Layout old manuscripts in a computational language.

Ideas
1

http://www.cecm.sfu.ca/personal/pborwein/PAPERS/CP4.pdf

borwein.jpg
borwein.jpg930×1231 133 KB

looks like this:

borwein2.jpg
borwein2.jpg1514×1424 225 KB

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2

How did you convert the shown pdf to your notebook file?

3

Retyping by hand! The Formulas can directly be checked, because it’s a computational language. Therefore there are no typos in the formulas possible:) So it’s a lot of work, but some articles are jewels. I did a lot on Euler’s work and there are a lot of typos in the formulas of Euler’s original papers written in Latin.

The process can be accelerated if more than one person works on it parallel:)

4

That’s a lot of work, but looks very nice! Because this forum allows notebook embedding in the posts – it would be really cool to see a complete notebook and post dedicated to a single article. Could you please share with other members and post any? I bet a lot of people here would highly appreciate it and want to play with the notebooks.

5

TextRecognize[ ] wrapped around a screen capture of your sample text did surprisingly well, getting everything except the rather eccentric Pi (in this font). So this could be the first pass in your project, saving you a lot of typing.

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6

Thanks for your replies. The file is in Attachments. I have not finished it, yet:) And probably I never will.

And now something from Euler:

Here is Theorem 8 from celebrating E72 (http://eulerarchive.maa.org/docs/originals/E072.pdf)

EulerE72_Theorem8.jpg
EulerE72_Theorem8.jpg963×1960 184 KB

with at least one typo (after Porro est) in the proof.

This can be set in Mathematica (I try to imitate the long S with an integral sign):

primes = 8; natural = 12; Column[{Style["Theorema 8.", 24, Black], 
  Style["Si ex \[Integral]\[NegativeThinSpace]erie numerorum primorum \
\[Integral]\[NegativeThinSpace]equens formetur, expressio", Black, 16,
    FontFamily -> "Times", FontSlant -> Italic], 
  someprimes = Table[Prime[i], {i, 1, primes}];
  Style[Row[Join[Table[p^n, {p, someprimes}], {"etc."}], 
     " \[CenterDot] "]/
    Row[Join[
      Table[Row[{"(", p^n, -1, ")"}], {p, someprimes}], {"etc."}]], 
   18, Black],
  Style["erit eius valor aequalis \
\[Integral]\[NegativeThinSpace]ummae huius \[Integral]\
\[NegativeThinSpace]eriei", Black, 16, FontFamily -> "Times", 
   FontSlant -> Italic],
  Style[Row[
    Join[{1}, 
     Table[1/(HoldForm[#1^n] &)[k], {k, 
       Range[2, natural]}], {"etc."}], "+"], 16, Black]}, Center, 
 Frame -> True, Spacings -> 1.5, Background -> LightBlue]

giving (using more terms than Euler):

EulerE72_Theorem8_M.jpg
EulerE72_Theorem8_M.jpg1264×567 67.3 KB

and now the proof (without typos in the formulas, maybe in the text):

Format[power[a_, b_]] := Superscript[a, b]
power[1, b_] := 1 (*1^(any number)=1, this is not always wanted*)

primes = 10; natural = 9; size = 14; Column[{Style["Demonstratio.", 
   24, Black], 
  Style["Sit", Blue, 16, FontFamily -> "Times", FontSlant -> Italic], 
  someprimes = Prime[Range[primes]];
  Style[Row[{"x=", 
     Row[Join[{1}, 
       Table[1/power[k, n], {k, Range[2, natural]}], {"etc."}], 
      "+"]}], size, Red],
  Style["erit", Blue, 16, FontFamily -> "Times", FontSlant -> Italic],
  Style[Row[{1/power[2, n], "x=", 
     Row[Join[Table[1/power[2 k, n], {k, Range[natural]}], {"etc."}], 
      "+"]}], size, Red],
  Style["vnde oritur", Blue, 16, FontFamily -> "Times", 
   FontSlant -> Italic], 
  Style[Row[{Row[Table[Row[{"(", p^n, -1, ")"}], {p, {2}}]]/
      Row[Table[p^n, {p, {2}}], " \[CenterDot] "], "x=", 
     Row[Join[
       Table[1/power[2 k - 1, n], {k, Range[natural]}], {"etc."}], 
      "+"]}], size, Red],
  Style["Porro est", Blue, 16, FontFamily -> "Times", 
   FontSlant -> Italic],
  Style[Row[{Row[Table[Row[{"(", p^n, -1, ")"}], {p, {2}}]]/
      Row[Table[p^n, {p, {2, 3}}], " \[CenterDot] "], "x=", 
     Row[Join[
       Table[1/power[3 k, n], {k, 
         Select[Range[2 natural], (Mod[#, 2] != 0) &]}], {"etc."}], 
      "+"]}], size, Red],
  Style["vnde fiet", Blue, 16, FontFamily -> "Times", 
   FontSlant -> Italic],
  Style[Row[{Row[Table[Row[{"(", p^n, -1, ")"}], {p, {2, 3}}]]/
      Row[Table[p^n, {p, {2, 3}}], " \[CenterDot] "], "x=", 
     Row[Join[
       Table[1/power[k, n], {k, 
         Select[Range[
           3 natural], (Mod[#, 2] != 0 && 
             Mod[#, 3] != 0) &]}], {"etc."}], "+"]}], size, Red],
  Style["Similibus ergo operationibus pro singulis numeris primis\n\
institutis omnes seriei termini praeter primum tollentur,\n\
reperieturque", Blue, 16, FontFamily -> "Times", FontSlant -> Italic],
  Style[Row[{"1=", 
     Row[Join[
        Table[Row[{"(", p^n, -1, ")"}], {p, 
          Prime[Range[primes]]}], {"etc."}]]/
      Row[Join[Table[p^n, {p, Prime[Range[primes]]}], {"etc"}], 
       " \[CenterDot] "], "x"}], size, Red],
  Style["et loco x Serie restitura sit", Blue, 16, 
   FontFamily -> "Times", FontSlant -> Italic],
  Style[Row[{Row[Join[Table[p^n, {p, Prime[Range[primes]]}], {"etc"}],
        " \[CenterDot] "]/
      Row[Join[
        Table[Row[{"(", p^n, -1, ")"}], {p, 
          Prime[Range[primes]]}], {"etc."}]], "=x"}], size, Red], 
  Style[Row[{"=", 
     Row[Join[{1}, 
       Table[1/power[k, n], {k, Range[2, natural]}], {"etc."}], 
      "+"]}], size, Red],
  Style["Q.E.D.", Blue, 16, FontFamily -> "Times", FontSlant -> Italic]
  }, Frame -> True, Spacings -> 1.5, Background -> LightCyan]

giving (using more terms than Euler):

EulerE72_Theorem8_MProof.jpg
EulerE72_Theorem8_MProof.jpg1419×1887 187 KB

2020_Borwein_Ramanujan_Pi^-1.nb (48.5 KB)

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