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
>
11
12
13
14
15
16
17
18
19
20
<
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
|<
<
(17)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div44
"
type
="
section
"
level
="
1
"
n
="
30
">
<
pb
o
="
17
"
file
="
0037
"
n
="
37
"
rhead
="
"/>
</
div
>
<
div
xml:id
="
echoid-div48
"
type
="
section
"
level
="
1
"
n
="
31
">
<
head
xml:id
="
echoid-head36
"
xml:space
="
preserve
">PROBL. IV. PROP. VI.</
head
>
<
p
>
<
s
xml:id
="
echoid-s672
"
xml:space
="
preserve
">Data in quodam plano recta linea terminata, quæ ad alteram
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0037-01
"
xlink:href
="
note-0037-01a
"
xml:space
="
preserve
">Prop. 53.
<
lb
/>
primico-
<
lb
/>
nic.</
note
>
partem in infinitum producatur: </
s
>
<
s
xml:id
="
echoid-s673
"
xml:space
="
preserve
">inuenire in dato plano coni-ſe-
<
lb
/>
ctionem, quę dicitur Hyperbole, cuius diameter ſit producta linea,
<
lb
/>
vertex eius terminus, tranſuerſum latus ſit data linea terminata, re-
<
lb
/>
ctum verò ſit alia quæcunque data linea finita, & </
s
>
<
s
xml:id
="
echoid-s674
"
xml:space
="
preserve
">ad ipſius diametr@
<
lb
/>
ordinatim ductæ efficiant angulos dato angulo æquales.</
s
>
<
s
xml:id
="
echoid-s675
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s676
"
xml:space
="
preserve
">SInt datæ rectæ lineæ terminatæ AB, BC, quæ in ſubiecto plano ad angu-
<
lb
/>
lum ABC, dato angulo P æqualem conſtituantur, & </
s
>
<
s
xml:id
="
echoid-s677
"
xml:space
="
preserve
">harum altera AB
<
lb
/>
ſit vtcunque producta ad BD: </
s
>
<
s
xml:id
="
echoid-s678
"
xml:space
="
preserve
">oportet in ſubiecto plano Hyperbolen deſcri-
<
lb
/>
bere, cuius diameter ſit BD, vertex B, tranſuerſum latus AB rectum BC, & </
s
>
<
s
xml:id
="
echoid-s679
"
xml:space
="
preserve
">
<
lb
/>
ordinatim ductæ ad diametrō BD conſtituant angulos, dato, angulo P æquales.</
s
>
<
s
xml:id
="
echoid-s680
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s681
"
xml:space
="
preserve
">Iungatur AC, & </
s
>
<
s
xml:id
="
echoid-s682
"
xml:space
="
preserve
">producatur, ſu-
<
lb
/>
<
figure
xlink:label
="
fig-0037-01
"
xlink:href
="
fig-0037-01a
"
number
="
14
">
<
image
file
="
0037-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0037-01
"/>
</
figure
>
maturq; </
s
>
<
s
xml:id
="
echoid-s683
"
xml:space
="
preserve
">in BD quodlibet punctum
<
lb
/>
D, per quod agatur in ſubiecto pla-
<
lb
/>
no recta linea DE ipſi BC parallela,
<
lb
/>
à qua, hinc inde producta, deman-
<
lb
/>
tur partes DF, DG, quæ ſint mediæ
<
lb
/>
proportionales inter BD, & </
s
>
<
s
xml:id
="
echoid-s684
"
xml:space
="
preserve
">DE; </
s
>
<
s
xml:id
="
echoid-s685
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s686
"
xml:space
="
preserve
">
<
lb
/>
per rectam FG intelligatur planum
<
lb
/>
IFHG, diuerſum à plano, quod per
<
lb
/>
AD, & </
s
>
<
s
xml:id
="
echoid-s687
"
xml:space
="
preserve
">FG tranſit, quorum cõmunis
<
lb
/>
ſectio ſit recta FG, cui per D in pla-
<
lb
/>
no IFHG perpendicularis ducatur
<
lb
/>
IDH, in qua, ad partes I, ſumptum
<
lb
/>
ſit quodcunque punctum I, & </
s
>
<
s
xml:id
="
echoid-s688
"
xml:space
="
preserve
">fiat vt
<
lb
/>
ID ad DF, ita DF ad DH; </
s
>
<
s
xml:id
="
echoid-s689
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s690
"
xml:space
="
preserve
">erit re-
<
lb
/>
ctangulum IDH æquale quadrato DF, uel
<
gap
/>
quadrato DG, ſed rectæ IH, FG ſe
<
lb
/>
mutuò ſecant ad rectos angulos in D, quare ſi circa IH circulus deſeribatur,
<
lb
/>
tranſibit ipſe per puncta FG. </
s
>
<
s
xml:id
="
echoid-s691
"
xml:space
="
preserve
">Tandem iungatur HA, & </
s
>
<
s
xml:id
="
echoid-s692
"
xml:space
="
preserve
">IB producatur ſe-
<
lb
/>
cans AH in L, & </
s
>
<
s
xml:id
="
echoid-s693
"
xml:space
="
preserve
">intelligatur conus cuius vertex L, baſis circulus I H, & </
s
>
<
s
xml:id
="
echoid-s694
"
xml:space
="
preserve
">cõ-
<
lb
/>
munis ſectio ſuperficiei conicæ cum ſubiecto plano ſit linea FMBNG. </
s
>
<
s
xml:id
="
echoid-s695
"
xml:space
="
preserve
">Dico
<
lb
/>
hanc eſſe quæſitam Hyperbolen.</
s
>
<
s
xml:id
="
echoid-s696
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s697
"
xml:space
="
preserve
">Conus enim LIH, cuius vertex L, & </
s
>
<
s
xml:id
="
echoid-s698
"
xml:space
="
preserve
">diameter baſis, I H, plano per axem
<
lb
/>
ſecatur triangulum facient LIH, & </
s
>
<
s
xml:id
="
echoid-s699
"
xml:space
="
preserve
">ſecatur altero plano (quod eſt datum pla-
<
lb
/>
num ſubiectum) ſecante baſim coni ſecundum rectam lineam F G, quæ ad
<
lb
/>
IH baſim trianguli per axem, eſt perpendicularis, & </
s
>
<
s
xml:id
="
echoid-s700
"
xml:space
="
preserve
">communis ſectio ſubie-
<
lb
/>
cti plani, & </
s
>
<
s
xml:id
="
echoid-s701
"
xml:space
="
preserve
">trianguli per axem, hoc eſt DB, producta ad B conuenit cum al-
<
lb
/>
tero latere HL extra verticem producto in puncto A, erit, per primam hu-
<
lb
/>
ius, ſectio FBG Hyperbole, cuius vertex B, diameter BD, & </
s
>
<
s
xml:id
="
echoid-s702
"
xml:space
="
preserve
">ordinatim du-
<
lb
/>
ctæ FG cum diametro BD, ad angulum FDB, angulo CBA, ſeu dato P æ-
<
lb
/>
qualem applicantur, ex conſtructione. </
s
>
<
s
xml:id
="
echoid-s703
"
xml:space
="
preserve
">Cumque factum ſit vt BD, ad DF
<
lb
/>
ita DF ad DE, erit rectangulum EDB æquale quadrato DF, ſiue </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>