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
>
41
(21)
42
(22)
43
(23)
44
(24)
45
(25)
46
(26)
47
(27)
48
(28)
49
(29)
50
(30)
<
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
|<
<
(21)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div55
"
type
="
section
"
level
="
1
"
n
="
34
">
<
p
>
<
s
xml:id
="
echoid-s795
"
xml:space
="
preserve
">
<
pb
o
="
21
"
file
="
0041
"
n
="
41
"
rhead
="
"/>
plicetur NMO fectionem, ac diametrum ſecans in N, O.</
s
>
<
s
xml:id
="
echoid-s796
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s797
"
xml:space
="
preserve
">Quoniam igitur eodem pænitus argumento, quo ſuperius demonſtratum
<
lb
/>
eſt rectangulum AHB ad quadratum HI, eſſe vt quadratum CB ad BD, eſt
<
lb
/>
quoque rectangulum AOB ad quadratum ON, vt idem quadratum C B ad
<
lb
/>
BD, vel vt quadratum BO ad OM, erit permutando, rectangulum AOB ad
<
lb
/>
quadratum BO, vt quadratum NO ad OM, ſed rectangulum AOB ſuperat
<
lb
/>
quadratum BO, (exceſſus enim eſt rectangulum ABO) ergo & </
s
>
<
s
xml:id
="
echoid-s798
"
xml:space
="
preserve
">quadratum
<
lb
/>
NO, maius eſt quadrato MO; </
s
>
<
s
xml:id
="
echoid-s799
"
xml:space
="
preserve
">ſed punctum N eſt in ipſa ſectione, quare pun-
<
lb
/>
ctum M cadit intra: </
s
>
<
s
xml:id
="
echoid-s800
"
xml:space
="
preserve
">ideoque iuncta CM ſectionem prius ſecat. </
s
>
<
s
xml:id
="
echoid-s801
"
xml:space
="
preserve
">Non eſt ergo
<
lb
/>
altera aſymptotos, quæ diuidat angulum ab aſymptotis factum. </
s
>
<
s
xml:id
="
echoid-s802
"
xml:space
="
preserve
">Quod erat
<
lb
/>
ſecundò demonſtrandum.</
s
>
<
s
xml:id
="
echoid-s803
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div59
"
type
="
section
"
level
="
1
"
n
="
35
">
<
head
xml:id
="
echoid-head40
"
xml:space
="
preserve
">MONITVM.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s804
"
xml:space
="
preserve
">HIs itaque præoſtenſis, ipſarum ope, ac tertiæ ſecundi conico-
<
lb
/>
rum demonſtremus aliter decimam quartam eiuſdem, abſq;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s805
"
xml:space
="
preserve
">auxilio præcedentium 5. </
s
>
<
s
xml:id
="
echoid-s806
"
xml:space
="
preserve
">10. </
s
>
<
s
xml:id
="
echoid-s807
"
xml:space
="
preserve
">12. </
s
>
<
s
xml:id
="
echoid-s808
"
xml:space
="
preserve
">ac 13. </
s
>
<
s
xml:id
="
echoid-s809
"
xml:space
="
preserve
">quibus ipſa 14. </
s
>
<
s
xml:id
="
echoid-s810
"
xml:space
="
preserve
">in-
<
lb
/>
diget, præmiſſo tantum ſequenti Lemmate.</
s
>
<
s
xml:id
="
echoid-s811
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div60
"
type
="
section
"
level
="
1
"
n
="
36
">
<
head
xml:id
="
echoid-head41
"
xml:space
="
preserve
">LEMMA II. PROP. IX.</
head
>
<
p
>
<
s
xml:id
="
echoid-s812
"
xml:space
="
preserve
">Sit rectangulum ABD æquale quadrato BC. </
s
>
<
s
xml:id
="
echoid-s813
"
xml:space
="
preserve
">Dico addita qua-
<
lb
/>
cunque BE, rectangulum AED maius eſſe quadrato EC.</
s
>
<
s
xml:id
="
echoid-s814
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s815
"
xml:space
="
preserve
">CVm enim rectangulum ABD æquale ſit quadrato mediæ BC, erit AB
<
lb
/>
ad BC, vt BC ad BD, & </
s
>
<
s
xml:id
="
echoid-s816
"
xml:space
="
preserve
">diuidendo, & </
s
>
<
s
xml:id
="
echoid-s817
"
xml:space
="
preserve
">permutando AC ad CD, vt
<
lb
/>
<
figure
xlink:label
="
fig-0041-01
"
xlink:href
="
fig-0041-01a
"
number
="
17
">
<
image
file
="
0041-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0041-01
"/>
</
figure
>
CB ad BD. </
s
>
<
s
xml:id
="
echoid-s818
"
xml:space
="
preserve
">Et cum ſit DB minor
<
lb
/>
DE, habebit CD ad DB maiorem
<
lb
/>
rationem quam ad DE, & </
s
>
<
s
xml:id
="
echoid-s819
"
xml:space
="
preserve
">compo-
<
lb
/>
nendo CB ad BD, hoc eſt AC ad CD maiorem habebit rationem
<
note
symbol
="
a
"
position
="
right
"
xlink:label
="
note-0041-01
"
xlink:href
="
note-0041-01a
"
xml:space
="
preserve
">28. quin-
<
lb
/>
ti elem.</
note
>
CE ad ED, & </
s
>
<
s
xml:id
="
echoid-s820
"
xml:space
="
preserve
">permutando AC ad CE maiorem rationem quam CD
<
note
symbol
="
b
"
position
="
right
"
xlink:label
="
note-0041-02
"
xlink:href
="
note-0041-02a
"
xml:space
="
preserve
">27. quin-
<
lb
/>
ti elem.</
note
>
DE, & </
s
>
<
s
xml:id
="
echoid-s821
"
xml:space
="
preserve
">componendo AE ad EC maiorem quam EC ad ED. </
s
>
<
s
xml:id
="
echoid-s822
"
xml:space
="
preserve
">Si fiat ergo vt AE ad EC, ita EC ad EF, habebit quoque EC ad EF maiorem rationem
<
lb
/>
<
note
symbol
="
c
"
position
="
right
"
xlink:label
="
note-0041-03
"
xlink:href
="
note-0041-03a
"
xml:space
="
preserve
">28. quin-
<
lb
/>
ti elem.</
note
>
quam EC ad ED, vnde EF erit minor ED, ſed (cum factum ſit AE ad EC,
<
lb
/>
vt EC ad EF) rectangulum AEF æquale eſt quadrato EC, quare rectangu-
<
lb
/>
lum AED maius erit quadrato EC. </
s
>
<
s
xml:id
="
echoid-s823
"
xml:space
="
preserve
">Quod erat &</
s
>
<
s
xml:id
="
echoid-s824
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s825
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div62
"
type
="
section
"
level
="
1
"
n
="
37
">
<
head
xml:id
="
echoid-head42
"
xml:space
="
preserve
">THEOR. III. PROP. X.</
head
>
<
p
>
<
s
xml:id
="
echoid-s826
"
xml:space
="
preserve
">Aſymptoti, & </
s
>
<
s
xml:id
="
echoid-s827
"
xml:space
="
preserve
">ſectio in infinitum productæ ad ſe propius acce-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0041-04
"
xlink:href
="
note-0041-04a
"
xml:space
="
preserve
">Prop. 14.
<
lb
/>
ſec. con.</
note
>
dunt, & </
s
>
<
s
xml:id
="
echoid-s828
"
xml:space
="
preserve
">ad interuallum perueniunt minus quolibet dato interuallo.</
s
>
<
s
xml:id
="
echoid-s829
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s830
"
xml:space
="
preserve
">SIt Hyperbole, cuius aſymptoti CD, CE, & </
s
>
<
s
xml:id
="
echoid-s831
"
xml:space
="
preserve
">datum interuallum ſit M.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s832
"
xml:space
="
preserve
">Dico aſymptotos CD, CE, & </
s
>
<
s
xml:id
="
echoid-s833
"
xml:space
="
preserve
">ſectionem productas, ad ſe ſe propius
<
lb
/>
accedere, & </
s
>
<
s
xml:id
="
echoid-s834
"
xml:space
="
preserve
">ad interuallum peruenire minus dato interuallo M.</
s
>
<
s
xml:id
="
echoid-s835
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>