Bošković, Ruđer Josip
,
Theoria philosophiae naturalis redacta ad unicam legem virium in natura existentium
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of handwritten notes
<
1 - 4
[out of range]
>
<
1 - 4
[out of range]
>
page
|<
<
(105)
of 389
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
type
="
section
"
level
="
0
"
n
="
0
">
<
p
>
<
s
xml:space
="
preserve
">
<
pb
o
="
105
"
file
="
0157
"
n
="
157
"
rhead
="
PARS SECUNDA.
"/>
ac ſi actione externa velocitas imprimatur punctis ejuſmodi,
<
lb
/>
quæ flexionem, vel contractionem, aut diſtractionem inducat,
<
lb
/>
tum ipſa puncta permittantur ſibi libera; </
s
>
<
s
xml:space
="
preserve
">habebitur oſcillatio
<
lb
/>
quædam, angulo jam in alteram plagam obverſo, jam in al-
<
lb
/>
teram oppoſitam, ac longitudine ejus veluti virgæ conſtantis
<
lb
/>
iis tribus punctis jam aucta, jam imminuta, fieri poterit; </
s
>
<
s
xml:space
="
preserve
">ut
<
lb
/>
oſcillatio ipſa ſenſum omnem effugiat, quod quidem exhibebit
<
lb
/>
nobis ideam virgæ, quam vocamus rigidam, & </
s
>
<
s
xml:space
="
preserve
">ſolidam, con-
<
lb
/>
tractionis nimirum, & </
s
>
<
s
xml:space
="
preserve
">dilatationis incapacem, qua
<
gap
/>
proprieta-
<
lb
/>
tes nulla virga in Natura habet accurate tales, ſed tantummo-
<
lb
/>
do ad ſenſum. </
s
>
<
s
xml:space
="
preserve
">Quod ſi vires ſint aliquanto debiliores, tum
<
lb
/>
vero & </
s
>
<
s
xml:space
="
preserve
">inflexio ex vi externa mediocri, & </
s
>
<
s
xml:space
="
preserve
">oſcillatio, ac tre-
<
lb
/>
mor erunt majores, & </
s
>
<
s
xml:space
="
preserve
">jam hinc ex ſimpliciſſimo trium pun-
<
lb
/>
ctorum ſyſtemate habebitur ſpecies quædam ſatis idonea ad ſi-
<
lb
/>
ſtendum animo diſcrimen, quod in Natura obverſatur quoti-
<
lb
/>
die oculis, inter virgas rigidas, ac eas, quæ ſunt flexiles, & </
s
>
<
s
xml:space
="
preserve
">
<
lb
/>
ex elaſticitate trementes.</
s
>
<
s
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:space
="
preserve
">227. </
s
>
<
s
xml:space
="
preserve
">Ibidem ſi binæ vires, ut AQ, BT fuerint perpendicu-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0157-01
"
xlink:href
="
note-0157-01a
"
xml:space
="
preserve
">Syſtemate in-
<
lb
/>
flexo per vires
<
lb
/>
parallelas vis
<
lb
/>
puncti medii
<
lb
/>
contraria ex-
<
lb
/>
tremis, & ęqua-
<
lb
/>
lis eo
<
gap
/>
um ſun
<
gap
/>
-
<
lb
/>
mæ.</
note
>
lares ad AB, vel etiam utcunque parallelæ inter ſe, tertia
<
lb
/>
quoque erit parallela illis, & </
s
>
<
s
xml:space
="
preserve
">æqualis earum ſummæ, ſed di-
<
lb
/>
rectionis contrariæ. </
s
>
<
s
xml:space
="
preserve
">Ducta enim CD parallela iis, tum ad
<
lb
/>
illam KI parallela BA, erit ob CK, VB æquales, triangulum
<
lb
/>
CIK æquale ſimili BT V, ſive TB S, adeoque CI æqualis
<
lb
/>
BT, IK æqualis B S, ſive A R, vel QP. </
s
>
<
s
xml:space
="
preserve
">Quare ſi ſumpta
<
lb
/>
IF æquali AQ ducatur K F; </
s
>
<
s
xml:space
="
preserve
">erit triangulum FIK æquale
<
lb
/>
AQ P, ac proinde FK æqualis, & </
s
>
<
s
xml:space
="
preserve
">parallela A P, ſive LC,
<
lb
/>
& </
s
>
<
s
xml:space
="
preserve
">CL FK parallelogrammum, ac CF, diameter ipſius, ex-
<
lb
/>
primet vim puncti C utique parallelam viribus AQ, BT,
<
lb
/>
& </
s
>
<
s
xml:space
="
preserve
">æqualem earum ſummæ, ſed directionis contrariæ. </
s
>
<
s
xml:space
="
preserve
">Quo-
<
lb
/>
niam vero eſt SB ad BT, ut BD ad DC; </
s
>
<
s
xml:space
="
preserve
">ac AQ ad AR,
<
lb
/>
ut DC ad DA; </
s
>
<
s
xml:space
="
preserve
">erit ex æqualitate perturbata AQ ad BT, ut
<
lb
/>
BD ad DA, nimirum vires in A, & </
s
>
<
s
xml:space
="
preserve
">B in ratione reciproca
<
lb
/>
diſtantiarum AD, DB a recta CD ducta per C ſecundum di-
<
lb
/>
rectionem virium.</
s
>
<
s
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:space
="
preserve
">228. </
s
>
<
s
xml:space
="
preserve
">Ea, quæ hoc poſtremo numero demonſtravimus, æque
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0157-02
"
xlink:href
="
note-0157-02a
"
xml:space
="
preserve
">Poſtremum
<
lb
/>
theorema gene-
<
lb
/>
rale, ubietiam
<
lb
/>
tria puncta non
<
lb
/>
jaceant in di
<
gap
/>
<
lb
/>
rectum.</
note
>
pertinent ad actione; </
s
>
<
s
xml:space
="
preserve
">mutuas trium punctorum habentium po-
<
lb
/>
ſitionem mutuam quamcunque, etiam ſi a rectilinea recedat
<
lb
/>
quantumlibet; </
s
>
<
s
xml:space
="
preserve
">nam demonſtratio generalis eſt: </
s
>
<
s
xml:space
="
preserve
">ſed ad maſſas
<
lb
/>
utcunque inæquales, & </
s
>
<
s
xml:space
="
preserve
">in ſe agentes viribus etiam divergenti-
<
lb
/>
bus, multo generalius traduci poſſunt, ac traducentur inferius,
<
lb
/>
& </
s
>
<
s
xml:space
="
preserve
">ad æquilibrii leges, & </
s
>
<
s
xml:space
="
preserve
">vectem, & </
s
>
<
s
xml:space
="
preserve
">centra oſcillationis ac
<
lb
/>
percuſſionis nos deducent. </
s
>
<
s
xml:space
="
preserve
">Sed interea pergemus alia nonnul-
<
lb
/>
la perſequi pertinentia itidem ad puncta tria, quæ in directum
<
lb
/>
non jaceant.</
s
>
<
s
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
right
"
xml:space
="
preserve
">Æquilibrium
<
lb
/>
trium puncto-
<
lb
/>
rum non in di-
<
lb
/>
rectum jacen-
<
lb
/>
tium impoſſi-
<
lb
/>
bile ſine vi
<
lb
/>
externa, niſi</
note
>
<
p
>
<
s
xml:space
="
preserve
">229. </
s
>
<
s
xml:space
="
preserve
">Si tria puncta non jaceant in directum, tum vero ſi-
<
lb
/>
ne externis viribus non poterunt eſſe in æquilibrio; </
s
>
<
s
xml:space
="
preserve
">niſi omnes
<
lb
/>
tres diſtantiæ, quæ latera trianguli conſtituunt, ſint diſtantiæ
<
lb
/>
limitum figuræ 1. </
s
>
<
s
xml:space
="
preserve
">Cum enim vires illæ mutuæ non </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>