Marci of Kronland, Johannes Marcus
,
De proportione motus figurarum recti linearum et circuli quadratura ex motu
,
1648
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
page
|<
<
of 145
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
063/01/081.jpg
"/>
nuò augetur. </
s
>
<
s
>In proiectis verò tota gravitas ſuperatur ab
<
lb
/>
impulſu,
<
expan
abbr
="
atq;
">atque</
expan
>
in lineam trahitur nonnaturalem. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
PROBLEMA IV.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
<
emph
type
="
italics
"/>
Datâ Proportione impulſûs ad grauitatem, lineam motûs
<
lb
/>
inflexi inuenire.
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Data ſit proportio impulſûs ad gravitatem, VG ſeſcupla.
<
lb
/>
aſſumatur autem recta AB via motûs, ad AC motum verti
<
lb
/>
calem in eadem ratione: & ſecetur AB in ſegmenta æqualia
<
lb
/>
ALMNOPB. </
s
>
<
s
>Quòd ſi
<
expan
abbr
="
itaq;
">itaque</
expan
>
maneret eadem proportio im
<
lb
/>
pulſus ad gravitatem, motus medius eſſet diameter parallelo
<
lb
/>
grammi ABDC per prop: 32. </
s
>
<
s
>At verò quia plaga impul
<
lb
/>
ſum continuò abſumit: gravitas verò eadem manet; neceſſe
<
lb
/>
continuò mutari hanc proportionem: pro ratione nimirum
<
lb
/>
ſpatij tranſmiſſi Igitur abſumptâ parte impulſus æquali AL:
<
lb
/>
principium motûs reliqui determinat AT diameter parallelo
<
lb
/>
grammi APTC in E. propterea quòd TC ſit æqualis reſiduo
<
lb
/>
impulſui LB. </
s
>
<
s
>Rurſum peractâ plagâ æquali AM; erit princi
<
lb
/>
pium motûs in F communi ſectione MF.
<
expan
abbr
="
atq;
">atque</
expan
>
AS lineæ dia
<
lb
/>
gonalis parallelogrammi AOSC,
<
expan
abbr
="
eademq;
">eademque</
expan
>
ratione invenie
<
lb
/>
mus puncta reliqua motûs ſinuoſi in GH I&c. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
THEOREMA XIV.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
<
emph
type
="
italics
"/>
Linea motûs proiectorum non eſt circulus, ne〈que〉 ulla ſectionum
<
lb
/>
conicarum.
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
<
emph
type
="
italics
"/>
Supponamus primùm eſſe lineam circularem.
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Quoniam
<
expan
abbr
="
itaq;
">itaque</
expan
>
triangula APT, AEV ſuntſimilia, erit FV ad
<
lb
/>
AV, ut AP ad TP. eſt autem TP pars 5 AP per probl: 4 Igitur & </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>