Pappus 1660

Pappus Alexandrinus (1660), Mathematicae collectiones ​ECHO

Part of WO1. Sent with DESpecs version 1.1.2.

Sent: ok/date. Returned: ok/date/ ​raw text, separate unknown characters list with <001> and <002>: see attachment.

1. First Analysis

Difficulties

• Greek text. Throughout the book, the typographer has often (but not always) placed the accent on the first letter of a diphthong. This can be corrected via post-processing. A rule for the automated correction, e.g. type \~ου as οῦ, would probably not work well.

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):

​p.37 (part of the work sample)

 1 vero $i <sc>A</sc> $it ip$ius <sc>B</sc> 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_ <sc>D</sc> _ad_ <sc>E</sc>, _bt_
 5 <sc>A B</sc> _ad_ <sc>B</sc>, _Vel Vt_ <sc>B C</sc>
 6 _ad_ <sc>C</sc> _ex lis_, _quc ante demon$trata $unt. Po$tquam Vero o$tendit ex analogia æqualitatis_

1: χαί, συναμφοτέραυ: unnecessary typos.

2: ἔςιν: The general problem of telling sigma and stigma apart without using positional rules. Can be solved during post-processing. ἐιη ἑιη: doubled. ἠμισις: The smooth breathing is there, but the acute is missing (however, ἔ in ἔςιν is correct).

3: {καὶ}: not a ligature, i.e. the braces are superfluous. συναμφότεος: unnecessary typo (should be συναμφότερος). τοῦ β is missing.

4: ὁ becomes "ο`;": incorrect reading and incorrect notation; the diacritic is not bhind but above the ο. _bt_: The typographer uses different small v in italics in the same line, and they interpret different letter shapes as denoting different letters, which somehow seems reasonable (also note the capital _Videtur_ in line 3).

6: _ex lis_ should be _ex iis_ or rather _ex <007>is_ (missing i dot).

​p.153

   <h it>COMMENTARIVS.</h>
 1 <p it><ac A>_Dimidium eius, quod fit a recta linea <sc>HF</sc>]_</ac> Græcus codex habet τὸ ἢμισυ τ{οῦ} ἀπὸ τῆς
 2 {ἐπὶ} τά θ ζ. Sed nos per$picuitatis cau$$a ita Vtendum cen$uimus.</p>
 3 <p it><ac B>_Hoc enim in XX. Theoremate e$t demon$tratum]_</ac> In Græco codice legitur τ{οῦ}το γαρ ἐν
 4 {τῷ} δευτέρω θεωρήματι δέδ{ει}χθ{αι}.</p>
 5 <p it><ac C>_Sed rectantgulo <sc>BAL</sc> vna cum eo, quod <sc>BA</sc>, <sc>LR</sc>, continetur, hoc e$t rectangulo_
 6 _<sc>BAR</sc>]_</ac> Ex prima $ecundi libri elementorum.</p>
 7 <p it><ac D>_Aequale e$t quod fit ex <sc>AG</sc>]_</ac> iuncta enim <sc>_BG_</sc> triangula <sc>_ABGAGR_</sc> $imilia $unt ex octaua
 8 $exti libri elementorum. ergo vt <sc>_BA_</sc> ad <sc>_AG_</sc>, ita <sc>_GA_</sc> ad <sc>_AR_</sc>, ac propterea rectangulo <sc>_BAR_</sc>
   <mgr>4 $exti.
   17</mgr>
 9 æquale e$t quadratum ex <sc>_AG_</sc>.</p>
10 <p it><ac E>_Ergo & quod fit ex <sc>AG</sc> vna cum rectangulo <sc>GHK</sc>]_</ac> 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.</p>
12 <p it><ac F>_Et ante o$ten$um e$t figuram quidem con$tantem ex $uperficiebus conicis.]_</ac> In Græ
13 co codice legitur. καὶ ἐδεχθη πρὸ ἑνος. Illud Vero o$ten$um e$t in 24. propo$itione huius.</p>

5: (rectantgulo: typo in the book.)

11, 13: καὶ: unlike in line 3 in the previous example, it is a ligature here, i.e. missing braces.

13: (ἐδεχθη is correctly transcribed.)

​p.183

 1 <p it><ac K>_Erunt quadrata ex <sc>BK</sc>, <sc>KM</sc> quadrati ex <sc>FG</sc> tripla._</ac> Nam cum quadratum quidem ex
 2 <sc>_FG_</sc> ad quadratum ex <sc>_BH_</sc> proportionem habeat, quam quinque ad tria, quadrata vero ex <sc>_BK_
 3 _KM_</sc> ad idem quadratum ex <sc>_BH_</sc> eam habeat, quam quinque ad Vium, hoc e$t quam quinde-
 4 cim ad tria, habebunt quadrata ex <sc>_BK_</sc>, <sc>_KM_</sc> ad quadratum ex <sc>_FG_</sc> 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 $ic corrigendum arbitror. ἐν δὲ {τῷ} ι τὰ ἀπὸ β κ, κ μ πενδαπλάσια τ{οῦ}
 8 @πὸ β θ. τὰ ἂρα ἀπὸ β κ, κ μ {τρ}ιπλάσια τ{οῦ} ἀπο ζ η.</p>
 9 <p it><ac L>_Vtin tertiodecimo libro elementorum demon$tratur]_</ac> propo$itione 1 @.</p>
10 <p it><ac M>_Ergo ex ante demon$tratis vt <sc>BK</sc>, ad <sc>NX</sc>, ita <sc>KM</sc> ad <sc>NO</sc>, & eorum quadrata, &_
11 _vt vnum ad vnum, ita omnia ad omnia. quadrata igitur ex <sc>BK</sc>, <sc>KM</sc> tripla $unt quadra-_
12 _torum ex <sc>NX</sc>, <sc>NO</sc>]_</ac> e$t eni nex 45. huius vt <sc>_BK_</sc> ad _<sc>KM</sc>,_ ita <sc>_XN_</sc> ad <sc>_NO_</sc> permutandoque
13 Vt <sc>_BK_</sc> ad _<sc>XN</sc>,_ ita <sc>_KM_</sc> ad _<sc>NO</sc>._ Vt quadratum ex <sc>_BK_</sc> ad quadratum ex _<sc>NX</sc>,_ ita quidratum
   <mgr>22. $exti.</mgr>
14 ex <sc>_KM_</sc> ad quadratum ex _<sc>NO</sc>._ vt autem vnum ad Vnum, ita omnia ad omnia. Sed quadra
   <mgr>12. quinti</mgr>
15 tum ex <sc>_BK_</sc> triplum e$t quadrati ex _<sc>NX</sc>._ quadrata igitur ex _<sc>BK</sc>,_ <sc>_KM_</sc> quadratorum ex _<sc>NX</sc>,_
16 <sc>_NO_</sc> $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 <gap> 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.</p>

5: _Videlicet_, see above.

8: @πὸ: ok.

9: _Vtin: missing space, somehow acceptable.

12: eni nex: ok. But why, then, cann they read permutandoque in the same line?

13: quidratum: ok, but they should have added <?>. In general, they should use <?> more often.

14: <gap> emead tuimus: ok, but again they should use <?> more often.

​p.282

 1 <p><ac F>Ita rectangulum <sc>FDE</sc> ad rectangulum <sc>AEC</sc>, & componendo, vt <sc>DB</sc> ad <sc>BE</sc>, ita re-
 2 ctangulum <sc>FDE</sc> vna cum rectangulo <sc>AEC</sc> ad rectangulum <sc>AEC</sc>. Sed rectangulum
 3 <sc>FDE</sc> vna cum rectangulo <sc>AEC</sc> æquale e$t rectangulo <sc>ADC</sc> ex anteced\~ete]</ac> _Hun@ loc\~u_
 4 _ita re$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._</p>

​p.370

 1 <p><ac D>Et ei, quod ad quadratum ex <sc>DB</sc> eandem, quam <sc>AD</sc> ad <sc>DB</sc> proportionem habet,
 2 & præterea ei, quod ad quadratum ex <sc>DC</sc> eandem habet proportionem, quam <sc>AB</sc> ad
 3 <sc>BD</sc> ]</ac> _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. $uperuacanea videntur_.</p>
 8 <p><ac E>Quadratum igitur ex <sc>AC</sc>, & id, quod ad quadratum ex <sc>CB</sc> proportionem habet
 9 eandem, quam <sc>AD</sc> ad <sc>DB</sc>, hoc e$t datam, æquale e$t quadrato ex <sc>AD</sc>, & proportio-
10 nem habenti ad quadratum ex <sc>DE</sc> eandem quam <sc>AD</sc> ad <sc>DB</sc>, hoc e$t æquale rectan-
11 gulo <sc>BAD</sc>, videlicet dato, & adhuc æquale ei, quod ad quadratum ex <sc>DC</sc> eandem ha-
12 bet, quam <sc>AE</sc> ad <sc>BD</sc> proportionem, nimirum datam]</ac> _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._</p>

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