= Pappus 1660 = Pappus Alexandrinus (1660), Mathematicae collectiones [http://echo.mpiwg-berlin.mpg.de/ECHOdocuView/ECHOzogiLib?mode=imagepath&url=/mpiwg/online/permanent/library/A0VHBVNN/pageimg ECHO] Part of [wiki:WO1]. Sent with DESpecs version 1.1.2. Sent: ok/date. Returned: ok/date/ [http://pythia.mpiwg-berlin.mpg.de/department1/mpdl/raw-texts/WO1_Pappus_1660.txt/WO1_Pappus_1660_V2.txt raw text], separate unknown characters list with <001> and <002>: see attachment. == 1. First Analysis == === Difficulties === * Greek text. === Special Instructions === * None, but we requested a work sample of 50 pages. == 2. Questions From Formax == === Question 1 === === Reply 1 === A 2008-12-14: Please be so kind as to note the following two points: (1) in general, if you have difficulty recognizing a Greek ligature, it is best just to assign it an unknown character code e.g. <005> and we will identify it later. If you do feel its is necessary to query us about a ligature or other glyph, please be so kind as to send us a complete line of text containing the unknown character. === Final Instructions === == 3. Analysis of the Result == === Findings === <001> occurs six times and seems to be simply a badly printed {ou}, as in "ἠγ<001>μέν{ου}" (where, by the way, they got the breathing wrong because it is already wrong in the original.) <002> is not clear to me. It occurs twice, once in "Græcus codex habet. δ{ει} γαρ & c. <002> τῆς ζη {πρ}ὸς η δ ego legendum puto {τὸν} τῆς δ η {πρ}ὸς η κ". The second time it doesn't look like the first <002>, but is optically as well as contextually clearly recognizeable as {tais}: "ἐν <002> συζυγῖαις". Some random samples (line numbers added): [http://echo.mpiwg-berlin.mpg.de/ECHOdocuView/ECHOzogiLib?pn=37&ws=1&wx=0.0258&wy=0.1388&ww=0.7586&wh=0.1189&mode=imagepath&url=%2Fmpiwg%2Fonline%2Fpermanent%2Flibrary%2FA0VHBVNN%2Fpageimg p.37] (part of the work sample) {{{ 1 vero $i A $it ip$ius B dimidius] _In Græco codice $ic legitur_. χαί γὰρ συναμφοτέραυ α β γ 2 τ\~ου β τριπλάσιος μὲν ἔςιν, ἐι διπλασιος ἐιη ἑιη ὁ β τοῦ α. ἡμιόλιος δὲ ἡ θ α τ\~ου β ἠμισις ἔιη. 3 _Sed legendum Videtur_. {καὶ} γὰρ συναμφότεος α β τριπλάσιος μὲν ἔςιν, ἐι διπλάσιος 4 ἔιη ο`; α τ\~ου β, ἡμιόλιος δέ ἐι α τοῦ β ἡμισις ἔιη. _E$t enim_ D _ad_ E, _bt_ 5 A B _ad_ B, _Vel Vt_ B C 6 _ad_ C _ex lis_, _quc ante demon$trata $unt. Po$tquam Vero o$tendit ex analogia æqualitatis_ }}} [http://echo.mpiwg-berlin.mpg.de/ECHOdocuView/ECHOzogiLib?pn=153&ws=1&wx=0.0238&wy=0.6595&ww=0.7714&wh=0.1914&mode=imagepath&url=%2Fmpiwg%2Fonline%2Fpermanent%2Flibrary%2FA0VHBVNN%2Fpageimg p.153] {{{ COMMENTARIVS. 1

_Dimidium eius, quod fit a recta linea HF]_ Græcus codex habet τὸ ἢμισυ τ{οῦ} ἀπὸ τῆς 2 {ἐπὶ} τά θ ζ. Sed nos per$picuitatis cau$$a ita Vtendum cen$uimus.

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_Hoc enim in XX. Theoremate e$t demon$tratum]_ In Græco codice legitur τ{οῦ}το γαρ ἐν 4 {τῷ} δευτέρω θεωρήματι δέδ{ει}χθ{αι}.

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_Sed rectantgulo BAL vna cum eo, quod BA, LR, continetur, hoc e$t rectangulo_ 6 _BAR]_ Ex prima $ecundi libri elementorum.

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_Aequale e$t quod fit ex AG]_ iuncta enim _BG_ triangula _ABGAGR_ $imilia $unt ex octaua 8 $exti libri elementorum. ergo vt _BA_ ad _AG_, ita _GA_ ad _AR_, ac propterea rectangulo _BAR_ 4 $exti. 17 9 æquale e$t quadratum ex _AG_.

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_Ergo & quod fit ex AG vna cum rectangulo GHK]_ Græcus codex mancus e$t, qui ita 11 re$tituetur ἲσον ἂρα καὶ τὸ ἀπὸ τῆς α γ {μὲν} τ{οῦ} {ὑπὸ} η θ κ.

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_Et ante o$ten$um e$t figuram quidem con$tantem ex $uperficiebus conicis.]_ In Græ 13 co codice legitur. καὶ ἐδεχθη πρὸ ἑνος. Illud Vero o$ten$um e$t in 24. propo$itione huius.

}}} [http://echo.mpiwg-berlin.mpg.de/ECHOdocuView/ECHOzogiLib?pn=183&ws=1&wx=0.0178&wy=0.4192&ww=0.7276&wh=0.2606&mode=imagepath&url=%2Fmpiwg%2Fonline%2Fpermanent%2Flibrary%2FA0VHBVNN%2Fpageimg p.183] {{{ 1

_Erunt quadrata ex BK, KM quadrati ex FG tripla._ Nam cum quadratum quidem ex 2 _FG_ ad quadratum ex _BH_ proportionem habeat, quam quinque ad tria, quadrata vero ex _BK_ 3 _KM_ ad idem quadratum ex _BH_ eam habeat, quam quinque ad Vium, hoc e$t quam quinde- 4 cim ad tria, habebunt quadrata ex _BK_, _KM_ ad quadratum ex _FG_ proportionem eandem, quam 5 quindecim ad quinque, Videlicet triplam. In Græco codice omnia ferè $unt corrupta; qui $ic 6 habet ἐν δὲ {τῷ} α β ω τὰ ἀπὸ β ζ, ζ θ πενδαπλάσια τ{οῦ} ἀπὸ β θ. τὰ ἀρα ἀπὸ β ζ, ζ θ {τρ}ιπλά- 7 σια τ{οῦ} ἀπὸ ζ η. ego $ic corrigendum arbitror. ἐν δὲ {τῷ} ι τὰ ἀπὸ β κ, κ μ πενδαπλάσια τ{οῦ} 8 @πὸ β θ. τὰ ἂρα ἀπὸ β κ, κ μ {τρ}ιπλάσια τ{οῦ} ἀπο ζ η.

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_Vtin tertiodecimo libro elementorum demon$tratur]_ propo$itione 1 @.

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_Ergo ex ante demon$tratis vt BK, ad NX, ita KM ad NO, & eorum quadrata, &_ 11 _vt vnum ad vnum, ita omnia ad omnia. quadrata igitur ex BK, KM tripla $unt quadra-_ 12 _torum ex NX, NO]_ e$t eni nex 45. huius vt _BK_ ad _KM,_ ita _XN_ ad _NO_ permutandoque 13 Vt _BK_ ad _XN,_ ita _KM_ ad _NO._ Vt quadratum ex _BK_ ad quadratum ex _NX,_ ita quidratum 22. $exti. 14 ex _KM_ ad quadratum ex _NO._ vt autem vnum ad Vnum, ita omnia ad omnia. Sed quadra 12. quinti 15 tum ex _BK_ triplum e$t quadrati ex _NX._ quadrata igitur ex _BK,_ _KM_ quadratorum ex _NX,_ 16 _NO_ $unt tripla. In codice græco legitur διὰ τὸ ἐν αρχῆ τοίνυν {ἐστι}ν ὡς ἡ β ζ τῆς ν ξ, ἡ ζ η 17 {τρ}ὸς ν ο, {καὶ} τὰ τε{τρ}άγωνα, {καὶ} ὡς ἒμ{πρ}ο{σθ}εν πάντα {πρ}ος πάντα, τὰ ἄρα {ἀπὸ} β κ η {τῶν} {ἀπὸ} ξ ν ο 18 {ἐστι} {τρ}ιπλάσια. quæ nos emead tuimus διὰ τὸ ἐν αρχῆ τοὶνυν {ἐστι}ν ὡς ἡ β κ {πρ}ὸς ν ξ, ἡ 19 κ μ {πρ}ὸς ν ο {καὶ} τὰ τε{τρ}άγονα. {καὶ} ὡς ἐν {πρ}ὸς ἐν, πάντα {πρ}ὸς πάντα. τὰ ἂρα {ἀπὸ} β η μ τῆς 20 {ἀπὸ} ξ ν ο {ἐστι} {τρ}ιπλάσια.

}}} [http://echo.mpiwg-berlin.mpg.de/ECHOdocuView/ECHOzogiLib?pn=282&ws=1&wx=0.227&wy=0.2796&ww=0.7439&wh=0.1185&mode=imagepath&url=%2Fmpiwg%2Fonline%2Fpermanent%2Flibrary%2FA0VHBVNN%2Fpageimg p] {{{ 1

Ita rectangulum FDE ad rectangulum AEC, & componendo, vt DB ad BE, ita re- 2 ctangulum FDE vna cum rectangulo AEC ad rectangulum AEC. Sed rectangulum 3 FDE vna cum rectangulo AEC æquale e$t rectangulo ADC ex anteced\~ete] _Hun@ loc\~u_ 4 _ita re$tituendum cen$uimus, in Græco enim codice $ic legebatur {οὐ}τω τὸ {ὑπὸ} {τῶν} α ε γ διά τὸ {πρ}ο-_ 5 _γεγραμμένον ἲσον {ἐστὶ} τὸ {ὑπὸ} {τῶν} α δ γ, $ed forte ita re$tituetur. {οὑ}τω τὸ {ὑπὸ} {τῶν} ζ δ ε. {πρ}ὀς_ 6 _τὸ {ὑπὸ} {τῶν} α ε γ συνθέντι ἂρα ὠς ἡ δ β πρ ς {τὸν} β ε {οὒ}τω τὸ {ὑπὸ} {τῶν} ζ δ ε μετά {τοῦ} {ὑπὸ} {τῶν} α ε γ_ 7 _πρὸς τὸ {ὑπὸ} {τῶν} α ε γ ἂλλα τὸ {ὑπὸ} {τῶν} ζ δ ε μετά {τοῦ} {ὑπὸ} {τῶν} α ε γ διά τὸ {πρ}οτετρὰμμενον ἲσον_ 8 _{ἐστὶ} {τῷ} {ὑπὸ} {τῶν} α δ γ._

}}} [http://echo.mpiwg-berlin.mpg.de/ECHOdocuView/ECHOzogiLib?pn=370&ws=1&wx=0.2173&wy=0.3829&ww=0.7681&wh=0.2249&mode=imagepath&url=%2Fmpiwg%2Fonline%2Fpermanent%2Flibrary%2FA0VHBVNN%2Fpageimg p.370] {{{ 1

Et ei, quod ad quadratum ex DB eandem, quam AD ad DB proportionem habet, 2 & præterea ei, quod ad quadratum ex DC eandem habet proportionem, quam AB ad 3 BD ] _Græcus codex {καὶ} {τῷ} λὸγον ἒχοντι {πρ}ὸς τὸ {ἀπὸ} α β {τὸν} ἀυτὸ {τῷ} τῆς α δ πρὸς {τὴν} δ β {καὶ}_ 4 _@ν {τῷ} λόγον ἔχοντι {πρ}ὸς τὸ {ἀπὸ} α β {τὸν} ἀυτὸν {τῷ} τῆς α β {πρ}ὸς {τὴν} β δ. Sed legendum e$t, {καὶ}_ 5 _τὸ λὸγον ἒχοντι {πρ}ὸς τὸ {ἀπὸ} δ β {τὸν} ἀυτὸ {τῷ} τῆς α δ {πρ}ὸς τὴν δ β {καὶ} {ἐστι} {τῷ} λόγον ἔχοντι_ 6 _{πρ}ὸς τὸ {ἀπὸ} δ γ {τὸν} ἀυτόν {τῷ} τῆς α β πρὸς τὴν β δ. Quæ vero $equuntur in Græco codice V$-_ 7 _que eo. τὸ ἂρα ἁπὸ α γ & c. $uperuacanea videntur_.

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Quadratum igitur ex AC, & id, quod ad quadratum ex CB proportionem habet 9 eandem, quam AD ad DB, hoc e$t datam, æquale e$t quadrato ex AD, & proportio- 10 nem habenti ad quadratum ex DE eandem quam AD ad DB, hoc e$t æquale rectan- 11 gulo BAD, videlicet dato, & adhuc æquale ei, quod ad quadratum ex DC eandem ha- 12 bet, quam AE ad BD proportionem, nimirum datam] _Græcts codex corruptus, & man._ 13 _cus e$t, quem ita re$tituendum cen$eo. τὸ ἂρα ἄπὸ α γ {καὶ} τὸ λὸγον ἒχον πρὸς τὸ ἁπὸ γ β,_ 14 _@ ἁντὸ@ {τῷ} τῆς α δ πρὸς {τὴν} δ β {τοῦ}τ{ἐστι} {τῷ} δοθὲντι ἲσον {ἐστι} {τῷ}τε ἀπὸ α δ {καὶ} {τῷ} λόγον ἒχοντι_ 15 _προς τὸ ἀπό δ β {τὸν} ἁυτον {τῷ} τῆς α δ πρὸς {τὴν} δ β {τοῦ}τ{ἐστι} {τῷ}τε {ὑπὸ} β α δ, {τοῦ}τ{ἐστι} δοθὲντι {καὶ}_ 16 _{τῷ} λόγον ἒχοντι πρὸς τὸ ἁπὸ δ γ τόν ἁυτον {τῷ} τῆς α β πρὸς {τὴν} β δ, {τοῦ}τ{ἐστι} δοθὲντι._

}}} === Recommendation === The quality in the work sample seems to be inferior to the quality in the remaining text. Accept it or ask them to re-do the Greek text in the first 50 pages? (We had decided against any comments and to give our ok after looking at the work sample.) == 4. Post-Processing ==