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Full text: Clavius, Christoph: Christophori[i] Clavii Bambergensis Ex Societate Iesv In Sphaeram Ioannis De Sacro Bosco Commentarivs

Comment. in 1. Cap. Sphæræ

122. REGULAE, QVIBVS ET SVPERFICIES MA-
ximi circuli in orbeterreno, vel etiam in quocunque ſphæra,
& ſuperficies conuexa eiuſdem orbis terreni, vel
etiam cuiuſque ſphæræ, immo, & tota
ſoliditas inueniatur.

H actenvs ex probatis auctoribus vatios modos recenſuimus, quibus
terrę ambitus inueſtigetur, præcepta\'que propoſuimus, quibns ex circunferen-
tia nota diameter, & contra ex nota diametro circunferentia inueniatur: Nunc
uero tradam alia præcepta, quibus ex diametro, & circunferentia terrę, vel cu-
iuſuis alterius ſphęræ, ſuperficies maximi circuli in terra, vel alia ſphæra, inue
ſtiganda ſit; & ex hac ſuperficic ſuperficies conuexa eiuſdem terræ, vel ſphæræ,
& denique ex hac conuexa ſuperficie ſoliditas tota terræ, vel alterius ſphęræ. Ita
enim fiet, ut terræ magnitudo omni ex parte cognita reddatur, non autem tantũ
quod ad ambitum, quod auctor noſter præſtitit hoc loco.


Q vod igitur ad primum attinet, ſi multiplicetur ſemidiameter cuiuſuis
circuli in dimidiatam parte circunferentiæ, ſeu ambitus circuli, producetur area,
ſeu ſuperficies circuli intra circunferentiam contenta. Vt ſi circun ferentia alicu-
ius circuli fuerit 132. Diameter vero 42. Si 21. diametri dimidium, multiplicemus
per 66. circunferentiæ dimidiatam partem, producetur hic numerus 1386. pro
area circuli. Quod quidem ſupra à nobis demonſtratum eſt in tractatione de
figuris Iſoperi metris, propoſ. 4. in qua habetur, rectangulum comprehenſum ſub
ſemidiametro cuiuſuis cieculi, & dimidiata parte circunferentię eiuſdem, æquale
eſſe circulo. Ita que ſi multiplicetur ſemidiameter terræ, nempe ſtadia 4009010/44
ſecundum Eratoſthenem per dimidiatam partem ambitus, hoc eſt, ſecundum
Eratoſthenem, per ſtadia 126000. producetur area maximi cireuli in terra, ſta-
diorum 50524545455/11. hoc eſt, ſuperficies plana maximi circuli in terra
comprehendet tot quadrata, quorum quodlibet in ſingulis lateribus vnum ſta-
dium com plectatur, quot unitates ſunt in dicto numero. Areæ enim figurarum
planarum menſurantur per quadrata earum linearum, per quas latera, ſeu ambi-
tus earundem figurarum menſurari ſolent.

Q vod vero attinet ad ſecundum, ſi area circuli maximi in ſphæra per 4.
multiplicetur, procreabitur ſuperficies tota conuexa ſphęræ. Vt ſi fuerit ſphęra,
cuius maximi circuli ambitus ſit 132. Diameter vero 42 ex prima regula area cir
culi maximi 1389. vt dictum eſt, quæ ſi multiplicetur per 4. exurget mox ſuper-
ficies conuexa dictæ ſphæræ 5544. Hoc autem clariſſime ab Archimede eſt de-
monſtratum lib. 1. de ſphæra & cilyndro propoſ. 31. in qua concluditur, Superfi-
ciem conuexa cuiuslibet ſphęrę eſſe quadruplam maximi circuli in ſphęra. Ita-
que ſiarca maximi circuli in terra, qui continet, vt diximus ſtadia quadrata
50514545455/11 multiplicetur per 4. inuenietur ambitus orbis terreni, ſecundum
totã conuexamſuperficiem, vadiorum quadratorũ 202058181819/11, Poteſt ta
men eadem ſuperficies conuexa inueniri facilius, etiam ſi aream maximi circuli
non habemus, hac ratione.

M vltiplicetvr tota diameter in totam circunferentiam maxi-
mi circuli. Productus enim numerus dabit ſuperficiem conuexam ſphæræ. Vt
ſi multiplicetur diameter terræ continens ſtadia 801819/11. per totum ambitũ.
videlic et per ſtadia 252000. producetur conuexa ſuperficies terrę ſtadiorum

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