I think your question has both Latin and typographical elements to it.
You are correct in that Greek the letter sigma has two variants: ς, used only at the ends of words, and σ, used elsewhere which was then reflected in Latin cursive.
In Old Latin cursive "the letter s was written as a vertical downstroke with a small curve at the end of it, and a diagonal upstroke at the top. It looked almost like a check mark, with an added diagonal line on top of it. In new Roman cursive, which developed between the third and seventh century AD, s was written almost as we write the lowercase r today: a vertical downstroke, followed by an upstroke with a curve. This was the type of s that found its place in the Carolingian script, which was developed in the court of Charlemagne in order to provide a uniform and legible form of writing. It’s in this script that the r-like form evolved into the long s."
[Source: https://www.grammarly.com/blog/history-of-long-s/]
during the Renaissance in Italy humanists wanting to revive what they thought was the original Latin script revived Charlemagne's Carolingian minuscule script and created Humanist minuscule which they called litterae antiquae (the "ancient letters").
Humanist miniscule became the template for the typesetter's Roman typeface when printing became available.
I think that all of the other rules about the uses of the long and short s came into effect with the beginning of printing, and each countries' printers had different rules about when and where to use the long and short s.
For example in Britain and Ireland the following rules applied during the 17th and 18th centuries.:
• short s is used at the end of a word (e.g. his, complains, ſucceſs)
• short s is used before an apostrophe (e.g. clos'd, us'd)
• short s is used before the letter 'f' (e.g. ſatisfaction, misfortune, transfuſe, transfix, transfer, ſucceſsful)
• short s is used after the letter 'f' (e.g. offset), although not if the word is hyphenated (e.g. off-ſet) [see Short S before and after F for details]
• short s is used before the letter 'b' in books published during the 17th century and the first half of the 18th century (e.g. husband, Shaftsbury), but long s is used in books published during the second half of the 18th century (e.g. huſband, Shaftſbury) [see Short S before B and K for details]
• short s is used before the letter 'k' in books published during the 17th century and the first half of the 18th century (e.g. skin, ask, risk, masked), but long s is used in books published during the second half of the 18th century (e.g. ſkin, aſk, riſk, maſked) [see Short S before B and K for details]
• Compound words with the first element ending in double s and the second element beginning with s are normally and correctly written with a dividing hyphen (e.g. Croſs-ſtitch, Croſs-ſtaff), but very occasionally may be written as a single word, in which case the middle letter 's' is written short (e.g. Croſsſtitch, croſsſtaff).
• long s is used initially and medially except for the exceptions noted above (e.g. ſong, uſe, preſs, ſubſtitute)
• long s is used before a hyphen at a line break (e.g. neceſ-ſary, pleaſ-ed), even when it would normally be a short s (e.g. Shaftſ-bury and huſ-band in a book where Shaftsbury and husband are normal), although exceptions do occur (e.g. Mans-field)
• double s is normally written as double long s medially and as long s followed by short s finally (e.g. poſſeſs, poſſeſſion), although in some late 18th and early 19th century books a different rule is applied, reflecting contemporary usage in handwriting, in which long s is used exclusively before short s medially and finally [see Rules for Long S in some late 18th and early 19th century books for details]
• short s is used before a hyphen in compound words with the first element ending in the letter 's' (e.g. croſs-piece, croſs-examination, Preſs-work, bird's-neſt)
• long s is maintained in abbreviations such as ſ. for ſubſtantive, and Geneſ. for Geneſis (this rule means that it is practically impossible to implement fully correct automatic contextual substitution of long s at the font level)
To get a more detailed description on the various rules in different countries please read the following absolutely fascinating article linked below from which the above rules are copied:
https://www.babelstone.co.uk/Blog/2006/06/rules-for-long-s.html
To answer your question specifically would depend on the rules by which the printers in that country were following (far more specific examples on the link above which you could look through) but at a glance the following rules may apply:
"On the first line: Cum modo diSjectis…"
In Italy short s is used before an accented vowel (e.g. paſsò, ricusò, sù, sì, così), but not an unaccented letter (e.g. paſſo, ſi). Since j and i are used interchangeably in Latin the j in the above case is equivalent to a vowel.
On line 19: LEXELL aSSiduos inter…
The double s is normally written as double long s medially and as long s followed by short s finally (e.g. poſſeſs, poſſeſſion) would apply.
