Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 355
>
Scan
Original
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 355
>
page
|<
<
of 355
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
pb
pagenum
="
122
"
xlink:href
="
009/01/122.jpg
"/>
<
p
type
="
main
">
<
s
id
="
s.002116
">
<
arrow.to.target
n
="
marg169
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.002117
">
<
margin.target
id
="
marg169
"/>
168</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.002118
">Ibidem
<
emph
type
="
italics
"/>
(Si igitur circumducas ſemicirculŭm, in quo A, circa diametrum in qua
<
lb
/>
G K P, que à G, K, reflexæ ad id in quo M; in omnibus planis ſimiliter ſe habebunt,
<
lb
/>
& æqualem facient angulum, qui K M G, & quem etiam facient angulum, quæ
<
lb
/>
K P, & P M, ſuper eam, quæ G P, ſemper æqualis erit. </
s
>
<
s
id
="
s.002119
">Trianguli igitur ſuper eam,
<
lb
/>
quæ G P, æquales ei, qui G M P. conſiſtunt. </
s
>
<
s
id
="
s.002120
">horum autem perpendiculares ad idem
<
lb
/>
ſignum cadent eius, quæ G P, & æquales erunt, cadunt ad
<
foreign
lang
="
grc
">ω,</
foreign
>
centrum ergò circuli
<
lb
/>
<
foreign
lang
="
grc
">ω</
foreign
>
ſemicirculus autem, qui circa M N, abſectus eſt ab horizonte)
<
emph.end
type
="
italics
"/>
hac vltima
<
lb
/>
textus parte concludit Iridis portionem ſupra horizontem aſtro
<
expan
abbr
="
oriẽte
">oriente</
expan
>
exi
<
lb
/>
ſtentem eſſe ſemicirculum, hoc modo; ſi igitur imaginatione circumducas
<
lb
/>
ſemicirculum, in quo A, circa diametrum horizontis G K P, in hac circum
<
lb
/>
uolutione duæ lineæ G M, M K, in omnibus planis conſtitui poſſibilibus cir
<
lb
/>
ca prædictam diametrum, quæ ſupra etiam fieri à triangulis infinitis dixi
<
lb
/>
mus, ſucceſſiuè erunt; ſiue percurrent ſimiliter omnia illa plana, & facient
<
lb
/>
vbique angulum Iridis K M G, eundem: pariter duæ lineæ K P, P M, facient
<
lb
/>
vndique eundem angulum K P M. quare omnia triangula in predictis planis
<
lb
/>
imaginata, &
<
expan
abbr
="
cõſtituta
">conſtituta</
expan
>
ſuper linea G P, ſimilia ipſi G M P, & æqualia erunt;
<
lb
/>
ſi igitur ab angulis ipſorum, in quibus M, ductæ ſint perpendiculares ad la
<
lb
/>
tus G P, omnes cadent in idem punctum
<
foreign
lang
="
grc
">ω,</
foreign
>
vt in figura;
<
expan
abbr
="
quarũ
">quarum</
expan
>
vna erit M
<
foreign
lang
="
grc
">ω,</
foreign
>
<
lb
/>
quæ tamen cæteras omnes repreſentabit,
<
expan
abbr
="
eisq́
">eisque</
expan
>
; omnibus in volutatione axis
<
lb
/>
G K
<
foreign
lang
="
grc
">ω,</
foreign
>
coincidit; erunt autem omnes æquales, quandoquidem ſunt trian
<
lb
/>
gulorum æqualium. </
s
>
<
s
id
="
s.002121
">
<
expan
abbr
="
eruntq́
">eruntque</
expan
>
; in eodem eiuſdem circuli plano, & punctum
<
foreign
lang
="
grc
">ω,</
foreign
>
<
lb
/>
erit centrum ipſius. </
s
>
<
s
id
="
s.002122
">ſimilia dicta ſunt in Halone. </
s
>
<
s
id
="
s.002123
">Cum ergò ipſius centrum
<
lb
/>
<
foreign
lang
="
grc
">ω</
foreign
>
, ſit in diametro horizontis G K
<
foreign
lang
="
grc
">ω</
foreign
>
P O, manifeſtum fit portionem eius, quæ
<
lb
/>
ſupra horizontem eminet, eſſe ſemicirculum, qui in figura notatur lineis
<
lb
/>
L M N. </
s
>
<
s
id
="
s.002124
">Atque hoc accidit Sole, vel Luna in horizonte exiſtentibus; quod
<
lb
/>
erat primo loco demonſtrandum.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.002125
">Porrò ſciendum poſſe nos breuius polum prædictum inuenire, ſi nimirum
<
lb
/>
<
figure
id
="
id.009.01.122.1.jpg
"
place
="
text
"
xlink:href
="
009/01/122/1.jpg
"
number
="
63
"/>
<
lb
/>
ad M, ducatur M P, faciens angulum K P M, æqua
<
lb
/>
lem angulo G M K, per 23. primi, erunt enim duo
<
lb
/>
triangula
<
expan
abbr
="
æquiãgula
">æquiangula</
expan
>
G P M, K P M, angulus enim
<
lb
/>
P, eſt communis, angulus verò M K P, eſt æqualis
<
lb
/>
duobus G, & G M K, per 32. primi, ergo etiam
<
lb
/>
duobus ad M, ſiue toti G M P, & reliquus K M P,
<
lb
/>
reliquo, quare per 4.6. latera circa angulos æqua
<
lb
/>
les proportionalia erunt, & omologa G M, ad M K, ita G P, ad P M, quæ
<
lb
/>
æqualibus angulis ſubtenduntur. </
s
>
<
s
id
="
s.002126
">
<
expan
abbr
="
eaſdẽ
">eaſdem</
expan
>
autem proprietates habebant etiam
<
lb
/>
triangula Ariſt. in figura, de qua paulò ante dicebam. </
s
>
<
s
id
="
s.002127
">Verba illa
<
emph
type
="
italics
"/>
(Quæ ali
<
lb
/>
bi quam in ſemicirculo constituuntur)
<
emph.end
type
="
italics
"/>
ſunt perperam in antiqua tranſlatione
<
lb
/>
tranſlata, nam Græcè ſic,
<
foreign
lang
="
grc
">αι αλλοθι τοῡ ημικοκλνού συνισταμεναι,</
foreign
>
transferenda
<
lb
/>
eſſent, quæ in alio circuli loco concurrunt.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.002128
">
<
arrow.to.target
n
="
marg170
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.002129
">
<
margin.target
id
="
marg170
"/>
169</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.002130
">Ibidem
<
emph
type
="
italics
"/>
(Iterum ſit horizon quidem in quo A C. oriatur autem ſupra hunc G,
<
lb
/>
axis autem ſit nunc in quo G P. </
s
>
<
s
id
="
s.002131
">Alia igitur omnia ſimiliter oſtendentur vt & prius.
<
lb
/>
</
s
>
<
s
id
="
s.002132
">Polus autem circuli, in quo P, erit ſub horizonte eo, in quo A C, eleuato puncto,
<
lb
/>
in quo G. in eadem autem & polus, & centrum circuli, & terminantis nunc ortum,
<
lb
/>
eſt enim iſte, in quo G P. </
s
>
<
s
id
="
s.002133
">Quoniam autem ſupra diametrum, quæ A C, quod K G,
<
lb
/>
centrum vtique erit ſub horizonte priori eius, in quo A C, in linea K P, in quo
<
foreign
lang
="
grc
">ω,</
foreign
>
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>