Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of handwritten notes
<
1 - 2
[out of range]
>
<
1 - 2
[out of range]
>
page
|<
<
(440)
of 568
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div188
"
type
="
section
"
level
="
1
"
n
="
90
">
<
p
>
<
s
xml:id
="
echoid-s3509
"
xml:space
="
preserve
">
<
pb
o
="
440
"
file
="
0158
"
n
="
167
"
rhead
="
VERA CIRCULI
"/>
eadem F major eſt. </
s
>
<
s
xml:id
="
echoid-s3510
"
xml:space
="
preserve
">eadem modo utramque ſeriem in infini-
<
lb
/>
tum continuando, ſemper demonſtratur terminum quemlibet
<
lb
/>
ſeriei A B, C D, minorem eſſe quam idem numero terminus
<
lb
/>
ſeriei. </
s
>
<
s
xml:id
="
echoid-s3511
"
xml:space
="
preserve
">A B, G H; </
s
>
<
s
xml:id
="
echoid-s3512
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3513
"
xml:space
="
preserve
">igitur terminatio ſeriei A B, C D, nem-
<
lb
/>
pe Z minor erit terminatione ſeriei A B, G H, nempe X;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3514
"
xml:space
="
preserve
">atque ex hujus 7, terminatio ſeriei A B, G H, ſeu X æqua-
<
lb
/>
lis eſt majori duarum mediarum arithmeticè continuè propor-
<
lb
/>
tionalium inter A & </
s
>
<
s
xml:id
="
echoid-s3515
"
xml:space
="
preserve
">B, & </
s
>
<
s
xml:id
="
echoid-s3516
"
xml:space
="
preserve
">ideo Z eadem minor eſt, quod
<
lb
/>
demonſtrandum erat.</
s
>
<
s
xml:id
="
echoid-s3517
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div190
"
type
="
section
"
level
="
1
"
n
="
91
">
<
head
xml:id
="
echoid-head127
"
xml:space
="
preserve
">PROP. XXII. THEOREMA.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3518
"
xml:space
="
preserve
">IIsdem poſitis quæ ſupra; </
s
>
<
s
xml:id
="
echoid-s3519
"
xml:space
="
preserve
">dico Z
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0158-01
"
xlink:href
="
note-0158-01a
"
xml:space
="
preserve
">
<
lb
/>
A B # A B
<
lb
/>
C D # G H
<
lb
/>
E F # M N
<
lb
/>
K L # O P
<
lb
/>
Z # X
<
lb
/>
</
note
>
ſeu ſectorem circuli vel ellipſeos
<
lb
/>
minorem eſſe quam major duarum
<
lb
/>
mediarum geometricè continuè pro-
<
lb
/>
portionalium inter A & </
s
>
<
s
xml:id
="
echoid-s3520
"
xml:space
="
preserve
">B. </
s
>
<
s
xml:id
="
echoid-s3521
"
xml:space
="
preserve
">inter A
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s3522
"
xml:space
="
preserve
">B ſit media geometrica G, & </
s
>
<
s
xml:id
="
echoid-s3523
"
xml:space
="
preserve
">inter
<
lb
/>
G & </
s
>
<
s
xml:id
="
echoid-s3524
"
xml:space
="
preserve
">B ſit media geometrica H; </
s
>
<
s
xml:id
="
echoid-s3525
"
xml:space
="
preserve
">Item
<
lb
/>
inter G & </
s
>
<
s
xml:id
="
echoid-s3526
"
xml:space
="
preserve
">H media Geometrica M, & </
s
>
<
s
xml:id
="
echoid-s3527
"
xml:space
="
preserve
">inter M & </
s
>
<
s
xml:id
="
echoid-s3528
"
xml:space
="
preserve
">H media Geo-
<
lb
/>
metrica N; </
s
>
<
s
xml:id
="
echoid-s3529
"
xml:space
="
preserve
">continuetúrque hæc ſeries convergens A B, G H,
<
lb
/>
M N, O P, &</
s
>
<
s
xml:id
="
echoid-s3530
"
xml:space
="
preserve
">c, in infinitum, ut fiat ejus terminatio X. </
s
>
<
s
xml:id
="
echoid-s3531
"
xml:space
="
preserve
">ſatis
<
lb
/>
patet ex prædictis C & </
s
>
<
s
xml:id
="
echoid-s3532
"
xml:space
="
preserve
">G eſſe inter ſe æquales, item H majorem
<
lb
/>
eſſe quam D; </
s
>
<
s
xml:id
="
echoid-s3533
"
xml:space
="
preserve
">atque ob hanc rationem M media Geometrica in-
<
lb
/>
ter G & </
s
>
<
s
xml:id
="
echoid-s3534
"
xml:space
="
preserve
">H major eſt quam E media geometrica inter G & </
s
>
<
s
xml:id
="
echoid-s3535
"
xml:space
="
preserve
">D.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3536
"
xml:space
="
preserve
">deinde N media Geometrica inter M & </
s
>
<
s
xml:id
="
echoid-s3537
"
xml:space
="
preserve
">H major eſt media har-
<
lb
/>
monica inter easdem; </
s
>
<
s
xml:id
="
echoid-s3538
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3539
"
xml:space
="
preserve
">quoniam M major eſt quam E & </
s
>
<
s
xml:id
="
echoid-s3540
"
xml:space
="
preserve
">H
<
lb
/>
major quam D, erit media harmonica inter M & </
s
>
<
s
xml:id
="
echoid-s3541
"
xml:space
="
preserve
">H major quam
<
lb
/>
F media harmonica inter E & </
s
>
<
s
xml:id
="
echoid-s3542
"
xml:space
="
preserve
">D; </
s
>
<
s
xml:id
="
echoid-s3543
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3544
"
xml:space
="
preserve
">ideo N media Geometrica
<
lb
/>
inter M & </
s
>
<
s
xml:id
="
echoid-s3545
"
xml:space
="
preserve
">H major erit quam F. </
s
>
<
s
xml:id
="
echoid-s3546
"
xml:space
="
preserve
">eadem methodo utramque
<
lb
/>
ſeriem in infinitum continuando ſemper demonſtratur termi-
<
lb
/>
num quemlibet ſeriei A B, C D, minorem eſſe quam idem
<
lb
/>
numero terminus ſeriei A B, G H; </
s
>
<
s
xml:id
="
echoid-s3547
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3548
"
xml:space
="
preserve
">igitur terminatio ſeriei
<
lb
/>
A B, C D, nempe Z minor erit terminatione ſeriei A B,
<
lb
/>
G H, nempè X; </
s
>
<
s
xml:id
="
echoid-s3549
"
xml:space
="
preserve
">atque ex hujus 9 terminatio ſeriei A B,
<
lb
/>
G H, ſeu X, æqualis eſt majori duarum mediarum Geometri-
<
lb
/>
cè continuè proportionalium inter A & </
s
>
<
s
xml:id
="
echoid-s3550
"
xml:space
="
preserve
">B; </
s
>
<
s
xml:id
="
echoid-s3551
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3552
"
xml:space
="
preserve
">ideo Z eadem
<
lb
/>
minor eſt, quod demonſtrare oportuit.</
s
>
<
s
xml:id
="
echoid-s3553
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>