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
>
51
(31)
52
(32)
53
(33)
54
(34)
55
(35)
56
(36)
57
(37)
58
(38)
59
60
<
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
|<
<
(31)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div87
"
type
="
section
"
level
="
1
"
n
="
53
">
<
p
>
<
s
xml:id
="
echoid-s1088
"
xml:space
="
preserve
">
<
pb
o
="
31
"
file
="
0051
"
n
="
51
"
rhead
="
"/>
curuis AB, DE; </
s
>
<
s
xml:id
="
echoid-s1089
"
xml:space
="
preserve
">diametris BG, EH; </
s
>
<
s
xml:id
="
echoid-s1090
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1091
"
xml:space
="
preserve
">ſemi-applicatis AG, DH compre-
<
lb
/>
henſis, nempe trilineum ABG ad CBG, eſſe vt baſis AG ad GC, ſib æqua-
<
lb
/>
lem; </
s
>
<
s
xml:id
="
echoid-s1092
"
xml:space
="
preserve
">ac propterea diametrum BG Parabolen ABC bifariam ſecare; </
s
>
<
s
xml:id
="
echoid-s1093
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1094
"
xml:space
="
preserve
">vnũ-
<
lb
/>
quodque trilineorum eſſe ſemi-Parabolen; </
s
>
<
s
xml:id
="
echoid-s1095
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1096
"
xml:space
="
preserve
">ſemi-Parabolen ABG ad ſe-
<
lb
/>
mi-Parabolen DEH æqualis altitudinis, eſſe vt baſis AG ad baſim DH, & </
s
>
<
s
xml:id
="
echoid-s1097
"
xml:space
="
preserve
">
<
lb
/>
integram ABC ad dimidiam DEH eſſe vt baſis AC ad ſemi-baſim DH.</
s
>
<
s
xml:id
="
echoid-s1098
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div88
"
type
="
section
"
level
="
1
"
n
="
54
">
<
head
xml:id
="
echoid-head59
"
xml:space
="
preserve
">THEOR. VII. PROP. XV.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1099
"
xml:space
="
preserve
">Parabolæ æqualium baſium ſunt inter ſe vt altitudines.</
s
>
<
s
xml:id
="
echoid-s1100
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1101
"
xml:space
="
preserve
">SInt primò duæ Parabolæ ABC, ABC ſuper eandem baſim AC, & </
s
>
<
s
xml:id
="
echoid-s1102
"
xml:space
="
preserve
">circa
<
lb
/>
eandem diametrum BE. </
s
>
<
s
xml:id
="
echoid-s1103
"
xml:space
="
preserve
">Dico has eſſe inter ſe vt earum altitudines FA,
<
lb
/>
GA; </
s
>
<
s
xml:id
="
echoid-s1104
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1105
"
xml:space
="
preserve
">quod de ſemi-Parabolis EBC, EDC demonſtrabitur, idem inſe-
<
lb
/>
quetur de duplis.</
s
>
<
s
xml:id
="
echoid-s1106
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1107
"
xml:space
="
preserve
">Si enim non eſt vt FA
<
lb
/>
<
figure
xlink:label
="
fig-0051-01
"
xlink:href
="
fig-0051-01a
"
number
="
28
">
<
image
file
="
0051-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0051-01
"/>
</
figure
>
ad AG, ita ſemi-Parabo-
<
lb
/>
le EBC ad EDC, erit al-
<
lb
/>
tera ipſarum minor quàm
<
lb
/>
ſit opus ad hoc vt ſint pro-
<
lb
/>
portionales altitudinibus
<
lb
/>
FA, AG, ſitque, ſi poſſi-
<
lb
/>
bile eſt, minor EBC de-
<
lb
/>
fectu R, & </
s
>
<
s
xml:id
="
echoid-s1108
"
xml:space
="
preserve
">bifariam ſecta
<
lb
/>
EC in H, & </
s
>
<
s
xml:id
="
echoid-s1109
"
xml:space
="
preserve
">iterum EH
<
lb
/>
bifariam in I, &</
s
>
<
s
xml:id
="
echoid-s1110
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s1111
"
xml:space
="
preserve
">circum-
<
lb
/>
ſcribatur, vt in pręceden-
<
lb
/>
ti, trilineo ſemi-Parabo-
<
lb
/>
læ ECB figura BLCE ex
<
lb
/>
parallelogrammis ęque
<
lb
/>
altis conſtans, cuius ex-
<
lb
/>
ceſſus ſupra ſemi-Parabolen ſit minor R, ita vt ipſa circumſcripta figura
<
lb
/>
BLCE ad ſemi-Parabolen EDC adhuc minorem habeat rationem quàm
<
lb
/>
altitudo FA ad AG; </
s
>
<
s
xml:id
="
echoid-s1112
"
xml:space
="
preserve
">quo facto, ſemi-Parabolæ quoque EDC per æquidi-
<
lb
/>
ſtantium diametro interſectionem altera circumſcribatur figura DMNCE
<
lb
/>
ex totidem Parallelogrammis æque altis, &</
s
>
<
s
xml:id
="
echoid-s1113
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s1114
"
xml:space
="
preserve
">Et cum ſir ob Parabolas, re-
<
lb
/>
cta BE ad OI, vt rectangulum AEC ad AIC, vel vt DE ad PI, erit permu-
<
lb
/>
tando BE ad ED, vel parallelogrammum BI ad DI, vt OI ad IP, vel vt pa-
<
lb
/>
rallelogrammum OH, ad PH, & </
s
>
<
s
xml:id
="
echoid-s1115
"
xml:space
="
preserve
">ſic de reliquis circumſcriptæ BL CE, ad re-
<
lb
/>
liqua circumſcriptæ DMCE, ſingula ſingulis, quare vniuerſa circumſcripta
<
lb
/>
ALCE ad vniuerſam DMCE, erit vt vnum parallelogrammum BI ad vnum
<
lb
/>
DI, vel vt baſis BE ad ED, vel vt FA ad AG, ſed FA ad AG habet maiorem
<
lb
/>
rationem quàm circumſcripta ALCE ad ſemi-Parabolen EDC; </
s
>
<
s
xml:id
="
echoid-s1116
"
xml:space
="
preserve
">quare cir-
<
lb
/>
cumſcripta ALCE ad circumſcriptam DMCE, habebit maiorem rationem
<
lb
/>
quàm ad ſemi-Parabolen EDC, vnde circumſcripta DMCE minor erit in-
<
lb
/>
ſcripta ſemi-Parabola EDC; </
s
>
<
s
xml:id
="
echoid-s1117
"
xml:space
="
preserve
">totum parte, quod eſt abſurdum. </
s
>
<
s
xml:id
="
echoid-s1118
"
xml:space
="
preserve
">Non datur
<
lb
/>
ergo inter has ſemi-Parabolas minor quàm ſit opus, ad hoc vt ipſæ ſint </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>