D.C.43.37; at equal distance, Pl.R.617b: also in Math., ex aequali, of proportions, Euc.5 Def.17, al.; δι᾽ ἴ. ἐν τεταραγμένῃ ἀναλογίᾳ ex aequali in disturbed proportion, Archim. Sph.Cyl.2.4,al., Papp.932.11; ἐν ἴσῳ equally, Th.2.53, 4.65; ἐν ἴσῳ ἐστί it matters not, E.IA1199; “ἐν ἴσῳ [ἐστὶ] καὶ εἰ . . ” Th.2.60; “ἐν τῷ ἴσῳ εἶναι” Id.4.10; “ἐξ ἴσης” Pl.Lg.861a: more freq. “ἐξ ἴσου” Hdt.7.135, S.OT563, etc.; “ἐξ ἴ. τινί” Id.Ant.516, 644, Antipho 5.1, Pl.Grg.517a; evenly, “εὐθεῖα γραμμή ἐστιν ἥτις ἐξ ἴ. τοῖς ἐφ᾽ ἑαυτῆς σημείοις κεῖται” Euc. 1 Def.4; “ἐξ ἴ. καὶ . . ” S.OC254; “ὡς . . ” Id.OT61; οἱ ἐξ ἴ. persons of equal station, Pl.Lg.777d, cf. 919d; “ὁ ἐξ ἴ. κίνδυνος” Plb.9.4.4; “ἐκ τοῦ ἴ. γίγνεσθαί τινι” Th.2.3; “τοῖς ἐκ τοῦ ἴσου ἡμῖν οὖσι” X.Hier.8.5; “ἐξ ἴσου τισὶ τῆς πολιτείας μεταδιδόναι” Lys.25.3; ἐκ τοῦ ἴ. μάχεσθαι to be evenly matched, X.HG2.4.16; “ἐξ ἴ. πολεμεῖν” D.8.47; κατὰ μῆνα τὸ αἱροῦν ἐξ ἴ. the sum due in equal monthly instalments, PAmh.2.92.14, etc.; ἐπὶ or “ἐπ᾽ ἴσης, ἐπὶ ἴ. διαφέρειν τὸν πόλεμον” Hdt.1.74; “τοῦτο ἐπ᾽ ἴσης ἔχει” Id.7.50, cf. S.El.1062(lyr.), etc.; “ἐπ᾽ ἴσου” Plb.1.18.10; “ἐπ᾽ ἴσον” Id.6.38.4, cf. Docum. ap. D.18.106, Phld.Ir.p.21 W.; “ἐπὶ ἶσα μάχη τέτατο” Il.12.436; cf. “κατὰ ἶσα μάχην ἐτάνυσσε” 11.336; “κατ᾽ ἴσον” Dsc.1.68.6, Gal.UP1.19; μετ᾽ ἴσου equally, Demetr.Lac.Herc.124.12.
V. Comp. “ἰσαίτερος” E.Supp.441, Th.8.89, X.HG7.1.14: Sup. ἰσότατος Timo 68; “ἰσαίτατος” Ph.1.462. Adv. “ὡς ἰσαίτατα” Pl.Lg.744c, but “ὡς ἰσότατα” SIG531.30 (Dyme). [ι_ in early Ep. (exc. Hes.Op.752), cf. Sol.24.1: ι^ first in Thgn.678, Sapph.2.1 (but ἶσος Ead.91 s.v.l.), B. 5.46 (but “ἶσον” 1.62, Fr.2.2), and always in Pi. (exc. in compd. ι_σοδαίμων) and Trag. (A.Fr.216 is dub. l.) exc. in compd. ι_σό-θεος (q.v.); dub. in ἰσ-όνειρος. Both quantities are found in later poetry, sts. in same line, “ἔχοισαν ἴσον κάτω, ἶσον ἄνωθεν” Theoc.8.19; “πρέσβυν ἴσον κούροις, ἶσον ἁδόντα κόραις” APl.4.309.]

ἰσότης , ητος, ἡ, (ἴσος)
A. equality, Arist.Metaph.1054b3, etc.: in pl., Pl.Lg.733b; “ἰ. χρόνου” Id.Prm.140e: Math., ἰ. γεωμετρική equality of ratios, proportion, Id.Grg.508a; “ἀναλογία ἰ. λόγων” Arist.EN1131a31.
2. esp. political equality or justice, personified in E.Ph.536, cf. Pl.Lg.757a; “ἰ. πολιτική” Plb.6.8.4, etc.: in dual, Pl.Lg.757b, cf. Arist.Pol.1302a7, Isoc.7.21.
II. fair dealing, impartiality, Men. Mon.259, Plb.2.38.8, Ep.Col.4.1.
III. equiformity, of the earth, Epicur.Nat.11.10. (On the accent v. Hdn.Gr.1.83, 2.945; ἰσοτής is said to be Hellenistic by Moer.202.)

Ἶσις , ἡ, voc.
A. “Ἶσιν” UPZ81 ii 19 (ii B.C.), gen. “Ἴσιδος” BGU993ii10 (ii B.C.), Plu.2.353f, etc.; Ion. and later “Ἴσιος” Hdt.2.41, PPetr.3p.216 (iii B.C.), etc. (written “Ἔσιος” Schwyzer 749 (v B.C.)), dat. “Ἴσιδι” OGI175.4 (ii B.C.), etc., Ἴσι_ or “Ἴσει” Hdt.2.59, OGI61.4 (iii B.C.); acc. Ἶσιν:—Isis, Hdt. Il.cc., Call.Epigr.58, Apollod.2.1.3, Plu.2.351f, POxy.1380 (ii A.D.), etc.; Ἴσιδος τρίχες, name of a plant, Plu.2.939d, cf. Plin.HN13.142.
II. name of a plaster, Gal.11.126,13.774.
III. Pythag. name for the δυάς, Theol.Ar.12.

δυ^-άς , άδος, ἡ,
A. the number two, Pl.Phd.101c, Prm.149c, Arist.Ph.220a27, etc.
2. dyad, “ἡ ἀόριστος δ.” Arist.Metaph.1081a14, Alex.Aphr. in Metaph.58.12.
3. pair, Philostr.Im.1.6, Lib. Or.61.7.

The indelible notion of twoness is associated with "Is" and yet strength and tendons and fibres is fundamental to the simple "Is".Thus the notion of twoness goes beyond jus the notion of the abstract number2, into the figurate two the dynamic activity of splitting and dividing apart.

"Two" is not a number it is an action, an activity of division and fission, of spltting, but not shattering. The idea, the activity is dividing into veins, tendons, sinews, fibrea, atreams, rays and branches. Every plant, every leaf, every river exhibits "is", not as twoness but as "binary" fission, multiple fission where the pattern "two" is not a number but a description of separation.

The equality of "2" is a later notion, and not at all based on "exactness", but pragmaic judgement. The axial symmetry of 2 dividing streams, is discoverable in the notion of separating veins, and fibres.
The notion of "Angle" as a norse notion of "thorn" , "hooks" into this line of thought as a specialist branching, but by no means deserves to subsume the rich heritage it is attributed to.


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