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
>
71
(359)
72
(360)
73
(361)
74
(362)
75
(363)
76
(364)
77
(365)
78
(366)
79
80
<
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
|<
<
(366)
of 568
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div70
"
type
="
section
"
level
="
1
"
n
="
32
">
<
p
>
<
s
xml:id
="
echoid-s1370
"
xml:space
="
preserve
">
<
pb
o
="
366
"
file
="
0074
"
n
="
78
"
rhead
="
CHRISTIANI HUGENII
"/>
ad B H, ita K G ad C H. </
s
>
<
s
xml:id
="
echoid-s1371
"
xml:space
="
preserve
">Ergo major erit ratio E G ad
<
lb
/>
C H, quam duplicata ejus, quam habet K G ad C H. </
s
>
<
s
xml:id
="
echoid-s1372
"
xml:space
="
preserve
">Qua-
<
lb
/>
re major ratio E G ad K G, quam K G ad C H. </
s
>
<
s
xml:id
="
echoid-s1373
"
xml:space
="
preserve
">Ideoque
<
lb
/>
duæ ſimul E G, C H omnino majores duplâ K G. </
s
>
<
s
xml:id
="
echoid-s1374
"
xml:space
="
preserve
">Et ſumptis
<
lb
/>
omnium trientibus, erunt trientes utriuſque E G & </
s
>
<
s
xml:id
="
echoid-s1375
"
xml:space
="
preserve
">C H ſi-
<
lb
/>
mul majores duabus tertiis K G. </
s
>
<
s
xml:id
="
echoid-s1376
"
xml:space
="
preserve
">Quamobrem addito utrim-
<
lb
/>
que ipſius C H triente, erit triens E G cum duabus tertiis
<
lb
/>
C H, major duabus tertiis K G cum triente C H. </
s
>
<
s
xml:id
="
echoid-s1377
"
xml:space
="
preserve
">Hiſce
<
lb
/>
vero minor etiam eſt arcus C G . </
s
>
<
s
xml:id
="
echoid-s1378
"
xml:space
="
preserve
">Igitur duæ tertiæ C
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0074-01
"
xlink:href
="
note-0074-01a
"
xml:space
="
preserve
">per pra
<
unsure
/>
ced.</
note
>
ſimul cum triente ipſius E G majores omnino ſunt eodem ar-
<
lb
/>
cu C G. </
s
>
<
s
xml:id
="
echoid-s1379
"
xml:space
="
preserve
">Unde ſumptis omnibus toties quoties arcus C G
<
lb
/>
circumferentiâ totâ continetur, erunt quoque duæ tertiæ pe-
<
lb
/>
rimetri polygoni C D, cum triente perimetri polygoni E F,
<
lb
/>
majores circuli totius circumferentiâ. </
s
>
<
s
xml:id
="
echoid-s1380
"
xml:space
="
preserve
">Quod fuerat oſtenden-
<
lb
/>
dum.</
s
>
<
s
xml:id
="
echoid-s1381
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1382
"
xml:space
="
preserve
">Omnis igitur circumferentiæ arcus quadrante minor, mi-
<
lb
/>
nor eſt ſinus ſui beſſe & </
s
>
<
s
xml:id
="
echoid-s1383
"
xml:space
="
preserve
">tangentis triente.</
s
>
<
s
xml:id
="
echoid-s1384
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div72
"
type
="
section
"
level
="
1
"
n
="
33
">
<
head
xml:id
="
echoid-head54
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Problema</
emph
>
I.
<
emph
style
="
sc
">Prop</
emph
>
. X.</
head
>
<
head
xml:id
="
echoid-head55
"
style
="
it
"
xml:space
="
preserve
">Peripheriæ ad diametrum rationem invenire
<
lb
/>
quamlibet veræ propinquam.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1385
"
xml:space
="
preserve
">MInorem eſſe peripheriæ ad diametrum rationem quam tri-
<
lb
/>
plam ſeſquiſeptimam: </
s
>
<
s
xml:id
="
echoid-s1386
"
xml:space
="
preserve
">majorem vero quam 3 {10/71}, Archi-
<
lb
/>
medes oſtendit inſcripto circumſcriptoque 96 laterum po-
<
lb
/>
lygono. </
s
>
<
s
xml:id
="
echoid-s1387
"
xml:space
="
preserve
">Idem verò hic per dodecagona demonſtrabimus.</
s
>
<
s
xml:id
="
echoid-s1388
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1389
"
xml:space
="
preserve
">Quia enim latus inſcripti circulo dodecagoni majus eſt par-
<
lb
/>
tibus 5176 {3/8}, qualium radius continet 10000: </
s
>
<
s
xml:id
="
echoid-s1390
"
xml:space
="
preserve
">duodecim la-
<
lb
/>
tera proinde, hoc eſt, perimeter inſcripti dodecagoni major
<
lb
/>
erit quam 62116 {1/2}: </
s
>
<
s
xml:id
="
echoid-s1391
"
xml:space
="
preserve
">perimeter autem hexagoni inſcripti eſt
<
lb
/>
radii ſextupla, ideoque partium 60000. </
s
>
<
s
xml:id
="
echoid-s1392
"
xml:space
="
preserve
">Igitur dodecagoni
<
lb
/>
perimeter perimetrum hexagoni excedit amplius quam par-
<
lb
/>
tibus 2116 {1/2}. </
s
>
<
s
xml:id
="
echoid-s1393
"
xml:space
="
preserve
">Quare triens exceſſus major erit quam 705 {1/2}. </
s
>
<
s
xml:id
="
echoid-s1394
"
xml:space
="
preserve
">Igi-
<
lb
/>
tur dodecagoni perimeter unà cum triente exceſſus, quo pe-
<
lb
/>
rimetrum hexagoni ſuperat, major erit aggregato </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>