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
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 - 347
>
Scan
Original
21
1
22
2
23
3
24
4
25
5
26
6
27
7
28
8
29
9
30
10
31
11
32
12
33
13
34
14
35
15
36
16
37
17
38
18
39
19
40
20
41
21
42
22
43
23
44
24
45
25
46
26
47
27
48
28
49
29
50
30
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 347
>
page
|<
<
(62)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div201
"
type
="
section
"
level
="
1
"
n
="
94
">
<
p
style
="
it
">
<
s
xml:id
="
echoid-s2180
"
xml:space
="
preserve
">
<
pb
o
="
62
"
file
="
0086
"
n
="
86
"
rhead
="
"/>
noſtræ æquidiſtantium portiones non ſint MINIMAE, quæ à punctis alterutrius
<
lb
/>
ſectionis ſuper aliam educi queant: </
s
>
<
s
xml:id
="
echoid-s2181
"
xml:space
="
preserve
">unde ob hoc Hieronymum Cardanum aſſectari
<
lb
/>
nos debuiſſe, qui iuxta perpendiculares à punctis hyperbolicæ ſectionis ſuper aſym-
<
lb
/>
pton ductas, ipſarum linearum interualla meditatus eſt; </
s
>
<
s
xml:id
="
echoid-s2182
"
xml:space
="
preserve
">quod nullos alios, admi-
<
lb
/>
randum Apollonij hoc Theorema diſcutientes, animaduerſos fuiſſe, idem Barocius
<
lb
/>
in ſuo quodam commentario Geometrico ſæpiùs admonuit, inter alia hæc proferens;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2183
"
xml:space
="
preserve
">_quem errorem, omnes quos vidihuius rei Auctores commiſerunt, præter Car-_
<
lb
/>
_danum_. </
s
>
<
s
xml:id
="
echoid-s2184
"
xml:space
="
preserve
">Sed bùc tã bonum Virum edoctum velimus, hoc idem iamdiu nobis innotuiſſe,
<
lb
/>
verùm deditaopera, æ libenter in hoc deſicere nobis placuiſſe cum ſummis Viris, qua-
<
lb
/>
les, eos inter quos maximè colimus, ſunt Torricellius, & </
s
>
<
s
xml:id
="
echoid-s2185
"
xml:space
="
preserve
">Gregorius à S. </
s
>
<
s
xml:id
="
echoid-s2186
"
xml:space
="
preserve
">Vincentio,
<
lb
/>
immo ipſemet Apollonius tam reconditi ſymptomatis fortaſſe primus, & </
s
>
<
s
xml:id
="
echoid-s2187
"
xml:space
="
preserve
">acutiſsimus
<
lb
/>
indagator. </
s
>
<
s
xml:id
="
echoid-s2188
"
xml:space
="
preserve
">Præterea, nos quoque ſatis agnouiſſe, vnius puncti diſtantiam à quacun-
<
lb
/>
que ſeu recta, ſeu curua linea, ſtrictim aſſumendam eſſe iuxta MINIMAM ex
<
lb
/>
eodem puncto, ſuper datam lineam eductam. </
s
>
<
s
xml:id
="
echoid-s2189
"
xml:space
="
preserve
">Inſuper ipſam MINIMAM d@m@ſſas
<
lb
/>
quel, datæ rectæ, vel contingenti ad datam curuam in puncto occurſus perpendicu-
<
lb
/>
lariter inſiſtetc quæ omnia hùc in proximo noſtro libello perſpicuè apparebunt: </
s
>
<
s
xml:id
="
echoid-s2190
"
xml:space
="
preserve
">at-
<
lb
/>
tamen hiſce, alijſque notionibus de his inſtructi, alteram methodum conſultò eli-
<
lb
/>
gere maluimus. </
s
>
<
s
xml:id
="
echoid-s2191
"
xml:space
="
preserve
">Itaquè ab humaniſsimo Barocio de hoc, cui ſanè criminis nomen
<
lb
/>
falsò tribuitur, veniam expectamus; </
s
>
<
s
xml:id
="
echoid-s2192
"
xml:space
="
preserve
">dum nos etiam, & </
s
>
<
s
xml:id
="
echoid-s2193
"
xml:space
="
preserve
">ſua, quæquæ ſint ab ipſo
<
lb
/>
ſparſim prolata reticere parati ſumus. </
s
>
<
s
xml:id
="
echoid-s2194
"
xml:space
="
preserve
">Interea concedat quæſo, vt ad inuentionem
<
lb
/>
MAXIMARVM MINIMARV Mque coni- ſectionum per diuerſos vertices inſcri-
<
lb
/>
ptibilium, aut circumſcriptibilium, vel ſaltim vt genio quodam noſtro indulgendo,
<
lb
/>
harum ſectionum diſtantias per æquidiſtantium interpoſita ſegmenta nobis perſcru-
<
lb
/>
tari liceat. </
s
>
<
s
xml:id
="
echoid-s2195
"
xml:space
="
preserve
">Perlegat inſuper, ſimulque has meditationes percipiat; </
s
>
<
s
xml:id
="
echoid-s2196
"
xml:space
="
preserve
">quod ſi ex hac
<
lb
/>
hypotheſi ipſas euidenter comprobatas inuenerit, fateatur, ſi lubet, nos abundè in
<
lb
/>
his Geometræ partem expleuiſſe; </
s
>
<
s
xml:id
="
echoid-s2197
"
xml:space
="
preserve
">ſin aliter, incuſatione dignos exiſtimet.</
s
>
<
s
xml:id
="
echoid-s2198
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s2199
"
xml:space
="
preserve
">Scias itaque, ac iterum ſcias candide Lector nos, tum in decima huius, tum
<
lb
/>
in ſuperioribus, ac deinceps, vbi de non coincidentibus lineis diſſerimus, harum inter-
<
lb
/>
ualla ſemper aſſumpſiſſe iuxta interiecta parallelarum ſegmenta, licet hoc ſæpenu-
<
lb
/>
mero prætermittatur, cum ex ipſo demonſtrationum proceſſu id ſatis ſuperque ſe in
<
lb
/>
conſpectum præbeat. </
s
>
<
s
xml:id
="
echoid-s2200
"
xml:space
="
preserve
">Zuod ſi ſubijciat Barocius, non quidem intercapedines à pun-
<
lb
/>
ctis vnius ad alteram coni- ſectionem, verùm longitudines tantùm illarum æqui-
<
lb
/>
diſtantium portionum ſic meditari; </
s
>
<
s
xml:id
="
echoid-s2201
"
xml:space
="
preserve
">illum æquiter ratiocinaſſe nos ipſi profectò fa-
<
lb
/>
tebimur, quamuis & </
s
>
<
s
xml:id
="
echoid-s2202
"
xml:space
="
preserve
">eædem parallelarum portiones verè dici poſsint diſtantiæ à
<
lb
/>
punctis vnius ſectionis ad aliam; </
s
>
<
s
xml:id
="
echoid-s2203
"
xml:space
="
preserve
">prout lineæ omnes, ab vno eodemque puncto duci-
<
lb
/>
biles, dicuntur interualla ab ipſo puncto ad eandem lineam, etiamſi eductæ inter
<
lb
/>
ſe plurimùm differant longitudine.</
s
>
<
s
xml:id
="
echoid-s2204
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s2205
"
xml:space
="
preserve
">Zuò verò ad methodum iuxta MINIMAS, plura ſunt, quæ à nobis huc eſſent
<
lb
/>
in medium afferenda, ſed non eſt cur in præſens futilem diſceptationem aggredia-
<
lb
/>
mur. </
s
>
<
s
xml:id
="
echoid-s2206
"
xml:space
="
preserve
">At ſi quis nos ad huius Pelagi traiectionem deuinctos cenſeret (quamuis præ-
<
lb
/>
ſtantiori fortaſſe luce orbati, nempe conica Apollonij ineditorum librorum doctri-
<
lb
/>
na) diuino tamen præſidio, noſtris quibuſdam inuentis mox huc edendis innixi, na-
<
lb
/>
ue integra ad portum appellere non dubitaremus; </
s
>
<
s
xml:id
="
echoid-s2207
"
xml:space
="
preserve
">ſed interim eum, non proprij of-
<
lb
/>
ficij cauſa, ſed pro ſua tantùm humanitate, nonnulla valde iucunda Problemata
<
lb
/>
enodanda recipere exoptaremus, quæ nobis circa nouam quandam meditationem
<
lb
/>
nuper aſſequi datum eſt. </
s
>
<
s
xml:id
="
echoid-s2208
"
xml:space
="
preserve
">Sed miſsis parergis rem iam ſuſceptam progrediamur.</
s
>
<
s
xml:id
="
echoid-s2209
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>