The word 'pars' in geometry and proportion.

Chris Kirk

New Member

The meaning of 'pars'?

Thanks for the suggestions in a different thread. I agree with the Big White Dog: it's setting up a fraction. He's barking up the right tree.

'Saint' asked I give the passage. Take a deeeep breath . . . .

Here are two passages from a text in astronomy-theory I'm translating. First comes an Objection to solid spheres that carry the planets (like onion-shells that can slip past each other). The objection claims that If Venus has the shells it is supposed to, one of the shells - its epicycle - will cut across the Moon's shell and right across the Earth as well:

"2. Obiectio Fracastorii.
"SI Epicyclus Veneris tantae esset magnitudinis, ut eius semidiameter comprehendat gr 43. et tota diameter gra. 86. pertingeret fere usque ad centrum terrae. Nam si semidiameter praecise contineret gr. 45. transiret Epicyclus per centrum terrae praecise. quod ipse Geometrice conatur probare. Cum ergo hoc absurdum sit, et contra experientiam, non erit in rerum natura Epicyclus Veneris."

Here's my translation:

Fracastoro?s 2nd Objection
IF the epicycle of Venus is of such size that its radius encompasses 43° and a total diameter of 86°, it would be stretched almost right through the center of the earth. For, if the radius were only 45°, the epicycle would cut across the center of the earth just so ? which the same Geometry wanted to prevent. Therefore this is absurd, and against experience; an epicycle for Venus would not be among things with a nature.

[For 'gr.' and 'gra.' - *gradus* or 'step' - read 'degree']

Draw a circle; mark its center as 'earth.' Put a spot on its edge; mark it as 'the Moon.' Draw a bigger circle from the same center; then draw a smaller circle centered on the edge of that outer circle so that it almost touches 'earth,' and put a spot on that smaller circle - that's 'Venus.' If all those circles were shells instead, the small 'epicycle' that Venus is on would make the system impossible to work. So Clavius will show that Fracastoro is wrong: the epicycle of Venus isn't that big.

Here's (part of) Clavius's reply:

"Solutio 2. obiectionis Fracastorii.
"AD secundum argumentum Fracastorii respondemus, Astronomos non statuere, Epicycli Veneris semidiametrum continere grad. 43. sed partes 43. ex iis, quarum 60. in semidiametro circuli Eccentrici continentur. Ex quo fit, ut lineae ex centro terrae emissae, tangentesque Epicyclum auferant ex primo mobili ad utrasque partes lineae Augis gradus ferme 45. quot nimirum ad summum Venus recedere videtur a Sole tam versus ortum, quam versus occasum. Sed hinc non sequitur, Epicyclum fere ad terram usque pertingere. Cum enim, ut Fernelius Ambianas in sua Cosmotheoria refert, Eccentrici circuli semidiameter contineat semidiametros terrae ferme 689. comprehendet propemodum semidiameter Epicycli terrae semidiametros 435 2/3. quem numerum si subtrahamus ex distantia terrae ab opposito augis, quae complectitur semidiametros terrae 674 2/3. fere, continebit intervallum inter centrum terrae, et oppositum Augis Epicycli, dum Epicyclus terrae proximus est, nempe in opposito Augis Eccentrici, semidiametros terrae quasi 179. quae distantia plura milliaria continet, quam 640641."

And, here's my partial translation:

Solution to Fracastoro?s 2nd objection
[problematic transl?n: astronomical def?n of ?pars?]
To the second argument of Fracastoro?s we reply: astronomers have not established [that] the epicycle of Venus contains a radius of 43° but 43 *parts*; of which out of these 60[unit?] is contained in the circuit of the eccentric. It follows from this that as the lines are carried, going out from the center of the earth and tangent, from the first mover to either part of the line of apogee by as much as about 45°, Venus is seen to recede most from the Sun more towards rising, than towards setting. But from this it does not follow that the epicycle is carried to the earth and cuts right through. For as Fernelio Ambiano says in his View of the Cosmos, the radius of the epicyclic eccentric circuit is contained by almost roughly 689 earth-radii; of the epicycle, 435 ⅔ earth-radii, which number, if we draw the distance to the earth from perigee, embraces roughly 674 ⅔ earth-radii; when the epicycle is nearest the earth, it will contain a span of about 179 earth-radii between the earth?s center and perigee of the epicycle [and] perigee of the eccentric [as well]; this distance contains at most 640,641 miles.

The uncertain section comes before 'Cum enim,' but the rest will give the number-lovers something to figure out - the mile Clavius uses is pretty close to the English/ American mile, as is the measure of the Earth. It's rather fun to measure all this out on paper.

It's a big chunk; any help is apprecieated.

Vale, magistri(ae) et studenti(ae).

Kirk ('Templus'?)