362346GNOMONICES
DESCRIBEMVS in hoc horologio parallelos Horizontis, vt in polari eoſdem deſignaui
11Defcriptio pa-
rallel orum Ho
rizontis in eo-
dem horologio
declinante ab
Horizonte. mus propoſ. 41. ſuperioris lib. dummodo ea, quæ ſequuntur, diligenter obſeruentur. In priori
modo circulus Analemmatis A B C, referet Verticalem propriè dictum, qui nimirum per ſtylum
tranſiens ad planum horologij rectus eſt, facitq́ue fectionem B D: Paralleli autem Horizontis nõ
2210 mutantur. Rurſus pro axe E F, ducenda erit diameter, ſeu communis ſectio Verticalis, & circuli
maximi, cui horologiũ æquidiſtat, ita vt tam arcus C E, quàm B F, æqualis ſit declinationi propo-
240[Figure 240]
ſitæ ab Horizonte.
Huicautẽ diametro ducẽda
eſt parallela R Q, pro magnitudine ſtyli I K, vel
A K, ita vt recta D I, rectam R Q, ad rectos an-
gulos ſecans ſit ſtylo I K, æqualis. Puncta deni-
que L, M, N, O, P, accepta ex T, puncto, vbi
Horizon B C, rectam R Q, ſecat, tran sferenda
erunt in rectam B D, ex D, puncto horizonta-
lis lineæ verſus B, in ſuperiori horologio: In in-
3320 feriori autem transferẽda erunt interualla S T,
& alia, ſi qua fuerint, ex D, in eandem rectam
B D, ſed vltra D, productam. Nam ſectiones
conicæ circa diametros L Q, M Q, N Q, & c.
ſecundum doctrinam propoſ. 8. lib. 1. deſcri-
ptæ, & translatæ in horologium, ita vt diame-
tri earum rectæ B D, congruant, tranſeantq́ue
per puncta translata L, M, N, O, P, S, & c. &
cornua earum à linea horizontali auertantur,
dabunt parallelos Horizontis.
443011Defcriptio pa-
rallel orum Ho
rizontis in eo-
dem horologio
declinante ab
Horizonte. mus propoſ. 41. ſuperioris lib. dummodo ea, quæ ſequuntur, diligenter obſeruentur. In priori
modo circulus Analemmatis A B C, referet Verticalem propriè dictum, qui nimirum per ſtylum
tranſiens ad planum horologij rectus eſt, facitq́ue fectionem B D: Paralleli autem Horizontis nõ
2210 mutantur. Rurſus pro axe E F, ducenda erit diameter, ſeu communis ſectio Verticalis, & circuli
maximi, cui horologiũ æquidiſtat, ita vt tam arcus C E, quàm B F, æqualis ſit declinationi propo-
eſt parallela R Q, pro magnitudine ſtyli I K, vel
A K, ita vt recta D I, rectam R Q, ad rectos an-
gulos ſecans ſit ſtylo I K, æqualis. Puncta deni-
que L, M, N, O, P, accepta ex T, puncto, vbi
Horizon B C, rectam R Q, ſecat, tran sferenda
erunt in rectam B D, ex D, puncto horizonta-
lis lineæ verſus B, in ſuperiori horologio: In in-
3320 feriori autem transferẽda erunt interualla S T,
& alia, ſi qua fuerint, ex D, in eandem rectam
B D, ſed vltra D, productam. Nam ſectiones
conicæ circa diametros L Q, M Q, N Q, & c.
ſecundum doctrinam propoſ. 8. lib. 1. deſcri-
ptæ, & translatæ in horologium, ita vt diame-
tri earum rectæ B D, congruant, tranſeantq́ue
per puncta translata L, M, N, O, P, S, & c. &
cornua earum à linea horizontali auertantur,
dabunt parallelos Horizontis.
IN poſteriori autem modo recta A D, ſu-
menda eſt æqualis rectæ A B, quæ ex vertice ſtyli A, in figura præcedentis propoſ. in Zenith B,
cadit, & in rectam A B, transferenda ſunt interualla inter E, & lineas Verticales in linea hori-
zontali, & c. Pro linea autem meridiana, quæ dat Verticalem grad. 90. & horizontalem lineã
non ſecat, ducenda eſt D F, ipſi A B, parallela, & in alteram partem transferendæ lineæ, quæ ex
D, emiſ@æ rectam A B, ſecant, ſicut in lineis horarijs factum eſt in horizontali horologio. Eſt
enim hic A D, tanquam axis; A B, veluti radius Aequatoris, quanquam re uera radius ſit Horizon
tis; rectæ ex A, ductæ ſunt inſtar radiorum ſignorum, & c. Demonſtratio huius operationis eadẽ
eſt, quæ in horizontali horologio, ſi recta A D, rectæ A B, axi Horizontis congruat, punctumq́ue
A, puncto A, & punctum D, puncto B, & circa illam figura A D F, in qua continentur radij paral
5540 lelorum Horizontis, circumuertatur, quemadmodum in horologio horizontali figuram radio-
rum circa axem mundi moueri intelligimus, & c. Nam in hac ita ſe habent lineæ Verticales, vt
ibilineæ horariæ, ita vt punctum B, reſpondeat centro horologij, in quod axis A B, cadit, & linea
horizontalis ſit veluti æquinoctialis linea, & c. Quapropter parallelos Horizontis in eodem horo
logio declinante ab Horizonte repoſnimus. Quod erat faciendum.
menda eſt æqualis rectæ A B, quæ ex vertice ſtyli A, in figura præcedentis propoſ. in Zenith B,
cadit, & in rectam A B, transferenda ſunt interualla inter E, & lineas Verticales in linea hori-
zontali, & c. Pro linea autem meridiana, quæ dat Verticalem grad. 90. & horizontalem lineã
non ſecat, ducenda eſt D F, ipſi A B, parallela, & in alteram partem transferendæ lineæ, quæ ex
D, emiſ@æ rectam A B, ſecant, ſicut in lineis horarijs factum eſt in horizontali horologio. Eſt
enim hic A D, tanquam axis; A B, veluti radius Aequatoris, quanquam re uera radius ſit Horizon
tis; rectæ ex A, ductæ ſunt inſtar radiorum ſignorum, & c. Demonſtratio huius operationis eadẽ
eſt, quæ in horizontali horologio, ſi recta A D, rectæ A B, axi Horizontis congruat, punctumq́ue
A, puncto A, & punctum D, puncto B, & circa illam figura A D F, in qua continentur radij paral
5540 lelorum Horizontis, circumuertatur, quemadmodum in horologio horizontali figuram radio-
rum circa axem mundi moueri intelligimus, & c. Nam in hac ita ſe habent lineæ Verticales, vt
ibilineæ horariæ, ita vt punctum B, reſpondeat centro horologij, in quod axis A B, cadit, & linea
horizontalis ſit veluti æquinoctialis linea, & c. Quapropter parallelos Horizontis in eodem horo
logio declinante ab Horizonte repoſnimus. Quod erat faciendum.
SCHOLIVM.
PER ea, quæ in ſcholio propoſ.
2.
ſuperioris lib.
ſcripſimus, non erit difficile iudicare, quinam paral
66Qui paralleli
Horizontis in
horologio ſint
Hyperbolæ, Pa
rabolæ, aut El-
lipſes.7750 leli Horizontis in plano horologij ſint hyperbolę, & qui parabolæ, aut Ellipſes. Quando enim in figure,
in qua continentur radii parallelorum Horizontis, recta ex puncto D, egrediens, ſecans{q́ue} rectam A B,
in puncto, quod puncto A, eſt omnium propinquiſſimum, ſecat duos radios parallelorum oppoſitos ex A,
eductos, fient duæ hyperbolæ oppoſitæ, vt in exemplo nostro contingit in radijs parallelorum grad. 15.
Si verò eadem recta ex puncto D, emiſſa æquidiſtet alicui radio ad ſiniſtram rectæ A B, poſito, erit pa-
rallelus radii oppoſiti Parabole. Si denique recta eadem ex D, educta quempiam radiorum ad ſiniſtram
rectæ A B, neque ſecet, neque ei æquidiſtet, erit parallelus ex radio oppoſito deſcriptus, Ellipſis, vt ac-
cidit in propoſito exemplo in radiis parallelorum Horizontis grad. 30. 45. 60. & c. Quæ omnia ibi-
dem demonſtrata ſunt.
66Qui paralleli
Horizontis in
horologio ſint
Hyperbolæ, Pa
rabolæ, aut El-
lipſes.7750 leli Horizontis in plano horologij ſint hyperbolę, & qui parabolæ, aut Ellipſes. Quando enim in figure,
in qua continentur radii parallelorum Horizontis, recta ex puncto D, egrediens, ſecans{q́ue} rectam A B,
in puncto, quod puncto A, eſt omnium propinquiſſimum, ſecat duos radios parallelorum oppoſitos ex A,
eductos, fient duæ hyperbolæ oppoſitæ, vt in exemplo nostro contingit in radijs parallelorum grad. 15.
Si verò eadem recta ex puncto D, emiſſa æquidiſtet alicui radio ad ſiniſtram rectæ A B, poſito, erit pa-
rallelus radii oppoſiti Parabole. Si denique recta eadem ex D, educta quempiam radiorum ad ſiniſtram
rectæ A B, neque ſecet, neque ei æquidiſtet, erit parallelus ex radio oppoſito deſcriptus, Ellipſis, vt ac-
cidit in propoſito exemplo in radiis parallelorum Horizontis grad. 30. 45. 60. & c. Quæ omnia ibi-
dem demonſtrata ſunt.