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Isaac Newton expressed his three laws of motion as follows:

  1. Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.

  2. Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.

  3. Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi.

My question is: what is the significance of making the main verb in each sentence an infinitive? Does it have something to do with the reason grammarians have sometimes called the infinitive another mood alongside indicative, imperative, and subjunctive?

The infinitive verbs necessitate putting the subjects into the accusative case, which eliminates the nominative-accusative distinction, thereby introducing Latin's most famous grammatical ambiguity—something that I'd try to avoid in scientific writing. Ambiguity is not a problem in these sentences, but I found it jarring to find, for example, that mutationem was the subject of its sentence, not the object of a verb to come later.

The surrounding text (here) doesn't make the laws infinitive clauses in a larger sentence.


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From medieval scholasticism onward, the titles or summations of enumerated items in disputations are commonly phrased as subordinate clauses, either indirect statements (either accusative with infinitive or the Late Latin variant, quod + subjunctive) or indirect questions.

For instance, in Thomas Aquinas' Summa Theologiae, we find "Quaestio Prima" followed by "De sacra doctrina, qualis sit, et ad quae se extendat", followed by explanatory text. We can understand this as "Quaestio prima est de sacra doctrina, qualis sit, et ad quae se extendat."

Likewise, here in Newton, we have Lex I followed by a summary, followed by explanatory text. We can read this as Lex prima est ... or lex prima asserit or anything similar.

The formatting itself, within this genre, signals that the text is to be read with a general assertive or interrogative force.

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My Latin is nonexistent, so the following may be totally wrong, but it's too long for a comment and hopefully fills in the background correctly.

Mathematical instruction in Newton's era consisted of reading the Elements, and I think Newton would have read them in Latin. The Principia are written in a lordly, impersonal style, with Newton having erased all traces of what processes of thought and experiment he himself used to arrive at his laws of motion. The logical structure of the laws doesn't even fit correctly with the Euclidean model, but he's clearly intent on shoehorning them into a similar structure, presumably because of the prestige carried by Euclid along with, most likely, his personal feeling that it was a beautiful and worthy model.

The Elements are written in terms of recipes for construction, which is different from what Newton is trying to do when he expresses his universal laws of motion. But of course nobody had ever found a universal scientific law before, so he had to make up his own stylistic conventions for expressing such a law.

The original Greek of his Euclidean model would be expressed like this:

Καὶ πεπερασμένην εὐθεῖαν κατὰ τὸ συνεχὲς ἐπ εὐθείας ἐκβαλεῖν.

And to produce a finite straight-line continuously in a straight line. (Fitzgerald)

Here the verb ἐκβαλεῖν, to produce, is in the infinitive. The series of postulates is prefaced with "let it have been postulated," but each basically stands on its own as an impersonal statement.

My Latin is nonexistent, but I believe this sort of thing is a common construction in Latin called indirect discourse. It's the sort of thing we express in English as, "He was said to eat an elephant every morning." An example is Cato the Elder's famous "Ceterum censeo Carthaginem esse delendam" (using the infinitive), which can be shortened to "Carthago delenda est" (using the finite form). As in Cato's model, there is a tendency to omit the "framing" verb when it's obvious, as in a series of statements like Euclid's postulates and propositions, or Newton's laws of motion. "He was said to eat an elephant every morning. And to drink a bathtub of gin. And to chew up a dozen sycamores and spit them out as toothpicks."

I don't know what Latin translation Newton would have been using, but here is a Latin translation that existed in that era for the first proposition in Euclid:

Ἐπὶ τῆς δοθείσης εὐθείας πεπερασμένης τρίγωνον ἰσόπλευρον συστήσασθαι.

To construct an equilateral triangle on a given finite straight-line. (Fitzgerald)

Super rectam lineam definite quantitatis triangulum equilaterum constituere. (Gerard of Cremona)

The Greek verb συστήσασθαι is an aorist middle infinitive, to be constructed. In this Latin translation, looking up constituere tells me that it's actually an ambiguous form, but I believe it's functioning here as an active infinitive, to construct. Note that here, the proposition is just the first of many that compose the main body of the book. There is no framing finite verb that covers the whole book and introduces all these infinitives.

So I don't know how common it was in general in Latin to have an infinitive as the main verb of a sentence, but it seems that Newton probably did have models in front of him that were constructed that way, to express impersonal statements about how things ought to behave (deontic mood), especially when those statements were part of a list, or where the framing was understood.

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  • For someone whose Latin is non-existent, you're doing pretty well! My Ancient Greek is non-existent, so I must ask: could Euclid's sentences be understood as clauses—big verbal nouns—that serve only as section headings, as in English we might title a section "Constructing an equilateral triangle on a finite straight line"? No assertion is made by such a clause, just as one expects in the absence of a finite verb (except the implicit assertion "This section explains ____").
    – Ben Kovitz
    Nov 12 '21 at 10:48

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