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
page
|<
<
(144)
of 434
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div282
"
type
="
section
"
level
="
1
"
n
="
104
">
<
p
>
<
s
xml:id
="
echoid-s3272
"
xml:space
="
preserve
">
<
pb
o
="
144
"
file
="
0208
"
n
="
228
"
rhead
="
CHRISTIANI HUGENII
"/>
rum autem ſumma quadratorum data erit, ſi detur diſtantia
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0208-01
"
xlink:href
="
note-0208-01a
"
xml:space
="
preserve
">
<
emph
style
="
sc
">De centro</
emph
>
<
lb
/>
<
emph
style
="
sc
">O@CILLA-</
emph
>
<
lb
/>
<
emph
style
="
sc
">TIONIS</
emph
>
.</
note
>
centri gravitatis figuræ S Y T Z ab recta B Y vel D Z;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3273
"
xml:space
="
preserve
">nec non diſtantia indidem centri gravitatis cunei ſui abſciſſi
<
lb
/>
plano per eandem rectam . </
s
>
<
s
xml:id
="
echoid-s3274
"
xml:space
="
preserve
">Vel, figura S Y T Z
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0208-02
"
xlink:href
="
note-0208-02a
"
xml:space
="
preserve
">Prop. 9.
<
lb
/>
huj.</
note
>
exiſtente, ut S T ſit axis ejus, eadem quadratorum ſumma da-
<
lb
/>
bitur, ſi detur diſtantia centri gravitatis figuræ dimidiæ S Z T
<
lb
/>
ab axe S T, item centri gravitatis cunei, ſuper eadem di-
<
lb
/>
midia figura, abſciſſi plano per axem ducto . </
s
>
<
s
xml:id
="
echoid-s3275
"
xml:space
="
preserve
">Ergo,
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0208-03
"
xlink:href
="
note-0208-03a
"
xml:space
="
preserve
">Prop. 11.
<
lb
/>
huj.</
note
>
datis, dabitur quoque ſumma quadratorum à perpendicula-
<
lb
/>
ribus quæ, à particulis omnibus ſolidi A B C D, ductæ
<
lb
/>
intelliguntur in planum E A C. </
s
>
<
s
xml:id
="
echoid-s3276
"
xml:space
="
preserve
">Invenimus autem & </
s
>
<
s
xml:id
="
echoid-s3277
"
xml:space
="
preserve
">ſum-
<
lb
/>
mam quadratorum, à perpendicularibus omnibus in planum
<
lb
/>
per E G ductis. </
s
>
<
s
xml:id
="
echoid-s3278
"
xml:space
="
preserve
">Ergo & </
s
>
<
s
xml:id
="
echoid-s3279
"
xml:space
="
preserve
">aggregatum utriuſque ſummæ ha-
<
lb
/>
bebitur, hoc eſt, per ſuperius oſtenſa, ſumma quadratorum
<
lb
/>
perpendicularium quæ, à particulis omnibus ſolidi A B C D,
<
lb
/>
cadunt in rectam datam per E tranſeuntem, & </
s
>
<
s
xml:id
="
echoid-s3280
"
xml:space
="
preserve
">ad paginæ
<
lb
/>
hujus planum erectam. </
s
>
<
s
xml:id
="
echoid-s3281
"
xml:space
="
preserve
">quod erat faciendum.</
s
>
<
s
xml:id
="
echoid-s3282
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div286
"
type
="
section
"
level
="
1
"
n
="
105
">
<
head
xml:id
="
echoid-head131
"
xml:space
="
preserve
">PROPOSITIO XV.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s3283
"
xml:space
="
preserve
">IIsdem poſitis, ſi ſolidum A B C D ſit ejusmodi, ut
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0208-04
"
xlink:href
="
note-0208-04a
"
xml:space
="
preserve
">TAB. XXI.
<
lb
/>
Fig. 1. & 2.</
note
>
figura plana S Y T Z, ipſi proportionalis, non ha-
<
lb
/>
beat notam diſtantiam centri gravitatis à tangenti-
<
lb
/>
bus B Y vel D Z, vel, ut ſubcentrica cunei ſuper ipſa
<
lb
/>
abſciſſi, plano per easdem B Y vel D Z, ignoretur;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3284
"
xml:space
="
preserve
">in figura tamen proportionali, quæ à latere eſt,
<
lb
/>
O Q P, detur diſtantia Φ P, qua centrum gravita-
<
lb
/>
tis figuræ dimidiæ O P V abeſt ab axe O P; </
s
>
<
s
xml:id
="
echoid-s3285
"
xml:space
="
preserve
">li-
<
lb
/>
cebit hinc invenire ſummam quadratorum à diſtan-
<
lb
/>
tiis particularum ſolidi A B C D à plano E C. </
s
>
<
s
xml:id
="
echoid-s3286
"
xml:space
="
preserve
">O-
<
lb
/>
portet autem ut ſectiones omnes, N N, M M, ſint
<
lb
/>
plana ſimilia; </
s
>
<
s
xml:id
="
echoid-s3287
"
xml:space
="
preserve
">utque per omnium centra gravitatis
<
lb
/>
transeat planum E C; </
s
>
<
s
xml:id
="
echoid-s3288
"
xml:space
="
preserve
">quemadmodum in prismate,
<
lb
/>
pyramide, c
<
unsure
/>
ono, conoidibus, multisque aliis </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>