English actually has this same construction! Think of it as analogous to the phrase "Granted that" or "It is given that." It's used in philosophy as part of a hypothetical dialogue.
In Latin, the "giving" part led to a metaphorical usage of "permission." If I grant you the right to do something, I give you permission. Or allowance, etc. You can find this ...
You can find it under the solus dictionary entry in Lewis and Short:
Strengthened by modo, and joined with it in one word, sōlummŏdo (only late Lat., for the true reading, Plin. 34, 8, 19, § 92, is unam tantum, Jan. Detlef.; “whereas tantummodo is class.): de exercitore solummodo Praetor sentit,” Dig. 4, 9, 1, § 2: “pretii solummodo fieri aestimationem,...
A very literal translation:
Whence it comes that the beginning which they see natural things possess, they attach to substances.
A more natural translation:
This is why they ascribe to substances the same beginning that they see natural things possess.
Unde is strictly speaking a relative meaning "whence, from which place". But Latin often ...
This is a deponent verb.
Both the normal contemplare and the deponent contemplari exist and mean roughly the same thing.
I have the impression that the deponent one is more common, but the details surely depend on the era and author.
The deponent verb has passive forms but active meaning, and therefore the passive perfect participle has active meaning too.
You are correct that extra is a preposition here. Although it can be an adverb, it has a clear object here that would not make syntactical sense otherwise.
This particular argument follows Spinoza's earlier assertion that a cause must either "be contained" in a thing's nature or be given "outside of" that thing:
denique notandum hanc causam propter quam ...
Accusativum cum infinitivo triggered by sequitur, though the accusative has been ellipsed: 'it follows that it has...'
This use falls under definition 7 of sequor in the Oxford Latin Dictionary:
7 To follow from (a premiss), follow logically.
(w. acc. and inf.) nec si omne enuntiatum aut uerum aut falsum est, ~quitur ilico esse causas ...
The first thing to observe here is the quo–eo structure.
Quo plus edo, eo laetior sum.
The more I eat, the happier I am.
Therefore quo plus…eo plus means "the more…the more".
In the translation you quote this is rendered as "as reality increases, so also will increase".
These quo and eo are neuter ablatives, but it ...
That's quite a leap in logic there. First, people learned Latin in Latin schools, so their style would take after their teacher's, not necessarily the zeitgeist. Second, just because something is influenced by Cicero, does not mean it will be Ciceronian. Medieval Latin survived and was strong all throughout early modern Europe.
As for his actual style, ...
Yes, this does indeed appear to be a partitive genitive.
Changing the word order as you suggest is legitimate if it helps you.
I think it is most useful in its original place where una and sine alia are next to each other.
I like analyzing things sequentially, so let us start with the whole sentence.
To clarify the role of the relative clause, I will add ...
Literally, '...they do nothing different than if someone... (makes the other conclusion about a circle)'
Or, to translate a bit more loosely, '...what they do is no different than what some other person does if he/she... (makes the other conclusion)'
Or '...they act no differently than if some other person... (makes the other conclusion)'
The adjective ...
A Latin adjective can sometimes be read either as a mere attribute or more broadly.
For example, consider these two translations:
Homo conscius intelligit.
1. A conscious man understands.
2. A man, being conscious, understands.
In the first translation conscius is a mere attribute, describing what kind of a man is in question.
In the second one there ...
I would take cujuscunque rei causa to be a single noun phrase: "a cause for/of every individual thing". That is, assignari has a subject, but the object is left implied; if it were made explicit, it would be something like illi "…to that thing".
A cause of every individual thing must be assigned [to that thing]: either a reason why it exists, or a reason ...
The difference is not great between "The cause and reason ought to be assigned to each thing why or why not..." and "The cause and reason of each thing why or why not... ought to be assigned..." Though the Genitive after causa is more literal.
I think the most significant reason for choosing the Genitive rather than the dative is continuity. The formula "...
Pretty much everything put forward in other answers is correct in its way. I'm just a bit surprised that none has rendered the subjunctive by 'would', as in:
As would be obvious to anyone attentive enough
I strongly suggest you to read English translations of William White and Samuel Shirley. These are more precise than Elwes translation.
I fully expect that those who judge things confusedly, and who have not been accustomed to cognise things through their first causes, will find it difficult to comprehend the demonstration of the 7th Proposition, ...