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]
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
page
|<
<
(72)
of 445
>
>|
<
echo
version
="
1.0
">
<
text
type
="
book
"
xml:lang
="
la
">
<
div
xml:id
="
echoid-div7
"
type
="
body
"
level
="
1
"
n
="
1
">
<
div
xml:id
="
echoid-div7
"
type
="
chapter
"
level
="
2
"
n
="
1
">
<
div
xml:id
="
echoid-div211
"
type
="
math:theorem
"
level
="
3
"
n
="
112
">
<
p
>
<
s
xml:id
="
echoid-s962
"
xml:space
="
preserve
">
<
pb
o
="
72
"
rhead
="
IO. BAPT. BENED.
"
n
="
84
"
file
="
0084
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0084
"/>
<
reg
norm
="
primum
"
type
="
context
">primũ</
reg
>
<
reg
norm
="
reſiduum
"
type
="
context
">reſiduũ</
reg
>
. </
s
>
<
s
xml:id
="
echoid-s963
"
xml:space
="
preserve
">Ad hæc
<
reg
norm
="
numerum
"
type
="
context
">numerũ</
reg
>
<
reg
norm
="
milliariorum
"
type
="
context
">milliariorũ</
reg
>
, quæ
<
reg
norm
="
ſecundus
"
type
="
context
">ſecũdus</
reg
>
viator die
<
reg
norm
="
ſeqennti
"
type
="
context
">ſeqẽnti</
reg
>
<
var
>.s.f.</
var
>
confi
<
lb
/>
ciet
<
reg
norm
="
ſumatur
"
type
="
simple
">ſumat̃</
reg
>
, ex quo numerus
<
reg
norm
="
milliarium
"
type
="
context
">milliariũ</
reg
>
<
reg
norm
="
diurnorum
"
type
="
context
">diurnorũ</
reg
>
primi detrahatur,
<
reg
norm
="
residuumque
"
type
="
context simple
">reſiduũq́;</
reg
>
pariter re
<
lb
/>
ſeruetur,
<
reg
norm
="
voceturque
"
type
="
simple
">voceturq́;</
reg
>
ſecundum reſiduum, poſtmodum numerum milliarium primi
<
lb
/>
vnius diei multiplicetur per primum reſiduum ſeruatum,
<
reg
norm
="
productumque
"
type
="
simple
">productumq́;</
reg
>
per
<
reg
norm
="
ſecundum
"
type
="
context
">ſecundũ</
reg
>
<
lb
/>
reſiduum diuidatur
<
var
>.a.c.</
var
>
<
reg
norm
="
proueniens
"
type
="
context
">proueniẽs</
reg
>
(
<
reg
norm
="
quod
"
type
="
simple
">ꝙ</
reg
>
erit iter primi in ſequenti die) iungatur reſi-
<
lb
/>
ſiduo primo, tot enim erunt milliaria conficienda a ſecundo ſequenti die, vt
<
lb
/>
ſeſe conſequantur.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s964
"
xml:space
="
preserve
">Vtautem ſciamus quantam partem diei
<
reg
norm
="
ſeqenntis
"
type
="
context
">ſeqẽntis</
reg
>
, ſingulos itinere agere oporteat,
<
lb
/>
<
reg
norm
="
proueniens
"
type
="
context
">proueniẽs</
reg
>
per .24. horas multiplicetur (ſuppoſito quod
<
reg
norm
="
ambulantes
"
type
="
context
">ambulãtes</
reg
>
<
reg
norm
="
nullam
"
type
="
context
">nullã</
reg
>
<
reg
norm
="
requiem
"
type
="
context
">requiẽ</
reg
>
nec
<
lb
/>
die nec nocte
<
reg
norm
="
capiant
"
type
="
context
">capiãt</
reg
>
),
<
reg
norm
="
productumque
"
type
="
simple context simple
">ꝓductũq́;</
reg
>
<
reg
norm
="
per
"
type
="
simple
">ꝑ</
reg
>
<
reg
norm
="
numerum
"
type
="
context
">numerũ</
reg
>
milliariorum vuius diei primi viatoris di
<
lb
/>
uidatur, ex quo dabitur
<
reg
norm
="
quantitas
"
type
="
context
">quãtitas</
reg
>
<
reg
norm
="
horarum
"
type
="
context
">horarũ</
reg
>
, & pars horæ, qua
<
reg
norm
="
cuique
"
type
="
simple
">cuiq;</
reg
>
illa die
<
reg
norm
="
ambulandum
"
type
="
context
">ambulandũ</
reg
>
<
lb
/>
eſt. </
s
>
<
s
xml:id
="
echoid-s965
"
xml:space
="
preserve
">Idem accideret ſi primum reſiduum reſeruatum cum proueniente in ſummam
<
lb
/>
colligeretur,
<
reg
norm
="
eaque
"
type
="
simple
">eaq́;</
reg
>
ſumma per .24. horas multiplicaretur,
<
reg
norm
="
productumque
"
type
="
simple
">productumq́;</
reg
>
per
<
reg
norm
="
nume- rum
"
type
="
context
">nume-
<
lb
/>
rũ</
reg
>
milliariorum ſequenti die à ſecundo conficiendorum diuideretur. </
s
>
<
s
xml:id
="
echoid-s966
"
xml:space
="
preserve
">I dipſum quo-
<
lb
/>
que eueniret multiplicato primo reſiduo per .24. & producto per ſecundum reſi-
<
lb
/>
duum diuiſo.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s967
"
xml:space
="
preserve
">Exempli gratia, primus viator diurna milliaria vndecim conficit, ſecundus, pri-
<
lb
/>
ma die tria, ſecunda .6. tertia .9.
<
reg
norm
="
atque
"
type
="
simple
">atq;</
reg
>
ita deinceps, diuidatur ergo .11. per .3. vnde
<
lb
/>
pro numero
<
var
>.o.n.</
var
>
dabitur .3.
<
reg
norm
="
ſupereritque
"
type
="
simple
">ſupereritq́;</
reg
>
.2. </
s
>
<
s
xml:id
="
echoid-s968
"
xml:space
="
preserve
">quare:
<
var
>u.n.</
var
>
ab
<
var
>.e.n.</
var
>
duobus milliaribus ſu-
<
lb
/>
perabitur, et
<
var
>.i.t.</
var
>
dictum
<
var
>.e.n.</
var
>
vno milliario, ex quo ante diem
<
var
>.e.u.n.</
var
>
duobus diebus
<
lb
/>
iter egerunt,
<
reg
norm
="
totque
"
type
="
simple
">totq́;</
reg
>
diebus ambulandum erit poſt
<
var
>.t.i.</
var
>
hoceſt .6. in vniuerſum inte-
<
lb
/>
gris. </
s
>
<
s
xml:id
="
echoid-s969
"
xml:space
="
preserve
">Ad hęc multiplicato
<
var
>.o.f.</
var
>
hoc eſt .6. per
<
var
>.x.o.</
var
>
hoc eſt .3. habebimus
<
var
>.s.f.</
var
>
<
reg
norm
="
milliariorum
"
type
="
context
">milliariorũ</
reg
>
<
lb
/>
18.
<
reg
norm
="
tum
"
type
="
context
">tũ</
reg
>
<
reg
norm
="
coniuncto
"
type
="
context context
">cõiũcto</
reg
>
<
var
>.x.o.</
var
>
primo termino hoc eſt .3.
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
<
var
>.s.f.</
var
>
hoc eſt .18. vltimo termino, habe
<
lb
/>
bimus .21. quo multiplicato
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
dimidio
<
var
>.o.f.</
var
>
hoc eſt .3. habebimus totam ſummam
<
lb
/>
progreſſionis .63. ſex dierum integrorum ex .94. theoremate, tum multiplicato .11.
<
lb
/>
nempe numero
<
reg
norm
="
milliariorum
"
type
="
context
">milliariorũ</
reg
>
diurnorum primi cum .6. hoc eſt cum
<
var
>.o.f.</
var
>
habebimus pa
<
lb
/>
rallelogrammum à primo ſex diebus integris confectum milliariorum .66. ex quo
<
lb
/>
detracta .63. ſumma inquam progreſſionis, ſupererit pro primo reſiduo .3. ſumptis
<
lb
/>
poſtea milliaribus .21. pro itinere, quod ſecundus die ſequenti
<
var
>.s.f.</
var
>
conficeret, & ex
<
lb
/>
ijs detracto numero
<
reg
norm
="
milliariorum
"
type
="
context
">milliariorũ</
reg
>
diurnorum primi, nempe .11. ſecundum reſiduum
<
lb
/>
erit 10. quod pro diuidenti ſeruabitur. </
s
>
<
s
xml:id
="
echoid-s970
"
xml:space
="
preserve
">Iam multiplicato .11. cum primo reſiduo
<
num
value
="
3
">.
<
lb
/>
3.</
num
>
dabitur .33. qui diuiſus per .10. ſecundum reſiduum profert .3. cum tribus decimis,
<
lb
/>
<
reg
norm
="
eritque
"
type
="
simple
">eritq́</
reg
>
iter à primo viatore ſequenti die conficiendum, hoc etiam ipſum proueniens
<
lb
/>
cum primo reſiduo .3. coniunctum, dat .6. cum tribus decimis, quod eſt iter ſecundi
<
lb
/>
viatoris illa ſequenti die. </
s
>
<
s
xml:id
="
echoid-s971
"
xml:space
="
preserve
">Ad inueniendam autem quantitatem diei, qua vtrique
<
lb
/>
ambulandum eſt, perinde erit multiplicare proueniens .3. & tres decimas per .24. ho
<
lb
/>
ras, & productum per .11. dimidium iter primi viatoris partiri, ac multiplicare ſum
<
lb
/>
mam .6. & tres decimas cum .24. horis,
<
reg
norm
="
productumque
"
type
="
simple
">productumq́</
reg
>
diuidere per .21. hoc eſt periter
<
lb
/>
ſecundi viatoris ſequentis diei, vtrinque enim ſemper ſeptem horæcum .12. minu
<
lb
/>
tis prouenient. </
s
>
<
s
xml:id
="
echoid-s972
"
xml:space
="
preserve
">Idipſum accidet multiplicato per .24. horas primo reſiduo .3. pro-
<
lb
/>
<
reg
norm
="
ductoque
"
type
="
simple
">ductoq́;</
reg
>
diuiſo per ſecundum reſiduum .10.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s973
"
xml:space
="
preserve
">Quarum ſpeculationum gratia, totum iter parallelogrammi primi viatoris die-
<
lb
/>
rum integrorum fignificetur linea
<
var
>.n.e.</
var
>
ſumma verò progreſſionis ſecundi linea
<
var
>.f.m.</
var
>
<
lb
/>
parallela
<
var
>.n.e.</
var
>
<
reg
norm
="
eritque
"
type
="
simple
">eritq́;</
reg
>
<
var
>.f.m.</
var
>
minor
<
var
>.n.e</
var
>
. </
s
>
<
s
xml:id
="
echoid-s974
"
xml:space
="
preserve
">Conſtituamus deinde à termino
<
var
>.f.n.</
var
>
(majoris
<
lb
/>
<
reg
norm
="
intelligentię
"
type
="
context
">intelligẽtię</
reg
>
gratia) vtranque
<
reg
norm
="
perpendiculariter
"
type
="
context
">perpẽdiculariter</
reg
>
duci,
<
reg
norm
="
producatur
"
type
="
simple
">ꝓducatur</
reg
>
deinde
<
var
>.n.e.</
var
>
donec
<
var
>.e.
<
lb
/>
d.</
var
>
æqualis ſit itineri diurno primi viatoris, item etiam producatur
<
var
>.f.m.</
var
>
donec
<
var
>.m.K.</
var
>
<
lb
/>
æqualis ſit itineri à ſecundo confecto ſequenti die vltimum integrum progreſſio- </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>