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
page
|<
<
(439)
of 568
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div186
"
type
="
section
"
level
="
1
"
n
="
89
">
<
p
>
<
s
xml:id
="
echoid-s3462
"
xml:space
="
preserve
">
<
pb
o
="
439
"
file
="
0157
"
n
="
166
"
rhead
="
ET HYPERBOLÆ QUADRATURA.
"/>
ceſſus K ſupra E major exceſſus H ſupra G; </
s
>
<
s
xml:id
="
echoid-s3463
"
xml:space
="
preserve
">cumque E ma-
<
lb
/>
jor ſit quam G, manifeſtum eſt K majorem eſſe quam H:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3464
"
xml:space
="
preserve
">eodem prorſus modo demonſtratur in omni ſerierum A, C,
<
lb
/>
E; </
s
>
<
s
xml:id
="
echoid-s3465
"
xml:space
="
preserve
">A, C, G, continuatione, terminum quemcunque ſeriei
<
lb
/>
A, C, E, majorem eſſe quam idem numero terminus ſeriei
<
lb
/>
A, C, G; </
s
>
<
s
xml:id
="
echoid-s3466
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3467
"
xml:space
="
preserve
">ideo terminatio ſeriei A, C, E, nempe Z ma-
<
lb
/>
jor erit terminatione ſeriei A, C, G, nempe X, at ex Archi-
<
lb
/>
medis quadratura parabloæ conſtat X æqualem eſſe ipſi C
<
lb
/>
una cum triente exceſſus C ſupra A, & </
s
>
<
s
xml:id
="
echoid-s3468
"
xml:space
="
preserve
">proinde Z eadem
<
lb
/>
major eſt, quod demonſtrare oportuit.</
s
>
<
s
xml:id
="
echoid-s3469
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div188
"
type
="
section
"
level
="
1
"
n
="
90
">
<
head
xml:id
="
echoid-head126
"
xml:space
="
preserve
">PROP. XXI. THEOREMA.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3470
"
xml:space
="
preserve
">IIsdem poſitis quæ ſupra; </
s
>
<
s
xml:id
="
echoid-s3471
"
xml:space
="
preserve
">dico Z
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0157-01
"
xlink:href
="
note-0157-01a
"
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 continuè proportionalium
<
lb
/>
arithmeticè inter A & </
s
>
<
s
xml:id
="
echoid-s3472
"
xml:space
="
preserve
">B. </
s
>
<
s
xml:id
="
echoid-s3473
"
xml:space
="
preserve
">inter A & </
s
>
<
s
xml:id
="
echoid-s3474
"
xml:space
="
preserve
">
<
lb
/>
B ſit media Arithmetica G, & </
s
>
<
s
xml:id
="
echoid-s3475
"
xml:space
="
preserve
">inter
<
lb
/>
G & </
s
>
<
s
xml:id
="
echoid-s3476
"
xml:space
="
preserve
">B ſit media Arithmetica H; </
s
>
<
s
xml:id
="
echoid-s3477
"
xml:space
="
preserve
">item
<
lb
/>
inter G & </
s
>
<
s
xml:id
="
echoid-s3478
"
xml:space
="
preserve
">H ſit media Arithmetica M, & </
s
>
<
s
xml:id
="
echoid-s3479
"
xml:space
="
preserve
">inter M & </
s
>
<
s
xml:id
="
echoid-s3480
"
xml:space
="
preserve
">H ſed me-
<
lb
/>
dia Arithmetica N; </
s
>
<
s
xml:id
="
echoid-s3481
"
xml:space
="
preserve
">continueturque hæc ſeries convergens A B,
<
lb
/>
G H, M N, O P, in infinitum, ut fiat ejus terminatio X. </
s
>
<
s
xml:id
="
echoid-s3482
"
xml:space
="
preserve
">ſatis
<
lb
/>
pater ex prædictis G majorem eſſe quam C, atque H media
<
lb
/>
Arithmetica inter G & </
s
>
<
s
xml:id
="
echoid-s3483
"
xml:space
="
preserve
">B major eſt media harmonica inter eas-
<
lb
/>
dem G, B; </
s
>
<
s
xml:id
="
echoid-s3484
"
xml:space
="
preserve
">media autem harmonica inter G & </
s
>
<
s
xml:id
="
echoid-s3485
"
xml:space
="
preserve
">B major eſt quam
<
lb
/>
D media harmonica inter C & </
s
>
<
s
xml:id
="
echoid-s3486
"
xml:space
="
preserve
">B, quoniam G major eſt quam
<
lb
/>
C; </
s
>
<
s
xml:id
="
echoid-s3487
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3488
"
xml:space
="
preserve
">ideo media Arithmetica inter G & </
s
>
<
s
xml:id
="
echoid-s3489
"
xml:space
="
preserve
">B, hoc eſt H, major
<
lb
/>
eſt quam D media harmonica inter C & </
s
>
<
s
xml:id
="
echoid-s3490
"
xml:space
="
preserve
">B. </
s
>
<
s
xml:id
="
echoid-s3491
"
xml:space
="
preserve
">eodem modo M
<
lb
/>
media arithmetica inter G & </
s
>
<
s
xml:id
="
echoid-s3492
"
xml:space
="
preserve
">H major eſt media geometrica
<
lb
/>
inter easdem G & </
s
>
<
s
xml:id
="
echoid-s3493
"
xml:space
="
preserve
">H: </
s
>
<
s
xml:id
="
echoid-s3494
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3495
"
xml:space
="
preserve
">quoniam G eſt major quam C, & </
s
>
<
s
xml:id
="
echoid-s3496
"
xml:space
="
preserve
">
<
lb
/>
H quam D; </
s
>
<
s
xml:id
="
echoid-s3497
"
xml:space
="
preserve
">media geometrica inter G & </
s
>
<
s
xml:id
="
echoid-s3498
"
xml:space
="
preserve
">H major eſt quam
<
lb
/>
E media geometrica inter C & </
s
>
<
s
xml:id
="
echoid-s3499
"
xml:space
="
preserve
">D; </
s
>
<
s
xml:id
="
echoid-s3500
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3501
"
xml:space
="
preserve
">proinde M major
<
lb
/>
eſt quam E. </
s
>
<
s
xml:id
="
echoid-s3502
"
xml:space
="
preserve
">deinde N media arithmetica inter M & </
s
>
<
s
xml:id
="
echoid-s3503
"
xml:space
="
preserve
">H ma-
<
lb
/>
jor eſt media harmonica inter eaſdem, & </
s
>
<
s
xml:id
="
echoid-s3504
"
xml:space
="
preserve
">quoniam H major
<
lb
/>
eſt quam D & </
s
>
<
s
xml:id
="
echoid-s3505
"
xml:space
="
preserve
">M quam E, media harmonica inter M & </
s
>
<
s
xml:id
="
echoid-s3506
"
xml:space
="
preserve
">H
<
lb
/>
major eſt quam F media harmonica inter E & </
s
>
<
s
xml:id
="
echoid-s3507
"
xml:space
="
preserve
">D; </
s
>
<
s
xml:id
="
echoid-s3508
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3509
"
xml:space
="
preserve
">ideo </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>