Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
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166
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IO. BAPT. BENED.
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178
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0178
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cto
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>.c.</
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vnde linea
<
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mediante
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>.K.</
var
>
continget circunferentiam circuli minoris in pun
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cto .b: et
<
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>.K.g.</
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ex .34. primi Eucli. æqualis erit ipſi
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quia ex .17. tertii, anguli
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var
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et
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>.g.</
var
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ſunt æquales, vnde ex .28. primi
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et
<
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ſunt parallelæ. </
s
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<
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xml:id
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xml:space
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">& ſic erunt
<
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cum
<
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>.f.g.</
var
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ex
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eadem ſupradicta. </
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>
<
s
xml:id
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xml:space
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">Ratio autem, qua arcus
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>.g.b.</
var
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tranſierit lineam
<
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>.g.K.</
var
>
maiorem ipſa,
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/>
eſt, quia dum mouetur, quodlibet punctum ipſius
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>.g.b.</
var
>
virtute reuolutionis ipſius
<
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>.f.c.</
var
>
<
lb
/>
omne punctum eiuſdem arcus
<
var
>.g.b.</
var
>
vlterius verſus
<
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>.K.</
var
>
quam ſi moueretur virtute re-
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/>
uolutionis ipſius
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>.g.b.</
var
>
ſuper lineam
<
var
>.g.m.</
var
>
defertur. </
s
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<
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xml:id
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xml:space
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preserve
">vt exempli gratia, quando virtute
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reuolutionis maioris circuli, centrum
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var
>
reperitur in ſitu lineæ
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>.l.K.</
var
>
punctum
<
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>.g.</
var
>
confe
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lb
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cerit iter
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var
>
& punctum
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>.b.</
var
>
iter
<
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var
>
etiam reliqua omnia puncta inter
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>.g.b.</
var
>
magna
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itinera egerint, cum à magno circulo ſint ante delata. </
s
>
<
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xml:id
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xml:space
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">Imaginemur quoque hos cir
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culos eſſe delatos virtute reuolutionis circuli minoris, &
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type
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<
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var
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rectè
<
var
>.g.m.</
var
>
dimen-
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ſam fuiſſe ab arcu
<
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>.g.b</
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. </
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<
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Quando
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type
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ergo
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var
>
erit in
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>.t.</
var
>
factum erit iter
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>.b.t.</
var
>
ab ipſo
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>.b.</
var
>
et
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var
>.g.</
var
>
fa-
<
lb
/>
ciet iter
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>.g.n.</
var
>
quę itinera alijs multò breuiora ſunt, quia breuioribus cruribus reuolu-
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ta ſunt dicta puncta; </
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<
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xml:id
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xml:space
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">& ſic dico de reliquis omnibus punctis inter
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>.g.</
var
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et
<
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>.b.</
var
>
& in hoc ca
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lb
/>
ſu punctum
<
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>.f.</
var
>
erit in
<
var
>.q.</
var
>
& punctum
<
var
>.c.</
var
>
erit in
<
var
>.e</
var
>
. </
s
>
<
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xml:id
="
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xml:space
="
preserve
">Quamobrem omnia puncta
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norm
="
contingen- tiæ
"
type
="
context
">cõtingen-
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lb
/>
tiæ</
reg
>
inter
<
var
>.f.</
var
>
et
<
var
>.c.</
var
>
non ſolum non erunt delata anteà, ſed potius à primo ſitu retrorſum
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erunt repulſa. </
s
>
<
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xml:space
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preserve
">Vnde non eſt, quòd in tantam admirationem ducamur ſi dum reuol
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uitur circulus maior, arcus
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>.g.b.</
var
>
circuli minoris, totam lineam
<
var
>.g.K.</
var
>
tranſire videtur,
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/>
& dum reuoluitur minor, apparet arcum
<
var
>.f.c</
var
>
: maius iter quam ab
<
var
>.f.</
var
>
ad
<
var
>.e.</
var
>
non facere,
<
lb
/>
cum maiore ſeſe in orbem ferente, quodlibet punctum arcus
<
var
>.g.b.</
var
>
ad vnam
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eandemque
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type
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reg
>
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partem duos motus obtineat. </
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<
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xml:id
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xml:space
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preserve
">vt exempli gratia punctum
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>.b.</
var
>
non ſolum mouetur ver
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ſus
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>.m.</
var
>
quòd circa centrum
<
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>
feratur, cum ipſum etiam centrum moueatur verſus
<
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>.m.</
var
>
<
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ſed quia pręter hoc deferantur quoque à circulo maiori verſus
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vſque ad lineam
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<
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/>
k.l</
var
>
. </
s
>
<
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xml:space
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">Dum verò minor circulus in girum ducitur, habet quodlibet punctum arcus
<
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var
>
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/>
duos motus contrarios, quorum alter verſus
<
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>.i.</
var
>
virtute reuolutionis circuli minoris,
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lb
/>
& alter ex eo,
<
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type
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dictus circulus maior circa centrum
<
var
>.a.</
var
>
voluatur, vnde omne
<
reg
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="
punctum
"
type
="
context
">punctũ</
reg
>
<
lb
/>
contactus circuli maioris cum recta
<
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>.f.i.</
var
>
tetrorſum pellitur verſus
<
var
>.x</
var
>
.</
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