Theodosius <Bithynius>; Clavius, Christoph - Theodosii Tripolitae Sphaericorum libri tres

Scan	Original
111	99
112	100
113	101
114	102
115	103
116	104
117	105
118	106
119	107
120	108
121	109
122	110
123	111
124	112
125	113
126	114
127	115
128	116
129	117
130	118
131	119
132	120
133	121
134	122
135	123
136	124
137	125
138	126
139	127
140	128

5947 parallelorum circulorum in ſphæra auferunt, aut
per parallelorum polos tranſeunt, aut eundem v-
num parallelum tangunt.

IN ſphæra maximi circuli A B C, D B E, auferant ex paralleli: A D C,
F G, circunferentias ſimiles A D, F G. Dico maximos circulos A B C, D B E,

66[Figure 66] aut tranſire per polos parallelorum A D C,
F G, aut vnum eundem parallelum tangere.
Aut enim alter illorum, nempe A B C, tran-
ſit per polos parallelorum, atque ita oſten-
demus, alterum per eoſdem tranſire, aut nõ
tranſit quidẽ per polos parallelorũ, ſed alte
rũ tamen illorũ tangit, atq; ita demonſtra-
bimus, alterum cundem tangere; aut deniq;
neque per polos parallelorum incedit, neq;
alterum illorum tangit: quo poſito conclu
demus circulos maximos datos aliquẽ aliũ
parallelum tangere datis parallelis minorẽ.
Tranſeat enim primum A B C, per polos pa-
rallelorum. Dico & D B E, per eoſdem trã
ſire, hoc eſt, pũctum B, in quo ſe ſecant maximi circuli A B C, D B E, polum
eſſe parallelorum A D C, F G. Si namque B, non eſt eorum polus, ſit H, po-
lus ipſorum. Et quia circulus A B C, ponitur tranſire per eorum polos, erit
H, in circunferentia A B C. Per H, G, deſcribatur circulus maximus H G,
1120. 1. huius.2210. huius. ſecans A D C. in I. Eruntq́; arcus A I, F G, ſimiles, cum intercipiantur in-
ter maximos circulos A H, H I, per polum H, deſcriptos: Ponitur autem
& arcus A D, eidem arcui F G, ſimilis. Similes ergo ſunt arcus A I, A D;
atque adeo cum ſint eiuſdem circuli, inter ſe æquales erunt, totum & pars.
Quod eſt abſurdum. Non ergo aliud punctum, præter B, polus erit parallelo-
rum, ſi alter circulorum A B C, D B E, nempe A B C, per illorum polos du
citur, Quare vterque circulus maximus A B C, D B E, per polum B, paralle
lorum tranſit, ſi vnusipſorum tranſit.

67[Figure 67]

SED iam duo maximi circuli A B C, D E F,
auferant rurſum ex parallelis A D C, B E,
circunferentias ſimiles A D, B E, & neuter
illorum tranſeat per parallelorum polos,
ſed alter, nempe A B C, vnum eorum, puta
B E, tangat in B. Dico & circulum D E F,
eundem B E, tangere in E. Si enim non tan
git, ſed ſecat, deſcribatur per E, punctũ in
parallelo B E, datũ maximus circulus G E H,
3314. huius. tangens parallelum B E, in E; eruntq́; ſemi
circuli, quorum alter ex E, per G, ducitur,
alter vero ex B, per A, tranſit, non coeun-
tes, vt conſtat ex figura propoſ. 13. huius libri, & ex demonſtratis ibidem.
4413. huius.

Page concordance

Text layer

Text normalization

Search

Scan	Original
111	99
112	100
113	101
114	102
115	103
116	104
117	105
118	106
119	107
120	108
121	109
122	110
123	111
124	112
125	113
126	114
127	115
128	116
129	117
130	118
131	119
132	120
133	121
134	122
135	123
136	124
137	125
138	126
139	127
140	128

Scan	Original
111	99
112	100
113	101
114	102
115	103
116	104
117	105
118	106
119	107
120	108
121	109
122	110
123	111
124	112
125	113
126	114
127	115
128	116
129	117
130	118
131	119
132	120
133	121
134	122
135	123
136	124
137	125
138	126
139	127
140	128

Scan	Original
111	99
112	100
113	101
114	102
115	103
116	104
117	105
118	106
119	107
120	108
121	109
122	110
123	111
124	112
125	113
126	114
127	115
128	116
129	117
130	118
131	119
132	120
133	121
134	122
135	123
136	124
137	125
138	126
139	127
140	128