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. Mostly it is a simple, formalized style. 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 in the work sample

​p.20

In general, the results with Greek text are not so bad. Basically, I looked at paragraphs A to G on p.20 (i.e. <pb 4>), which is admittedly only a very small sample. Starting around C, the results become actually quite good.

Anchored comments again. The do not see that the marginal notes are the anchors of the comments. Not much we can do. The ] is sometimes typed as ] and sometimes as tau, even though it is printed well. No special instruction at the moment. And a reference to the special instruction for Conimbricensis would make things even more confusing, I guess.

A: stigma is typed as end-sigma and not resolved to {sigma tau}. Combinations of breathings and accents still do not work well. Single breathings or accents have a better chance of being correct.

B: The typesetter seems to stick to the convention that the accent should be above the first letter of a diphthong. The Chinese copy it faithfully. As "omikron tilde" is not allowed, they resort to \~omikron. I cannot decide (yet) whether this is really a convention of whether the typesetter is just careless. Sometimes the accent is on the sencond letter. The resolve λλ silently. This is of course against the rules, but it makes sense. An example where he is definitely careless: ἁπό. They copy it faithfully. well-printed {αῖ} becomes {αἱ}. α'πὸ becomes the correct ἀπὸ! And they do this correction regularly. πα ὰλληλοι: makes sense, somehow Apparently it is difficult to jump from Latin to Greek and back. Inbetween Greek characters, they forget to mark & _c._ as italics. Not too much of a problem, though.

C: ὃν ἕχ{ει} (wrong but clearly readable) becomes ὅν ἓχ{ει}. stigma again. iota becomes tau once. But in general it becomes surprisingly correct, even the accents and breathings and combinations of accents and breathings.

D: They do not recognize omikron + spiritus asper + cirkumflex, probably because the circumflex becomes a half-circle ("cap"?) --> unknown character. A line break where obviously there shouldn't be one. Does that count as typo? ] as tau.

E: ] as tau. stigma.

F: ] as tau. they use @@ sensibly. μολογόυμ ενον: there is just no space in the text.

G: ] as tau.

Non-Greek issues

They forget the <pb> in the preface, but type it correctly as soon as there are page numbers. Annoying, but I guess we shouldn't mention it.

<pb 2>: "small caps disaster": they mark every line (such as "A B") as small caps, and they're right. We can change <sc> to <var> afterwards. Problem: if one of the letters is a Greek character, they mark only the Latin part (and again, they're right). In other words, they refuse to see the obvious structure. --> additional rule or post-processing?

<pb 2>: Apparently, fractions are difficult. They mark them correctly, but sometimes forget the digit before the fraction, so e.g. 2.25 becomes 0.25. When a digit is just unintelligible, they still make a guess without using <?>.

Analysis of the unknown characters

<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".

Findings in the complete text

Some random samples (line numbers added) after the text had been completed:

​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. How could this survive double-keying and comparing?

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>

4: Hun@: ok.

5: {πρ}ὀς: optically this would be possible.

6: ἂρα ὠς: good enough (blame the typesetter).

​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>

They mark Greek letters as italics. Does it make sense ot explicitly tell them otherwise?

4 (@ν), 7 (ἁπὸ), 13 (ἄπὸ), 14 (@ ἁντὸ@), 14/15 ({τοῦ}τ{ἐστι}): They type faithfully what they see. No complaint here.

12: <sc>AE</sc>: typo in the Latin part (should be AB). _Græcts_: again, they should use <?>.

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