Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
page
|<
<
of 491
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
id
="
N1C940
">
<
p
id
="
N1CC74
"
type
="
main
">
<
s
id
="
N1CCC0
">
<
pb
pagenum
="
199
"
xlink:href
="
026/01/231.jpg
"/>
retineret pondus in L; </
s
>
<
s
id
="
N1CCC9
">ducatur autem KLG Tangens parallela CT; </
s
>
<
s
id
="
N1CCCD
">certè
<
lb
/>
eadem potentia in L per LG retinebit pondus in L; </
s
>
<
s
id
="
N1CCD3
">quæ idem retine
<
lb
/>
ret applicata in C per CT; </
s
>
<
s
id
="
N1CCD9
">cum enim RC & RL ſint æquales ſi ſint ap
<
lb
/>
plicatæ duæ potentiæ æquales in C quidem per CT, & in L per LG; </
s
>
<
s
id
="
N1CCDF
">
<
lb
/>
haud dubiè erit perfectum æquilibrium; </
s
>
<
s
id
="
N1CCE4
">igitur ſi pondus A pendeat in
<
lb
/>
H fune LGH, retinebit pondus L in plano inclinato GLK; </
s
>
<
s
id
="
N1CCEA
">eſt autem
<
lb
/>
pondus H ad pondus LN SR ad RL; </
s
>
<
s
id
="
N1CCF0
">ſed triangula RSL, & GKI
<
lb
/>
ſunt proportionalia; </
s
>
<
s
id
="
N1CCF6
">igitur pondus in H eſt ad pondus L, vt GI ad G
<
lb
/>
K; </
s
>
<
s
id
="
N1CCFC
">igitur ſi vires, quæ retinent pondus in plano inclinato GK ſunt ad vi
<
lb
/>
res, quæ retinent pondus in perpendiculari GI, vt GI ad GK; igitur im
<
lb
/>
petus ſeu motus mobilis in plano GK eſt ad impetum, ſeu motum eiuſ
<
lb
/>
dem in perpendiculo GI, vt GI ad GK. </
s
>
</
p
>
<
p
id
="
N1CD06
"
type
="
main
">
<
s
id
="
N1CD08
">Hæc omnia veriſſima ſunt, ſemper tamen deſiderari videtur ratio phy
<
lb
/>
ſica, cur idem pondus pendulum ex C in O, ſit eiuſdem momenti cum
<
lb
/>
pondere affixo puncto P, ſeu brachio libræ horizontalis PS. quod certè
<
lb
/>
Mechanica Axiomatis, vel hypotheſeos loco iure aſſumere poteſt; </
s
>
<
s
id
="
N1CD12
">at ve
<
lb
/>
rò phyſica non ſatis habet de re cognoſcere quod ſit, niſi ſciat propter
<
lb
/>
quid ſit; igitur nos aliquam afferre conabimur. </
s
>
<
s
id
="
N1CD1A
">Suppono tantùm tunc
<
lb
/>
eſſe æquilibrium perfectum duorum ponderum æqualium cum
<
expan
abbr
="
vtrimq;
">vtrimque</
expan
>
<
lb
/>
æqualia illa pondera ita ſunt appenſa, vt linea directionis vnius æqua
<
lb
/>
lis ſit lineæ directionis alterius, cur enim alterum præualeret ſi ſint æ
<
lb
/>
qualia? </
s
>
<
s
id
="
N1CD29
">hoc poſito. </
s
>
</
p
>
<
p
id
="
N1CD2C
"
type
="
main
">
<
s
id
="
N1CD2E
">Dico pondus affixum P æquale ponderi L facere æquilibrium; cum
<
lb
/>
enim linea directionis ſit PO, ſi deſcenderet liberè per PO. </
s
>
<
s
id
="
N1CD34
">L eodem
<
lb
/>
tempore attolleretur per LS, quod certè applicatis planis SL PO facilè
<
lb
/>
fieri poſſet; </
s
>
<
s
id
="
N1CD3C
">ſed eodem modo P grauitat, quo ſi deſcenderet per PO; </
s
>
<
s
id
="
N1CD40
">eſt
<
lb
/>
enim eius linea directionis; </
s
>
<
s
id
="
N1CD46
">atqui tunc faceret æquilibrium, quod oſten
<
lb
/>
do; </
s
>
<
s
id
="
N1CD4C
">æquale ſpatium conficeret L, per LS aſcendendo, quod P per PO
<
lb
/>
deſcendendo; </
s
>
<
s
id
="
N1CD52
">igitur ſi attolleret L in S, ſimiliter pondus L æquale P in S
<
lb
/>
attolleret pondus P ex O in P, igitur neutrum præualere poteſt; ſed quia
<
lb
/>
hæc fuſiùs explicabimus cum de libra, nunc tantùm indicaſſe ſufficiat. </
s
>
</
p
>
<
p
id
="
N1CD5A
"
type
="
main
">
<
s
id
="
N1CD5C
">Supereſt vt breuiter oſtendamus accipi non poſſe hanc proportio
<
lb
/>
nem imminutionis motus in plano inclinato à Tangente BE tùm
<
lb
/>
quia; </
s
>
<
s
id
="
N1CD64
">iam à ſecante accipi oſtendimus, tùm quia ſit Tangens BD æqualis
<
lb
/>
ſumi toti ſeu perpendiculari AB; </
s
>
<
s
id
="
N1CD6A
">ſequeretur motum per AD æqualem
<
lb
/>
eſſe motui per AB; </
s
>
<
s
id
="
N1CD70
">Equidem in maxima diſtantia accedit Tangens ad
<
lb
/>
ſecantem; igitur eò plùs impeditur motus, quò maius ſpatium conficien
<
lb
/>
dum eſt, &c. </
s
>
</
p
>
<
p
id
="
N1CD78
"
type
="
main
">
<
s
id
="
N1CD7A
">
<
emph
type
="
center
"/>
<
emph
type
="
italics
"/>
Theorema
<
emph.end
type
="
italics
"/>
6.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
id
="
N1CD87
"
type
="
main
">
<
s
id
="
N1CD89
">
<
emph
type
="
italics
"/>
Ex hoc ſequitur neceſſariò motum in plano inclinato eſſe ad motum in per
<
lb
/>
pendiculari, vt ipſa perpendicularis ad ipſum planum inclinatum,
<
emph.end
type
="
italics
"/>
v.g. velo
<
lb
/>
citas motus per AE eſt ad velocitatem motus per AB, vt ipſa AB eſt
<
lb
/>
ad ipſam AE, ſit enim AE dupla AB, velocitas per AB eſt dupla veloci
<
lb
/>
tatis per AE. </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>