Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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<
archimedes
>
<
text
>
<
front
>
<
section
>
<
pb
xlink:href
="
026/01/021.jpg
"/>
<
p
id
="
N10B1B
"
type
="
main
">
<
s
id
="
N10B1D
">4. Tantum eſt ab æqualitate prædicta ceſſionis, & reſiſtentiæ, ad
<
lb
/>
nullam ceſſionem, & notam reſiſtentiam, quantum eſt ad nullam
<
lb
/>
<
expan
abbr
="
reſiſtẽtiam
">reſiſtentiam</
expan
>
, & totam ceſſionem: </
s
>
<
s
id
="
N10B28
">hinc, cùm à tota ceſſione ad æqua
<
lb
/>
litatem prædictam acquiratur tantùm noua determinato æqualis
<
lb
/>
priori; </
s
>
<
s
id
="
N10B30
">igitur ab eadem æqualitate ad nullam ceſſionem tantun
<
lb
/>
dem acquiritur; </
s
>
<
s
id
="
N10B36
">igitur dupla prioris, vt iam ſuprà dictum eſt; </
s
>
<
s
id
="
N10B3A
">nulla
<
lb
/>
eſſet reſiſtentia in vacuo; nulla eſt ceſſio, cùm ipſum corpus refle
<
lb
/>
ctens nullo modo mouetur ab ictu. </
s
>
</
p
>
<
p
id
="
N10B42
"
type
="
main
">
<
s
id
="
N10B44
">5. Determinatio noua per lineam obliquam, eſt ad nouam per
<
lb
/>
lineam perpendicularem, vt ſinus rectus anguli incidentiæ, ad ſi
<
lb
/>
num totum, in qualibet hypotheſi; </
s
>
<
s
id
="
N10B4C
">quia ſunt hæ, vt ictus, per vtran
<
lb
/>
que lineam; </
s
>
<
s
id
="
N10B52
">ictus verò vt grauitationes in horizontale planum, &
<
lb
/>
in planum inclinatum, ſub angulo complementi anguli incidentiæ: </
s
>
<
s
id
="
N10B58
">
<
lb
/>
hinc noua determinatio per lineam obliquam, eſt vt dupla ſinus re
<
lb
/>
cti anguli incidentiæ, ad ſinum totum: </
s
>
<
s
id
="
N10B5F
">hinc ſupra angulum inci
<
lb
/>
dentiæ 30, noua eſt maior priore, infrà minor; in ipſo angulo 30.
<
lb
/>
æqualis, ſuppoſita hypotheſi plani reflectentis immobilis. </
s
>
</
p
>
<
p
id
="
N10B67
"
type
="
main
">
<
s
id
="
N10B69
">6. Ex hoc poſitiuo principio demonſtratur accuratiſſimè æqua
<
lb
/>
litas anguli reflexionis, & incidentiæ, quod certè demonſtratum
<
lb
/>
non fuit ab Ariſt. in problematis, ſect. 17. problem. 4. & 13. quibus
<
lb
/>
in locis fusè ſatis explicatur hoc Theorema, ducta comparatione,
<
lb
/>
tùm à grauibus, quæ cadunt, tùm ab orbibus, quæ rotantur, rùm à
<
lb
/>
ſpeculis: ſed minimè demonſtratur ex certis principiis ſine petitio
<
lb
/>
ne principij. </
s
>
<
s
id
="
N10B79
">In puncto reflexionis, poſita hypotheſi plani immo
<
lb
/>
bilis reflectentis, nulla datur quies; </
s
>
<
s
id
="
N10B7F
">quia vnum tantùm eſt conta
<
lb
/>
ctus inſtans; ſed eo inſtanti eſt motus, quo primo acquiritur locus. </
s
>
</
p
>
<
p
id
="
N10B85
"
type
="
main
">
<
s
id
="
N10B87
">7. Omnes lineæ reflexæ per ſe ſunt æqualis longitudinis, & ab
<
lb
/>
eodem puncto contactus, ad communem peripheriam terminan
<
lb
/>
tur: </
s
>
<
s
id
="
N10B8F
">ſi globus impactus ſit æqualis reflectenti, ſitque linea inciden
<
lb
/>
tiæ obliqua quælibet terminata ad idem punctum contactus, re
<
lb
/>
flectitur prædictus globus per lineam tangentem globum refle
<
lb
/>
ctentem in eodem puncto; </
s
>
<
s
id
="
N10B99
">quia hæc tangens eſt diagonalis com
<
lb
/>
munis, & determinatio mixta communis omnibus lineis inciden
<
lb
/>
tiæ: eſt tamen modò longior, modò breuior linea reflexa, éſtque vt
<
lb
/>
vt ſinus complementi anguli incidentiæ, ad ſinum totum, qui ſit
<
lb
/>
determinatio prior, vt facilè demonſtramus. </
s
>
</
p
>
<
p
id
="
N10BA5
"
type
="
main
">
<
s
id
="
N10BA7
">8. Si globus impactus ſit minor corpore reflectente, reflectitur
<
lb
/>
etiam per ipſam perpendicularem, & determinatio noua eſt dupla
<
lb
/>
prioris, minùs ratione globorum v. g. ſi globus impactus ſit ſubdu-</
s
>
</
p
>
</
section
>
</
front
>
</
text
>
</
archimedes
>