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 concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
451 - 480
481 - 510
511 - 540
541 - 568
>
Scan
Original
121
122
123
399
124
400
125
401
126
402
127
403
128
404
129
130
131
132
133
134
135
136
137
138
139
140
413
141
414
142
415
143
416
144
417
145
418
146
419
147
420
148
421
149
422
150
423
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
451 - 480
481 - 510
511 - 540
541 - 568
>
page
|<
<
(419)
of 568
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div152
"
type
="
section
"
level
="
1
"
n
="
69
">
<
pb
o
="
419
"
file
="
0137
"
n
="
146
"
rhead
="
ET HYPERBOLÆ QUADRATURA.
"/>
</
div
>
<
div
xml:id
="
echoid-div154
"
type
="
section
"
level
="
1
"
n
="
70
">
<
head
xml:id
="
echoid-head105
"
xml:space
="
preserve
">SCHOLIUM.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2879
"
xml:space
="
preserve
">Duæ præcedentes propoſitiones eodem modo demon-
<
lb
/>
ſtrari poſſunt de duobus quibuſcunque polygonis
<
lb
/>
complicatis loco polygonorum complicatorum ABIP,
<
lb
/>
A B D L P; </
s
>
<
s
xml:id
="
echoid-s2880
"
xml:space
="
preserve
">polygonum enim à tangentibus comprehenſum
<
lb
/>
tot continet æqualia trapezia, quot continet polygonum à
<
lb
/>
ſubtendentibus comprehenſum æqualia triangula: </
s
>
<
s
xml:id
="
echoid-s2881
"
xml:space
="
preserve
">atque hinc
<
lb
/>
evidens eſt has polygonorum analogias ita ſe habere in infi-
<
lb
/>
nitum, ducendo nimirum rectas AN, AK, AG, AC, per
<
lb
/>
puncta R, T, S, V, & </
s
>
<
s
xml:id
="
echoid-s2882
"
xml:space
="
preserve
">adhuc alia & </
s
>
<
s
xml:id
="
echoid-s2883
"
xml:space
="
preserve
">alia polygona intra & </
s
>
<
s
xml:id
="
echoid-s2884
"
xml:space
="
preserve
">
<
lb
/>
extra ſemper ſcribendo: </
s
>
<
s
xml:id
="
echoid-s2885
"
xml:space
="
preserve
">notandum nos appellare hanc poly-
<
lb
/>
gonorum inſcriptionem & </
s
>
<
s
xml:id
="
echoid-s2886
"
xml:space
="
preserve
">circumſcriptionem, inſcriptionem
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s2887
"
xml:space
="
preserve
">circumſcriptionem ſubduplam, ex prædictis patet (ſi po-
<
lb
/>
natur triangulum A B P =
<
emph
style
="
super
">a</
emph
>
, & </
s
>
<
s
xml:id
="
echoid-s2888
"
xml:space
="
preserve
">trapezium A B F P =
<
emph
style
="
super
">b</
emph
>
) tra-
<
lb
/>
pezium A B I P eſſe vqab & </
s
>
<
s
xml:id
="
echoid-s2889
"
xml:space
="
preserve
">polygonum A B D L P {2ab/a + vqab}:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2890
"
xml:space
="
preserve
">eodem modo poſito trapezio A B I P =
<
emph
style
="
super
">c</
emph
>
, & </
s
>
<
s
xml:id
="
echoid-s2891
"
xml:space
="
preserve
">polygono
<
lb
/>
A B D L P =
<
emph
style
="
super
">d</
emph
>
, erit polygonum A B E I O P = vqcd & </
s
>
<
s
xml:id
="
echoid-s2892
"
xml:space
="
preserve
">po-
<
lb
/>
lygonum A B C G K N P = {2cd/c + vqcd,}, ita ut evidens ſit hanc
<
lb
/>
polygonorum ſeriem eſſe convergentem; </
s
>
<
s
xml:id
="
echoid-s2893
"
xml:space
="
preserve
">atque in infinitum
<
lb
/>
illam continuando, manifeſtum eſt tandem exhiberi quanti-
<
lb
/>
tatem ſectori circulari, elliptico vel hyperbolico A B E I O P
<
lb
/>
æqualem; </
s
>
<
s
xml:id
="
echoid-s2894
"
xml:space
="
preserve
">differentia enim polygonorum complicatorum in
<
lb
/>
ſeriei continuatione ſemper diminuitur, ita ut omni exhibita
<
lb
/>
quantitate fieri poſſit minor, ut in ſequentis theorematis
<
lb
/>
Scholio demonſtrabimus: </
s
>
<
s
xml:id
="
echoid-s2895
"
xml:space
="
preserve
">ſi igitur prædicta polygonorum ſe-
<
lb
/>
ries terminari poſſet, hoc eſt, ſi inveniretur ultimum illud
<
lb
/>
polygonum inſcriptum (ſi ita loqui liceat) æquale ultimo
<
lb
/>
illi polygono circumſcripto, daretur infallibiliter circuli & </
s
>
<
s
xml:id
="
echoid-s2896
"
xml:space
="
preserve
">
<
lb
/>
hyperbolæ quadratura: </
s
>
<
s
xml:id
="
echoid-s2897
"
xml:space
="
preserve
">ſed quoniam difficile eſt, & </
s
>
<
s
xml:id
="
echoid-s2898
"
xml:space
="
preserve
">in geo-
<
lb
/>
metria omnino fortaſſe inauditum tales ſeries terminare; </
s
>
<
s
xml:id
="
echoid-s2899
"
xml:space
="
preserve
">præ-
<
lb
/>
mittendæ ſunt quædam propoſitiones è quibus inveniri poſ-
<
lb
/>
ſint hujuſmodi aliquot ſerierum terminationes, & </
s
>
<
s
xml:id
="
echoid-s2900
"
xml:space
="
preserve
">tandem </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>