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
Table of contents
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 163
[out of range]
>
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 163
[out of range]
>
page
|<
<
(384)
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-div477
"
type
="
chapter
"
level
="
2
"
n
="
6
">
<
div
xml:id
="
echoid-div737
"
type
="
section
"
level
="
3
"
n
="
42
">
<
div
xml:id
="
echoid-div737
"
type
="
letter
"
level
="
4
"
n
="
1
">
<
p
>
<
s
xml:id
="
echoid-s4554
"
xml:space
="
preserve
">
<
pb
o
="
384
"
rhead
="
IO. BAPT. BENED.
"
n
="
396
"
file
="
0396
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0396
"/>
eiuſdem erit vt
<
var
>.a.d.</
var
>
ad
<
var
>.d.b</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4555
"
xml:space
="
preserve
">Idem etiam dico in ſecunda parabola, ſed ipſius
<
var
>.x.o.</
var
>
ad
<
lb
/>
<
var
>o.r.</
var
>
eſt vt
<
var
>.a.b.</
var
>
ad
<
var
>.b.d.</
var
>
ex .6. ſexti Eucli. </
s
>
<
s
xml:id
="
echoid-s4556
"
xml:space
="
preserve
">vnde ex .11. quinti
<
var
>.n.f.</
var
>
ad
<
var
>.f.x.</
var
>
erit vt
<
var
>.ω.y.</
var
>
<
lb
/>
ad
<
var
>.y.g</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4557
"
xml:space
="
preserve
">Sed in precedenti iam tibi dixi
<
var
>.a.b.</
var
>
mediam proportionalem eſſe inter
<
var
>.h.</
var
>
<
lb
/>
et
<
var
>.b.d</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4558
"
xml:space
="
preserve
">Sit nunc
<
var
>.z.</
var
>
pro ſecunda parabola, ita ut
<
var
>.h.</
var
>
eſt pro prima, vnde
<
var
>.o.x.</
var
>
crit media
<
lb
/>
proportionalis inter
<
var
>.z.</
var
>
et
<
var
>.o.r.</
var
>
& ex .11. quinti ita erit
<
var
>.h.</
var
>
ad
<
var
>.a.b.</
var
>
vt
<
var
>.z.</
var
>
ad
<
var
>.x.o.</
var
>
& ex .22.
<
lb
/>
h. ad
<
var
>.a.x.</
var
>
ut z. ad
<
var
>.x.g.</
var
>
& quia ex .16. ſexti
<
var
>.a.x.</
var
>
media proportionalis eſt inter
<
var
>.h.</
var
>
et
<
var
>.f.
<
lb
/>
x.</
var
>
cum ſupponatur productum
<
var
>.h.</
var
>
in
<
var
>.f.x.</
var
>
æquale eſſe quadrato
<
var
>.a.x</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4559
"
xml:space
="
preserve
">Idem dico
<
var
>.x.g.</
var
>
<
lb
/>
mediam eſſe proportionalem inter
<
var
>.z.</
var
>
et
<
var
>.g.y.</
var
>
</
s
>
<
s
xml:id
="
echoid-s4560
"
xml:space
="
preserve
">quare ex .11. iam dicta, ita erit
<
var
>.a.x.</
var
>
ad
<
var
>.f.
<
lb
/>
x.</
var
>
vt
<
var
>.y.g.</
var
>
ad
<
var
>.x.o.</
var
>
& ex eadem, ita erit ipſius
<
var
>.f.n.</
var
>
ad
<
var
>.a.b.</
var
>
ut
<
var
>.y.ω.</
var
>
ad
<
var
>.x.o.</
var
>
& ſic
<
var
>.f.n.</
var
>
ad
<
var
>.d.a.</
var
>
<
lb
/>
vt
<
var
>.y.ω.</
var
>
ad
<
var
>.x.r.</
var
>
ſed
<
var
>.f.m.</
var
>
ad
<
var
>f.n.</
var
>
eſt vt
<
var
>.y.t.</
var
>
ad
<
var
>.y.ω.</
var
>
ex .18. quinti vnde
<
var
>.f.m.</
var
>
ad
<
var
>.a.d.</
var
>
erit vt
<
lb
/>
<
var
>y.t.</
var
>
ad
<
var
>.x.r</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4561
"
xml:space
="
preserve
">Idem dico de eorum duplis.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4562
"
xml:space
="
preserve
">Ex ijſdem rationibus dico ita eſſe
<
var
>.b.d.</
var
>
ad
<
var
>.b.m.</
var
>
vt
<
var
>.o.r.</
var
>
ad
<
var
>.o.t.</
var
>
& ex .17. quinti
<
var
>.d.m.</
var
>
<
lb
/>
ad
<
var
>.b.m.</
var
>
vt
<
var
>.r.t.</
var
>
ad
<
var
>.t.o</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4563
"
xml:space
="
preserve
">Reliqua tibi conſideranda relinquo.</
s
>
</
p
>
<
figure
position
="
here
"
number
="
437
">
<
image
file
="
0396-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0396-01
"/>
</
figure
>
<
p
>
<
s
xml:id
="
echoid-s4564
"
xml:space
="
preserve
">In reliquis verò propoſitionibus illius lib. nullo pacto poteris dubitare: </
s
>
<
s
xml:id
="
echoid-s4565
"
xml:space
="
preserve
">Verum ne
<
lb
/>
in .4. aliquid tibi noui exurgat, te ſcire volo
<
ref
id
="
ref-0025
">corollarium .20. in libr. de quadratu
<
lb
/>
ra parabolę</
ref
>
docere poſſibile eſſe inſcriptionem rectilineæ, ea tamen conditione
<
reg
norm
="
quam
"
type
="
context
">quã</
reg
>
<
lb
/>
dicit Archimedes.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4566
"
xml:space
="
preserve
">In quinta poſtea animaduertendum eſt, quod prima pars, probat tantummodo de
<
lb
/>
centro trianguli, et .2. pars probat de centro pentagoni, à te ipſo deinde potes pro-
<
lb
/>
bare de centro nonanguli: </
s
>
<
s
xml:id
="
echoid-s4567
"
xml:space
="
preserve
">& ſic de cæteris: </
s
>
<
s
xml:id
="
echoid-s4568
"
xml:space
="
preserve
">eo quod cum probatum fuerit de centro
<
lb
/>
figuræ in medio locatæ ſi conſtitutæ poſtea fuerint ſimiles figuræ in portionibus la-
<
lb
/>
teralibus habebitur propoſitum in infinitum.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4569
"
xml:space
="
preserve
">Idem intelligendum eſt in .3. propoſitione quamuis exemplum vlterius non ex-
<
lb
/>
tendatur quam ad pentagonos.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4570
"
xml:space
="
preserve
">Sexta verò
<
reg
norm
="
propoſitio
"
type
="
simple
">ꝓpoſitio</
reg
>
tibi ſacilis erit, quæ nihilominus
<
reg
norm
="
pont
"
type
="
context
">põt</
reg
>
<
reg
norm
="
demonſtrari
"
type
="
context
">demõſtrari</
reg
>
hoc
<
reg
norm
="
mon
"
type
="
context
">mõ</
reg
>
ſcili
<
lb
/>
cet. </
s
>
<
s
xml:id
="
echoid-s4571
"
xml:space
="
preserve
">Sint .4.
<
reg
norm
="
quantitates
"
type
="
context
">quãtitates</
reg
>
<
var
>.a.b.c.d.</
var
>
ipſius Archimedis
<
reg
norm
="
ſupponendo
"
type
="
context
">ſupponẽdo</
reg
>
<
var
>.a.</
var
>
pro figura rectilinea
<
lb
/>
inſcripta in parabola, et
<
var
>.b.</
var
>
pro reſiduo ipſius parabolę et
<
var
>.c.</
var
>
pro triangulo
<
var
>.a.b.c.</
var
>
in me
<
lb
/>
dio ipſius parabolę et
<
var
>.d.</
var
>
pro triangulo
<
var
>.r</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4572
"
xml:space
="
preserve
">Nunc cum
<
var
>.a.</
var
>
maior ſit
<
var
>.c.</
var
>
prout totum ma-
<
lb
/>
ius eſt ſua parte, ideo ex .8. quinti maior proportio habebit
<
var
>.a.</
var
>
ad
<
var
>.b.</
var
>
quam
<
var
>.c.</
var
>
ad
<
var
>.b.</
var
>
<
lb
/>
Cum autem
<
var
>.b.</
var
>
minor ſit
<
var
>.d.</
var
>
ex ſuppoſito, ideo ex eadem dicta, maior proportio habe
<
lb
/>
bit
<
var
>.a.</
var
>
ad
<
var
>.b.</
var
>
quam
<
var
>.c.</
var
>
ad
<
var
>.d.</
var
>
cum verò centrum cuiuſuis figuræ plenæ neceſſariò ſit intra
<
lb
/>
ipſam figuram, idcirco centrum reſidui ipſius parabolę intra ipſam reperietur. </
s
>
<
s
xml:id
="
echoid-s4573
"
xml:space
="
preserve
">quod
<
lb
/>
ita
<
reg
norm
="
clarum
"
type
="
context
">clarũ</
reg
>
<
reg
norm
="
per
"
type
="
simple
">ꝑ</
reg
>
ſe eſt,
<
reg
norm
="
quemadmodum
"
type
="
wordlist
">quẽadmodũ</
reg
>
quoduis aliud axioma, & quia
<
reg
norm
="
dictum
"
type
="
context
">dictũ</
reg
>
<
reg
norm
="
centrum
"
type
="
context
">centrũ</
reg
>
ex .8. primi
<
lb
/>
de centris, neceſſariò eſt in linea
<
var
>.b.h.</
var
>
inter
<
var
>.b.</
var
>
et
<
var
>.h</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4574
"
xml:space
="
preserve
">Sit igitur
<
var
>.g.</
var
>
vnde ex eadem .8. ita
<
lb
/>
erit
<
var
>.g.h.</
var
>
ad
<
var
>.h.e.</
var
>
vt
<
var
>.a.</
var
>
ad
<
var
>.b.</
var
>
ergo
<
var
>.g.h.</
var
>
ad
<
var
>.h.e.</
var
>
maior proportio erit
<
reg
norm
="
quam
"
type
="
context
">quã</
reg
>
<
var
>.c.</
var
>
ad
<
var
>.d.</
var
>
hoc eſt
<
lb
/>
quam
<
var
>.b.h.</
var
>
ad
<
var
>.f.</
var
>
ex .12. quinti. </
s
>
<
s
xml:id
="
echoid-s4575
"
xml:space
="
preserve
">Sed
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
<
var
>.h.b.</
var
>
maior ſit ipſa
<
var
>.h.g.</
var
>
prout omne totum ma-
<
lb
/>
ius eſt ſua parte, ideo maior proportio habebit
<
var
>.h.b.</
var
>
ad
<
var
>.h.e.</
var
>
quam
<
var
>.h.g.</
var
>
ad
<
var
>.h.e.</
var
>
vnde
<
lb
/>
multo
<
reg
norm
="
maiorem
"
type
="
context
">maiorẽ</
reg
>
<
reg
norm
="
quam
"
type
="
context
">quã</
reg
>
<
var
>.h.b.</
var
>
ad
<
var
>.f.</
var
>
ex
<
reg
norm
="
coni
"
type
="
context
">cõi</
reg
>
<
reg
norm
="
conceptu
"
type
="
context
">cõceptu</
reg
>
, </
s
>
<
s
xml:id
="
echoid-s4576
"
xml:space
="
preserve
">quare
<
var
>.h.e.</
var
>
erit minor ipſa
<
var
>.f.</
var
>
ex .10.
<
reg
norm
="
quinti
"
type
="
context
">quĩti</
reg
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4577
"
xml:space
="
preserve
">Septima verò et .8. propoſitio nullius tibi erit difficultatis.</
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>