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

Comment. in ij. Cap. Sphæræ
[figure]

gula intelligenda eſt, qñ
uterq; locus uel in Bo-
ream, uel in Auſtrum ab
Aequatore recedit. Nam
ſi alter eorum, nempe A, in
Auſtrum vergat, & alter,
uidelicet B, in Boream,
ducendæ erunt perpendi-
culares ex punctis H, &
I, ad rectam H I, in diuer-
ſas partes, quales ſunt
I L, & H M, ita tantum, ut
vurſus I L, æqualis ſit
rectæ I G, & H M, rectæ
H F. Nam recta L M, con-
iungens puncta L, & M,
erit iterum chorda arcus
diſtantiæ unius loci ab-
altero. Itaque ſi coap-
tetur in circulo recta
D O, æqualis rectæ L M,
erit arcus D O, diſtan-
tia duorum locorum propoſitorum.

S it deinde d\~ria longitudinũ arcus A B D, ſemicirculo maior, (Nã qñ hæc
differentia ſemicirculus eſt dictum eſt ſupra, qua rõne inueſtigãda ſit diſtantia
locorũ) & a pũctis A, & D, ducãtur diametri A E C, D E B. Ponatur, dein de latitu
do loci A, ęqualis arcui A F, & loci D, latitudo ęqualis arcui D R, demittãturq;
ad ꝓprias diametros ꝑpendiculares F H, R Q Poſt hęc, ad ductã rectã Q H, ad
eaſdẽ partes, ſi uterq; loc 9 borealis ẽ, vel auſtralis, ꝑpendiculares ducã\~t QT, HS,
ꝑpendicularib. Q R, H F, ęquales, ſingulę ſing ulis hoc ẽ, Q T, ipſi Q R, & H Si
ipſi H F, æqualis. Nã recta cõiũgẽs pũcta T, S, erit chorda arcus diſtãtiæ uni 9 lo
ci ab altero. Quare ſi accõmodetur in circulo recta D P, rectæ T S, æqualis, erit
arc 9 D P, diſtãtia ꝓpoſitorũ locorũ, ut prius. Si uero locus A, fuerit v.g. borea-
lis, & D, auſtralis, ducendæ erũt ex Q H, ꝑpendiculares ad Q H, in diuerſas par
tes ẽt, quales ſunt Q T, H V. ita tñ, ut rurſus Q T, ipſi Q R, & H V, ipſi H F,
ſit ęqualis. Nã recta T V, erit chorda arcus diſtãtię unius loci ab altero: ac ꝓ in
de ſi aptetur in circulo recta D X, rectæ T V, æqualis, erit arcus D X, diſtãtia lo
corũ ꝓpoſi torũ. Demõſtrationẽ huius operationis, \~q quidẽ pulcherrima, eſt ac
breuiſſima, ignorare nõ poterit is, qui uel mediocriter uerſatus fuerit in doctri
na ſinuũ, & rẽ diligentius introſpexerit in ſphæra aliqua materiali. Nã circulus
A B C D, referet Aequatorẽ: Dlametri A C, B D, cões ſectiones Aequatoris cum
Meridianis locorum propo ſitorum: Puncta H, & I, in Aequatoris plano, erunt
ea, in quæ incidunt ſinus recti latitu dinũ dictorumlocorum. Vnde ſi a punctis
H, & I erigantur ad planũ Aequatoris perpendiculares, erunt eæ ip ſæ ſinus re-
cti latitudinũ, perueniẽt\'q; ad ipſa loca in ſuperficie ſphęræ, ęquales\'q; omnino
erunt rectis H K, I L, ut conſtat. Quocirca recta K L, æqualis erit chordæ arcus,
qui inter dicta loca interponitur. Nam rectæ H K, I L, ſunt æquales ſinibus re-
ctis, latitudinũ. Hæc eadem precepta inſeruiunt ad inueſtigandã diſtantiã inter

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