Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 347
>
81
(57)
82
(58)
83
(59)
84
(60)
85
(61)
86
(62)
87
(63)
88
(64)
89
(65)
90
(66)
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 347
>
page
|<
<
(64)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div202
"
type
="
section
"
level
="
1
"
n
="
95
">
<
pb
o
="
64
"
file
="
0088
"
n
="
88
"
rhead
="
"/>
</
div
>
<
div
xml:id
="
echoid-div205
"
type
="
section
"
level
="
1
"
n
="
96
">
<
head
xml:id
="
echoid-head101
"
xml:space
="
preserve
">THEOR. XVI. PROP. XXXV.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2235
"
xml:space
="
preserve
">Si recta linea diametro Hyperbolæ vltrà centrum occurrens, al-
<
lb
/>
teram ipſius aſymptoton ſecet, producta ſectionem quoq; </
s
>
<
s
xml:id
="
echoid-s2236
"
xml:space
="
preserve
">ſecabit.</
s
>
<
s
xml:id
="
echoid-s2237
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2238
"
xml:space
="
preserve
">ESto Hyperbole ABC, cuius cẽtrum
<
lb
/>
<
figure
xlink:label
="
fig-0088-01
"
xlink:href
="
fig-0088-01a
"
number
="
58
">
<
image
file
="
0088-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0088-01
"/>
</
figure
>
D, aſymptotos DE, diameter BD
<
lb
/>
F, è cuius puncto G vltrà cẽtrum aſſum-
<
lb
/>
pto ducta ſit quæpiam linea GE aſym-
<
lb
/>
ptoton ſecans in E; </
s
>
<
s
xml:id
="
echoid-s2239
"
xml:space
="
preserve
">Dico, ſi produca-
<
lb
/>
tur, ſectionem quoque ſecare.</
s
>
<
s
xml:id
="
echoid-s2240
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2241
"
xml:space
="
preserve
">Ducta enim ex vertice B recta BH
<
lb
/>
parallela ad DE, ipſa ad partes A nun-
<
lb
/>
quam ſectioni occurret, cum ei
<
note
symbol
="
a
"
position
="
left
"
xlink:label
="
note-0088-01
"
xlink:href
="
note-0088-01a
"
xml:space
="
preserve
">Coroll.
<
lb
/>
11. huius.</
note
>
rat in B, ſed GE ſecat alteram Paralle-
<
lb
/>
larum DE, quare producta ſecabit, & </
s
>
<
s
xml:id
="
echoid-s2242
"
xml:space
="
preserve
">
<
lb
/>
reliquam BH, vnde neceſſariò ſectio-
<
lb
/>
nem priùs ſecabit. </
s
>
<
s
xml:id
="
echoid-s2243
"
xml:space
="
preserve
">Quod, &</
s
>
<
s
xml:id
="
echoid-s2244
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s2245
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div208
"
type
="
section
"
level
="
1
"
n
="
97
">
<
head
xml:id
="
echoid-head102
"
xml:space
="
preserve
">THEOR. XVII. PROP. XXXVI.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2246
"
xml:space
="
preserve
">Hyperbolæ per eundem verticem ſimul adſcriptæ, æquale re-
<
lb
/>
ctum latus habentes ſunt inter ſe nunquam coeuntes, & </
s
>
<
s
xml:id
="
echoid-s2247
"
xml:space
="
preserve
">ſemper in-
<
lb
/>
ter ſe magis recedentes, & </
s
>
<
s
xml:id
="
echoid-s2248
"
xml:space
="
preserve
">in infinitum productæ ad interuallum
<
lb
/>
perueniunt maius quocunque dato interuallo.</
s
>
<
s
xml:id
="
echoid-s2249
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2250
"
xml:space
="
preserve
">SInt duæ Hyperbolæ ABC, DBE per eundem verticem B ſimul adſcriptę,
<
lb
/>
quarum rectumlatus ſit idem BF, tranſuerſum verò Hyperbolæ ABC
<
lb
/>
ſit minor recta BH, & </
s
>
<
s
xml:id
="
echoid-s2251
"
xml:space
="
preserve
">regula HF; </
s
>
<
s
xml:id
="
echoid-s2252
"
xml:space
="
preserve
">Hyperbolæ autem DBE ſit maior recta
<
lb
/>
BG eiuſque regula ſit GF: </
s
>
<
s
xml:id
="
echoid-s2253
"
xml:space
="
preserve
">dico primùm has inter ſe ſimul eſſe non coeuntes.</
s
>
<
s
xml:id
="
echoid-s2254
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2255
"
xml:space
="
preserve
">Cum enim Hyperbole DBE, maius habens trãſuerſum latus, inſcripta
<
note
symbol
="
a
"
position
="
left
"
xlink:label
="
note-0088-02
"
xlink:href
="
note-0088-02a
"
xml:space
="
preserve
">4. Corol.
<
lb
/>
19. huius.</
note
>
Hyperbolæ ABC, patet ipſas, licet in infinitum producantur, nunquam in-
<
lb
/>
ter ſe conuenire, vnde erunt ſimul non coeuntes.</
s
>
<
s
xml:id
="
echoid-s2256
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2257
"
xml:space
="
preserve
">Iam dico ipſas eſſe ſimul ſemper recedentes. </
s
>
<
s
xml:id
="
echoid-s2258
"
xml:space
="
preserve
">Applicatis enim duabus
<
lb
/>
quibuſcunque rectis CEILM, PONQR, iungatur quoque FN rectam MI
<
lb
/>
ſecans in S. </
s
>
<
s
xml:id
="
echoid-s2259
"
xml:space
="
preserve
">Cum ſit LS minor LI habebit ML ad L S maiorem rationem
<
lb
/>
quàm ML ad LI, & </
s
>
<
s
xml:id
="
echoid-s2260
"
xml:space
="
preserve
">componendo MS ad SL, ſiue RN ad NQ, hoc eſt
<
note
symbol
="
b
"
position
="
left
"
xlink:label
="
note-0088-03
"
xlink:href
="
note-0088-03a
"
xml:space
="
preserve
">4. Co-
<
lb
/>
roll. prop.
<
lb
/>
19. huius.</
note
>
dratum PN ad NO, habebit maiorem rationem, quàm MI ad IL, hoc
<
note
symbol
="
c
"
position
="
left
"
xlink:label
="
note-0088-04
"
xlink:href
="
note-0088-04a
"
xml:space
="
preserve
">ibidem.</
note
>
quàm quadratum CI ad IE, ſiue applicata PN ad NO maiorem habebit ra-
<
lb
/>
tionem quàm applicata CI ad IE: </
s
>
<
s
xml:id
="
echoid-s2261
"
xml:space
="
preserve
">ſi ergo fiat vt PN ad NO, ita CI ad IT,
<
lb
/>
habebit CI ad IT maiorem rationem quàm CI ad IE, ergo IT erit minor IE,
<
lb
/>
ideoque CT maior CE: </
s
>
<
s
xml:id
="
echoid-s2262
"
xml:space
="
preserve
">cumque ſit PN ad NO vt CI ad IT, erit per conuer-
<
lb
/>
ſionem rationis, & </
s
>
<
s
xml:id
="
echoid-s2263
"
xml:space
="
preserve
">permutando PN ad CI vt PO ad CT, ſed eſt PN
<
note
symbol
="
d
"
position
="
left
"
xlink:label
="
note-0088-05
"
xlink:href
="
note-0088-05a
"
xml:space
="
preserve
">32. h.</
note
>
CI; </
s
>
<
s
xml:id
="
echoid-s2264
"
xml:space
="
preserve
">quare PO maior erit ipſa CT, eſtque CT maior CE, ergo PO </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>