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
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 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 540
541 - 550
551 - 560
561 - 568
>
161
(434)
162
(435)
163
(436)
164
(437)
165
(438)
166
(439)
167
(440)
168
(441)
169
(442)
170
(443)
<
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 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 540
541 - 550
551 - 560
561 - 568
>
page
|<
<
(443)
of 568
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div195
"
type
="
section
"
level
="
1
"
n
="
94
">
<
p
>
<
s
xml:id
="
echoid-s3623
"
xml:space
="
preserve
">
<
pb
o
="
443
"
file
="
0161
"
n
="
170
"
rhead
="
ET HYPERBOLÆ QUADRATURA.
"/>
G H, nempe X; </
s
>
<
s
xml:id
="
echoid-s3624
"
xml:space
="
preserve
">atque ex hujus 7 terminatio ſeriei A B,
<
lb
/>
G H, nempe X, æqualis eſt minori duarum mediarum arith-
<
lb
/>
meticè continuè proportionalium inter A & </
s
>
<
s
xml:id
="
echoid-s3625
"
xml:space
="
preserve
">B, & </
s
>
<
s
xml:id
="
echoid-s3626
"
xml:space
="
preserve
">ideo Z ea-
<
lb
/>
dem minor eſt, quod demonſtrare oportuit.</
s
>
<
s
xml:id
="
echoid-s3627
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div197
"
type
="
section
"
level
="
1
"
n
="
95
">
<
head
xml:id
="
echoid-head131
"
xml:space
="
preserve
">PROP. XXV. THEOREMA.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3628
"
xml:space
="
preserve
">Iisdem poſitis; </
s
>
<
s
xml:id
="
echoid-s3629
"
xml:space
="
preserve
">dico Z ſeu ſectorem
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0161-01
"
xlink:href
="
note-0161-01a
"
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
>
hyperbolæ minorem eſſe quam mi-
<
lb
/>
nor duarum mediarum geometricè con-
<
lb
/>
tinuè proportionalium inter A & </
s
>
<
s
xml:id
="
echoid-s3630
"
xml:space
="
preserve
">B.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3631
"
xml:space
="
preserve
">Inter A & </
s
>
<
s
xml:id
="
echoid-s3632
"
xml:space
="
preserve
">B ſit media geometrica G,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s3633
"
xml:space
="
preserve
">inter G & </
s
>
<
s
xml:id
="
echoid-s3634
"
xml:space
="
preserve
">B media geometrica H; </
s
>
<
s
xml:id
="
echoid-s3635
"
xml:space
="
preserve
">
<
lb
/>
Item inter G & </
s
>
<
s
xml:id
="
echoid-s3636
"
xml:space
="
preserve
">H media geometrica M, & </
s
>
<
s
xml:id
="
echoid-s3637
"
xml:space
="
preserve
">inter M & </
s
>
<
s
xml:id
="
echoid-s3638
"
xml:space
="
preserve
">H media
<
lb
/>
geometriea N; </
s
>
<
s
xml:id
="
echoid-s3639
"
xml:space
="
preserve
">continueturque hæc ſeries convergens AB, GH,
<
lb
/>
MN, OP, &</
s
>
<
s
xml:id
="
echoid-s3640
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s3641
"
xml:space
="
preserve
">in infinitum ut fiat ejus terminatio X. </
s
>
<
s
xml:id
="
echoid-s3642
"
xml:space
="
preserve
">ſatis patet
<
lb
/>
ex prædictis C & </
s
>
<
s
xml:id
="
echoid-s3643
"
xml:space
="
preserve
">G eſſe inter ſe æquales, & </
s
>
<
s
xml:id
="
echoid-s3644
"
xml:space
="
preserve
">H majorem eſſe
<
lb
/>
quam D; </
s
>
<
s
xml:id
="
echoid-s3645
"
xml:space
="
preserve
">atque ob hanc rationem M media geometrica inter G
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s3646
"
xml:space
="
preserve
">H major eſt quam E media geometrica inter C & </
s
>
<
s
xml:id
="
echoid-s3647
"
xml:space
="
preserve
">D. </
s
>
<
s
xml:id
="
echoid-s3648
"
xml:space
="
preserve
">Deinde
<
lb
/>
N media geometrica inter M & </
s
>
<
s
xml:id
="
echoid-s3649
"
xml:space
="
preserve
">H major eſt media harmonica
<
lb
/>
inter eaſdem; </
s
>
<
s
xml:id
="
echoid-s3650
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3651
"
xml:space
="
preserve
">quoniam M major eſt quam E & </
s
>
<
s
xml:id
="
echoid-s3652
"
xml:space
="
preserve
">H quam D, erit
<
lb
/>
media harmonica inter M & </
s
>
<
s
xml:id
="
echoid-s3653
"
xml:space
="
preserve
">H major quam F media harmo-
<
lb
/>
nica inter E & </
s
>
<
s
xml:id
="
echoid-s3654
"
xml:space
="
preserve
">D; </
s
>
<
s
xml:id
="
echoid-s3655
"
xml:space
="
preserve
">proinde N media geometrica inter M & </
s
>
<
s
xml:id
="
echoid-s3656
"
xml:space
="
preserve
">H
<
lb
/>
major eritquam F. </
s
>
<
s
xml:id
="
echoid-s3657
"
xml:space
="
preserve
">eadem methodo utramque ſeriem in in-
<
lb
/>
finitum continuando, ſemper demonſtratur terminum quem-
<
lb
/>
libet ſeriei A B, C D, minorem eſſe quam idem numero ter-
<
lb
/>
minus ſeriei A B, G H; </
s
>
<
s
xml:id
="
echoid-s3658
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3659
"
xml:space
="
preserve
">igitur terminatio ſeriei A B, C D,
<
lb
/>
nempe Z minor erit quam terminatio ſeriei A B, G H, nem-
<
lb
/>
pe X; </
s
>
<
s
xml:id
="
echoid-s3660
"
xml:space
="
preserve
">atque ex hujus 9 terminatio ſeriei A B, G H, ſeu X, æqua-
<
lb
/>
lis eſt minori duarum mediarum geometricè continuè propor-
<
lb
/>
tionalium inter A & </
s
>
<
s
xml:id
="
echoid-s3661
"
xml:space
="
preserve
">B; </
s
>
<
s
xml:id
="
echoid-s3662
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3663
"
xml:space
="
preserve
">ideo Z eadem minor eſt, quod
<
lb
/>
demonſtrare oportuit.</
s
>
<
s
xml:id
="
echoid-s3664
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3665
"
xml:space
="
preserve
">Ex dictis manifeſtum eſt hanc approximationem exactio-
<
lb
/>
rem eſſe illa, in antecedenti propoſitione, demonſtrata, et-
<
lb
/>
iamſi hæc ſit paulò laborioſior. </
s
>
<
s
xml:id
="
echoid-s3666
"
xml:space
="
preserve
">ſed non diſſimulandum
<
lb
/>
eſt duas poſſe eſſe ſeries æquales terminationes habentes, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>