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Some 17th century mathematics

I'm in the middle of translating a piece of academic mathematics from the mid 17th century. Everything has gone very well so far with one exception, the following passage:

item quod necessaria fit ad minimum talis generis curuae ad mechanicam talium aequationum resolutionem cum talibus innumeris

I'm not sure if I am missing some technical detail here, maybe some specific mathematical usage I'm not familiar with, but it really doesn't look like it should be ...
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...inter verba et cruciatus

From Orberg LLPSI Cap XLIII: the Horatius' father defends him against a charge of treason (for taking the law into his own hands and killing his sister) and pleads directly to the people

Inter haec senex iuvenem amplexus, spolia Curiatiorum fixa eo loco qui nunc 'Pila Horatia' appellatur ostentans, "Huncine" aiebat "quem modo decoratum ovantemque victoria incedentem vidistis, Quirites, eum vinctum inter verbera et cruciatus videre potestis?

In the meanwhile (as he was speaking)..the old ...
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Suetonius on J. Caesar, chapter LXXX

Context: Suetonius describes the growing fear that dictator Caesar intends soon to make himself king.

Quae causa coniuratis maturandi fuit destinata negotia, ne assentiri necesse esset.

Translation: This was why the conspirators accelerated their planned efforts , in order not to give assent .

After much thought, I am reading it like this:

Quae fuit causa: this was the cause. I am reading "quae" here as if it were a demonstrative ...
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Orberg Cap XLIII

Adapted from Livy Orberg tells the story of the battle of the Horatii and Curatii. It's down to the final two and he tells us:

Prius igitur quam alter — nec procul aberat — consequi posset, et alterum Curiatium conficit. Iamque singuli supererant, sed nec spe nec viribus pares. Alterum intactum ferro corpus et geminata victoria ferocem in certamen tertium dabat; alter, fessum vulnere fessum cursu corpus trahens victusque fratrum ante se strage, victori obicitur ...
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..corpus sineret.

Ergo, ut divideret pugnam eorum, capit fugam, ita ratus Albanos secuturos ut quemque vulnere affectum corpus sineret.

There's something I'm not getting. The part from ...ita ratus - in this way he thought the Albani following...' and then ut quemque vulnere affectum... so that he? / it? (the tactic) would allow each body to be affected with a wound...'

I'm having trouble with the subject of sineret.
Read more : ..corpus sineret. | Views : 952 | Replies : 6

translation problem

In Italia urbem desideratam habebitis. I think desideratam is a perfect participle and the way I translate this sentence is 'you will have longed for a city in Italy'. But this sounds like the future perfect tense which is covered later in the book. This one has me stumped.
Read more : translation problem | Views : 744 | Replies : 2

In Catilinam, second oration

1-2 were kind of tough but I think I've got it for the most part (at least I mostly get the sense); nevertheless I have a few problems:

Catiline has left town:

Nulla iam pernicies a monstro illo atque prodigio moenibus ipsis intra moenia comparabitur.

("Now no destruction from that monster, that prodigal one, will be set against the walls themselves (from) within them.")

Non enim iam inter latera nostra sica illa versabitur, non in ...
Read more : In Catilinam, second oration | Views : 2304 | Replies : 38

Asking grammar questions in Latin

I am a high school Latin teacher. My subdepartment uses Wheelock's, which of course yields excellent results on standardized tests and college placement exams but unfortunately has imparted almost no oral comprehension or intuitive sense of the language. I am planning to weave Orberg into the curriculum next year, but in the meantime, I would at least like to ask my students on grammar questions in Latin.

I am familiar with all of the Latin ...
Read more : Asking grammar questions in Latin | Views : 818 | Replies : 2

genti ea tempestate secundum Etruscos opulentissimae viris

In LLPSI Cap XLII Orberg Scribit:

Cum iam viribus suis satis confideret, Tullus Sabinis bellum indixit, genti ea tempestate secundum Etruscos opulentissimae viris armisque.

...genti ea tempestate secundum Etruscos opulentissimae viris armisque = Sabini genti opulentissimae in viris armisque (ablativi) ?
Read more : genti ea tempestate secundum Etruscos opulentissimae viris | Views : 1252 | Replies : 10

ea sancta

In LLPSI Tullus Mettium puniturus est ei loquit: 'Nunc, quoniam tuum insanabile ingenium est, at tu tuo supplicio doce humanum genus ea sancta credere quae a te violata sunt!

ea sancta = ea (res) sancta? ea sancta acc. neut pl?
Read more : ea sancta | Views : 952 | Replies : 5


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