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)
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):
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):
Attachments:
