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
Table of Notes
<
1 - 14
[out of range]
>
[Note]
Page: 80
[Note]
Page: 80
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 83
[Note]
Page: 83
[Note]
Page: 83
[Note]
Page: 83
[Note]
Page: 83
<
1 - 14
[out of range]
>
page
|<
<
(57)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div699
"
type
="
section
"
level
="
1
"
n
="
279
">
<
p
>
<
s
xml:id
="
echoid-s6688
"
xml:space
="
preserve
">
<
pb
o
="
57
"
file
="
0241
"
n
="
241
"
rhead
="
"/>
ctiones contingentes, quæ productæ, communi diametro G B E
<
note
symbol
="
a
"
position
="
right
"
xlink:label
="
note-0241-01
"
xlink:href
="
note-0241-01a
"
xml:space
="
preserve
">24. 25.
<
lb
/>
primi co-
<
lb
/>
nic.</
note
>
in L, M. </
s
>
<
s
xml:id
="
echoid-s6689
"
xml:space
="
preserve
">Dico primùm G A ad A D eſſe vt G B ad B E, & </
s
>
<
s
xml:id
="
echoid-s6690
"
xml:space
="
preserve
">contingentes
<
lb
/>
A L, D L inter ſe æquidiſtare.</
s
>
<
s
xml:id
="
echoid-s6691
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6692
"
xml:space
="
preserve
">Applicentur ex A, D ad diametrum communem G B M rectę A I, D H.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6693
"
xml:space
="
preserve
">Erit iam in ſectione D E F, rectangulum G H M ad quadratum H D,
<
note
symbol
="
b
"
position
="
right
"
xlink:label
="
note-0241-02
"
xlink:href
="
note-0241-02a
"
xml:space
="
preserve
">37. ibid.</
note
>
tranſuerſum ad rectum, vel, ob ſectionum ſimilitudinem, vt tranſuerſum ſe-
<
lb
/>
ctionis A B C ad eius rectum, vel vt rectangulum G I L ad quadratum I A,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s6694
"
xml:space
="
preserve
">quadratum D H ad H G, eſt vt quadratum A I ad I G, ergo ex æquo
<
lb
/>
rectangulum G H M ad quadratum G H, erit vt rectangulum G I L ad qua-
<
lb
/>
dratum I G, & </
s
>
<
s
xml:id
="
echoid-s6695
"
xml:space
="
preserve
">conuertendo quadratum G H ad rectangulum G H M, vt
<
lb
/>
quadratum I G ad rectangulum G I L, & </
s
>
<
s
xml:id
="
echoid-s6696
"
xml:space
="
preserve
">per conuerſionem rationis in pri-
<
lb
/>
ma figura, & </
s
>
<
s
xml:id
="
echoid-s6697
"
xml:space
="
preserve
">componendo in ſecunda, quadratum G H ad rectangulum.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6698
"
xml:space
="
preserve
">
<
figure
xlink:label
="
fig-0241-01
"
xlink:href
="
fig-0241-01a
"
number
="
199
">
<
image
file
="
0241-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0241-01
"/>
</
figure
>
H G M, vt quadratum I G ad rectangulum I G L, & </
s
>
<
s
xml:id
="
echoid-s6699
"
xml:space
="
preserve
">permutando quadra-
<
lb
/>
tum H G ad G I, vel quadratum D G ad G A, erit vt rectangulum H G M
<
lb
/>
ad rectangulum I G L, vel permutatis æqualibus, vt quadratum E G
<
note
symbol
="
c
"
position
="
right
"
xlink:label
="
note-0241-03
"
xlink:href
="
note-0241-03a
"
xml:space
="
preserve
">ibidem.</
note
>
quadratum G B, ſeulinea D G ad G A, vt linea E G ad G B, & </
s
>
<
s
xml:id
="
echoid-s6700
"
xml:space
="
preserve
">diuiden-
<
lb
/>
do, & </
s
>
<
s
xml:id
="
echoid-s6701
"
xml:space
="
preserve
">conuertendo G A ad A D, vt G B ad B E. </
s
>
<
s
xml:id
="
echoid-s6702
"
xml:space
="
preserve
">Quod primò erat, &</
s
>
<
s
xml:id
="
echoid-s6703
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s6704
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6705
"
xml:space
="
preserve
">Præterea, cum ſuperiùs demonſtratum ſit eſſe rectangulum G H M ad
<
lb
/>
quadratum H D, vt rectangulum G I L ad quadratum I A, erit permutan-
<
lb
/>
do rectangulum G H M ad G I L, vt quadratum H D ad I A; </
s
>
<
s
xml:id
="
echoid-s6706
"
xml:space
="
preserve
">ſed propor-
<
lb
/>
tio quadrati H D ad I A componitur ex du@bus rationibus H D ad I A,
<
lb
/>
vel ex duobus rationibus H G ad G I, & </
s
>
<
s
xml:id
="
echoid-s6707
"
xml:space
="
preserve
">proportio rectanguli G H M ad
<
lb
/>
G I L componitur ex duobus rationibus, nempe ex G H ad G I, & </
s
>
<
s
xml:id
="
echoid-s6708
"
xml:space
="
preserve
">ex H M
<
lb
/>
ad I L; </
s
>
<
s
xml:id
="
echoid-s6709
"
xml:space
="
preserve
">ergo proportio G H ad G I, hoc eſt H D ad I A, æqualis eſt pro-
<
lb
/>
portioni H M ad I I.</
s
>
<
s
xml:id
="
echoid-s6710
"
xml:space
="
preserve
">, & </
s
>
<
s
xml:id
="
echoid-s6711
"
xml:space
="
preserve
">permutando D H ad H M, erit vt A I ad I L, &</
s
>
<
s
xml:id
="
echoid-s6712
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>