Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of handwritten notes
<
1 - 5
[out of range]
>
<
1 - 5
[out of range]
>
page
|<
<
(291)
of 434
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div475
"
type
="
section
"
level
="
1
"
n
="
194
">
<
pb
o
="
291
"
file
="
0377
"
n
="
409
"
rhead
="
MECHANICAM.
"/>
</
div
>
<
div
xml:id
="
echoid-div476
"
type
="
section
"
level
="
1
"
n
="
195
">
<
head
xml:id
="
echoid-head251
"
xml:space
="
preserve
">IX.</
head
>
<
head
xml:id
="
echoid-head252
"
style
="
it
"
xml:space
="
preserve
">Chriſtiani Hugenii, Solutio Problematis de
<
lb
/>
linea in quam flexile ſe pondere pro-
<
lb
/>
prio curvat.</
head
>
<
p
>
<
s
xml:id
="
echoid-s6379
"
xml:space
="
preserve
">Si Catena C V A ſuſpenſa ſit ex filis F C, E A utrin-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0377-01
"
xlink:href
="
note-0377-01a
"
xml:space
="
preserve
">TAB.XXXIII.
<
lb
/>
Fig. 5.</
note
>
que annexis, ac gravitate carentibus, itaut capita C & </
s
>
<
s
xml:id
="
echoid-s6380
"
xml:space
="
preserve
">A
<
lb
/>
ſint pari altitudine, deturque Angulus inclinationis filorum
<
lb
/>
productorum C G A, & </
s
>
<
s
xml:id
="
echoid-s6381
"
xml:space
="
preserve
">catenæ totius poſitus, cujus vertex
<
lb
/>
ſit V, axis V B.</
s
>
<
s
xml:id
="
echoid-s6382
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6383
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s6384
"
xml:space
="
preserve
">Licebit hinc invenire tangentem in dato quovis catenæ
<
lb
/>
puncto. </
s
>
<
s
xml:id
="
echoid-s6385
"
xml:space
="
preserve
">Velut ſi punctum datum ſit L, unde ducta appli-
<
lb
/>
cata L H dividat æqualiter axem B V. </
s
>
<
s
xml:id
="
echoid-s6386
"
xml:space
="
preserve
">Jam ſi angulus C G A
<
lb
/>
ſit 60°, erit inclinanda a puncto A ad axem recta A W, æ-
<
lb
/>
qualis {1/2} A B, cui ducta parallela L R, tanget curvam in pun-
<
lb
/>
cto L. </
s
>
<
s
xml:id
="
echoid-s6387
"
xml:space
="
preserve
">Item ſi latera G B, B A, A G ſint partium 3, 4, 5,
<
lb
/>
erit A W ponenda partium 4 {1/2}.</
s
>
<
s
xml:id
="
echoid-s6388
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6389
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s6390
"
xml:space
="
preserve
">Invenitur porrò & </
s
>
<
s
xml:id
="
echoid-s6391
"
xml:space
="
preserve
">recta linea catenæ æqualis, vel da-
<
lb
/>
tæ cuilibet ejus portioni. </
s
>
<
s
xml:id
="
echoid-s6392
"
xml:space
="
preserve
">Semper enim dato angulo C G A,
<
lb
/>
data erit ratio axis B V ad curvam V A. </
s
>
<
s
xml:id
="
echoid-s6393
"
xml:space
="
preserve
">Velut ſi latera
<
lb
/>
G B, B A, A G ſint ut 3, 4, 5, erit curva V A tripla
<
lb
/>
axis V B.</
s
>
<
s
xml:id
="
echoid-s6394
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6395
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s6396
"
xml:space
="
preserve
">Item definitur radius curvitatis in vertice V, hoc eſt,
<
lb
/>
ſemidiameter circuli maximi, qui per verticem hunc deſcri-
<
lb
/>
ptus totus intra curvam cadat. </
s
>
<
s
xml:id
="
echoid-s6397
"
xml:space
="
preserve
">Nam ſi angulus C G A ſit 60°,
<
lb
/>
erit radius curvitatis ipſi axi B V æqualis. </
s
>
<
s
xml:id
="
echoid-s6398
"
xml:space
="
preserve
">Sin vero angulus
<
lb
/>
C G A ſit rectus, erit radius curvitatis æqualis curvæ V A.</
s
>
<
s
xml:id
="
echoid-s6399
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6400
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s6401
"
xml:space
="
preserve
">Poterit & </
s
>
<
s
xml:id
="
echoid-s6402
"
xml:space
="
preserve
">circulus æqualis inveniri ſuperficiei conoidis,
<
lb
/>
ex revolutione catenæ circa axem ſuum. </
s
>
<
s
xml:id
="
echoid-s6403
"
xml:space
="
preserve
">Ita ſi angulus C G A
<
lb
/>
ſit 60°, erit ſuperficies conoidis ex catena C V A genita æ-
<
lb
/>
qualis circulo, cujus radius poſſit duplum rectangulum
<
lb
/>
B V G.</
s
>
<
s
xml:id
="
echoid-s6404
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6405
"
xml:space
="
preserve
">5. </
s
>
<
s
xml:id
="
echoid-s6406
"
xml:space
="
preserve
">Inveniuntur etiam puncta quotlibet curvæ K N, cujus
<
lb
/>
evolutione, una cum recta K V, radio curvitatis in </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>