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
List of thumbnails
<
0 - 9
10 - 19
20 - 29
30 - 39
40 - 49
50 - 59
60 - 69
70 - 79
80 - 89
90 - 99
100 - 109
110 - 119
120 - 129
130 - 139
140 - 149
150 - 159
160 - 169
170 - 179
180 - 189
190 - 199
200 - 209
210 - 219
220 - 229
230 - 239
240 - 249
250 - 259
260 - 269
270 - 279
280 - 289
290 - 299
300 - 309
310 - 319
320 - 329
330 - 339
340 - 349
350 - 359
360 - 369
370 - 379
380 - 389
390 - 399
400 - 409
410 - 419
420 - 429
430 - 439
440 - 445
>
201
(189)
202
(190)
203
(191)
204
(192)
205
(193)
206
(194)
207
(195)
208
(196)
209
(197)
210
(198)
<
0 - 9
10 - 19
20 - 29
30 - 39
40 - 49
50 - 59
60 - 69
70 - 79
80 - 89
90 - 99
100 - 109
110 - 119
120 - 129
130 - 139
140 - 149
150 - 159
160 - 169
170 - 179
180 - 189
190 - 199
200 - 209
210 - 219
220 - 229
230 - 239
240 - 249
250 - 259
260 - 269
270 - 279
280 - 289
290 - 299
300 - 309
310 - 319
320 - 329
330 - 339
340 - 349
350 - 359
360 - 369
370 - 379
380 - 389
390 - 399
400 - 409
410 - 419
420 - 429
430 - 439
440 - 445
>
page
|<
<
(148)
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-div340
"
type
="
chapter
"
level
="
2
"
n
="
3
">
<
div
xml:id
="
echoid-div350
"
type
="
section
"
level
="
3
"
n
="
6
">
<
pb
o
="
148
"
rhead
="
IO. BABPT. BENED.
"
n
="
160
"
file
="
0160
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0160
"/>
</
div
>
<
div
xml:id
="
echoid-div352
"
type
="
section
"
level
="
3
"
n
="
7
">
<
head
xml:id
="
echoid-head207
"
style
="
it
"
xml:space
="
preserve
">De quibuſdam erroribus Nicolai Tartaleæ circa pondera
<
lb
/>
corporum & eorum motus, quorum aliqui deſumpti
<
lb
/>
fuerunt à fordano ſcriptore quodam antiquo.</
head
>
<
head
xml:id
="
echoid-head208
"
xml:space
="
preserve
">CAP. VII.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1761
"
xml:space
="
preserve
">CVm magis amici veritatis eſſe debeamus quàm cuiuſquam hominis, quemad-
<
lb
/>
modum Ariſto. ſcribit, detegam hoc loco quoſdam errores Nicolai Tartaleę
<
lb
/>
de ponderibus corporum, & velocitatibus motuum localium. </
s
>
<
s
xml:id
="
echoid-s1762
"
xml:space
="
preserve
">Et primum decipitur
<
lb
/>
is in .8. lib. ſuarum diuerſarum inuentionum in ſecunda propoſitione, cum non ani-
<
lb
/>
maduerterit quanti momenti ſint extrinſecæ reſiſtentiæ.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1763
"
xml:space
="
preserve
">Subiectum quoque tertiæ propoſitionis eſt malè demonſtratum, quia idem pla-
<
lb
/>
nè ex eius demonſtratione iam dicta corporibus hætereogeneis, aut figura diuerſis
<
lb
/>
contingeret, quod ad velocitates attinet.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1764
"
xml:space
="
preserve
">In quarta propoſitione, quod ad
<
reg
norm
="
diſputandum
"
type
="
context context
">diſputãdũ</
reg
>
proponit
<
reg
norm
="
non
"
type
="
context
">nõ</
reg
>
concludit melius. </
s
>
<
s
xml:id
="
echoid-s1765
"
xml:space
="
preserve
">
<
reg
norm
="
autem
"
type
="
context
">autẽ</
reg
>
id
<
lb
/>
ab eo
<
reg
norm
="
ſequitur
"
type
="
simple
">ſequit̃</
reg
>
, quod Archimedes in .6. propoſitione lib. primi de
<
reg
norm
="
ponderibus
"
type
="
context
">põderibus</
reg
>
<
reg
norm
="
probauit
"
type
="
simple
">ꝓbauit</
reg
>
.</
s
>
</
p
>
<
handwritten
number
="
8
"/>
<
p
>
<
s
xml:id
="
echoid-s1766
"
xml:space
="
preserve
">Sed in ſecunda parte quintę propoſitionis non uidet
<
reg
norm
="
quod
"
type
="
simple
">ꝙ</
reg
>
uigore ſitus eo modo, quo
<
lb
/>
ipſe diſputat, nulla elicitur ponderis differentia. </
s
>
<
s
xml:id
="
echoid-s1767
"
xml:space
="
preserve
">quia ſi corpus
<
var
>.B.</
var
>
deſcendere debet
<
lb
/>
per arcum
<
var
>.i.l.</
var
>
corpus
<
var
>.A.</
var
>
aſcendere debet per arcum
<
var
>.u.s.</
var
>
æqualem, & ſimilem. eadem
<
lb
/>
quoque ratione ſituatum, vt eſt arcus
<
var
>.i.l.</
var
>
vnde vt eſt facilè corpori
<
var
>.B.</
var
>
deſcendere
<
lb
/>
per arcum
<
var
>.i.l.</
var
>
difficile ita erit corpori
<
var
>.A.</
var
>
aſcendere per arcum
<
var
>.u.s</
var
>
. </
s
>
<
s
xml:id
="
echoid-s1768
"
xml:space
="
preserve
">Hęc autem qnin
<
lb
/>
ta propoſitio Tartaleæ eſt ſecuuda quæſtio à Iordano propoſita.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1769
"
xml:space
="
preserve
">Quòd autem ad primum corollarium dictæ propoſitionis attinet, verum ille qui
<
lb
/>
dem ſcribit, eius tamen effectus cauſa & à Iordano prius, & ab ipſo poſtea citata, na-
<
lb
/>
tura ſua vera non eſt. </
s
>
<
s
xml:id
="
echoid-s1770
"
xml:space
="
preserve
">quia vera cauſa per ſe ab eo oritur,
<
reg
norm
="
quod
"
type
="
simple
">ꝙ</
reg
>
à centro libræ dependeat
<
lb
/>
vt primo cap. huius tractatus oſtendi. </
s
>
<
s
xml:id
="
echoid-s1771
"
xml:space
="
preserve
">Secundum verò corollarium falſum eſſe, ijs ra
<
lb
/>
tionibus quas nunc ſubiungam, patebit. </
s
>
<
s
xml:id
="
echoid-s1772
"
xml:space
="
preserve
">Imaginemur
<
var
>.u.</
var
>
pro centro regionis ele-
<
lb
/>
mentaris, & libram
<
var
>.b.o.a.</
var
>
obliquam reſpectu ad
<
var
>.u.</
var
>
& brachijs æqualibus
<
reg
norm
="
conſtantem
"
type
="
context
">conſtãtem</
reg
>
,
<
lb
/>
& pondera in
<
var
>.a.</
var
>
et in
<
var
>.b.</
var
>
etiam æqualia. </
s
>
<
s
xml:id
="
echoid-s1773
"
xml:space
="
preserve
">lineæ autem inclinationum ſint
<
var
>.a.u.</
var
>
et
<
var
>.b.u.</
var
>
<
lb
/>
imaginemur etiam lineam
<
var
>.o.u.</
var
>
& à centro
<
var
>.o.</
var
>
libræ duas
<
var
>.o.t.</
var
>
et
<
var
>.o.e.</
var
>
perpendiculares
<
lb
/>
inclinationum lineis; </
s
>
<
s
xml:id
="
echoid-s1774
"
xml:space
="
preserve
">vnde pondus ipſius
<
var
>.a.</
var
>
in huiuſmodi ſitu tam erit proportiona
<
lb
/>
tum ponderi
<
var
>.b.</
var
>
quam proportionata erit linea
<
var
>.o.t.</
var
>
lineæ
<
var
>.o.e.</
var
>
ex eo
<
reg
norm
="
quod
"
type
="
simple
">ꝙ</
reg
>
tertio cap. hu-
<
lb
/>
iustractatus probaui, ſed linea
<
var
>.o.t.</
var
>
maior eſt linea
<
var
>.o.e.</
var
>
quod ſic probo. </
s
>
<
s
xml:id
="
echoid-s1775
"
xml:space
="
preserve
">Imaginemur
<
lb
/>
triangulum
<
var
>.u.a.b.</
var
>
circunſcriptum eſſe à circulo
<
var
>.u.a.n.b.</
var
>
cuius
<
var
>.c.</
var
>
ſit centrum,
<
reg
norm
="
quod
"
type
="
simple
">ꝙ</
reg
>
erit
<
lb
/>
extra lineam
<
var
>.u.o.</
var
>
cum ſupponatur
<
var
>.a.o.b.</
var
>
obliquam eſſe reſpectu ad
<
var
>.u.o</
var
>
. </
s
>
<
s
xml:id
="
echoid-s1776
"
xml:space
="
preserve
">Imagine-
<
lb
/>
mur deinde à centro
<
var
>.c.</
var
>
lineam
<
var
>.c.o.s.</
var
>
vſque ad circunferentiam, quæ perpendicula-
<
lb
/>
ris erit ipſi
<
var
>.a.b.</
var
>
ex tertia lib. 3. Eucli. </
s
>
<
s
xml:id
="
echoid-s1777
"
xml:space
="
preserve
">ſi poſteà imaginemur duas lineas
<
var
>.c.a.</
var
>
et
<
var
>.c.b.</
var
>
ha
<
lb
/>
bebimus ex .8. lib. primi, angulum
<
var
>.a.c.o.</
var
>
æqualem angulo
<
var
>.b.c.o</
var
>
. </
s
>
<
s
xml:id
="
echoid-s1778
"
xml:space
="
preserve
">Vnde ex .25. lib. 3.
<
lb
/>
arcus
<
var
>.a.s.</
var
>
æqualis erit arcui
<
var
>.b.s.</
var
>
ſed ſi imaginabimur
<
var
>.u.o.</
var
>
ad circunferentiam vſque
<
lb
/>
productam, clarum erit
<
reg
norm
="
quod
"
type
="
simple
">ꝙ</
reg
>
arcum
<
var
>.s.b.</
var
>
ſecaret in puncto
<
var
>.n.</
var
>
vnde arcus
<
var
>.n.b.</
var
>
minor erit
<
lb
/>
arcu
<
var
>.n.a.</
var
>
& ſic etiam angulus
<
var
>.n.u.b.</
var
>
minor erit angulo
<
var
>.n.u.a.</
var
>
ex
<
ref
id
="
ref-0024
">ultima lib. 6.</
ref
>
</
s
>
<
s
xml:id
="
echoid-s1779
"
xml:space
="
preserve
">Imagi-
<
lb
/>
nemur nunc alium quendam circulum, cuius
<
var
>.o.u.</
var
>
ſit diameter, cuius circunferentia
<
lb
/>
per duo puncta
<
var
>.e.</
var
>
et
<
var
>.t.</
var
>
<
reg
norm
="
prætergradiatur
"
type
="
simple
">prætergradiat̃</
reg
>
, cum in ipſis ſint angulirecti, quod quilibet ex
<
lb
/>
ſeratio cinando colligere poteſt, ſi .30. lib. 3. in mentem reuocauerit. </
s
>
<
s
xml:id
="
echoid-s1780
"
xml:space
="
preserve
">Sed cum angu-
<
lb
/>
lus
<
var
>.o.u.t.</
var
>
ſit maior angulo
<
var
>.o.u.e.</
var
>
arcus
<
var
>.o.t.</
var
>
maior erit arcu
<
var
>.o.e.</
var
>
ex vltima .6. vnde cor
<
lb
/>
da
<
var
>.o.t.</
var
>
maior erit corda ipſius
<
var
>.o.e.</
var
>
ex conuerſo .27. lib. 3. quod eſt propoſitum. </
s
>
<
s
xml:id
="
echoid-s1781
"
xml:space
="
preserve
">Pon-
<
lb
/>
<
handwritten
xlink:label
="
hd-0160-01
"
xlink:href
="
hd-0160-01a
"
number
="
9
"/>
dusigitur ipſius
<
var
>.a.</
var
>
in huiuſmodi ſitu, pondere ipſius
<
var
>.b.</
var
>
grauius erit. </
s
>
<
s
xml:id
="
echoid-s1782
"
xml:space
="
preserve
">Quod è directo ijs
<
lb
/>
repugnat quæ Tartalea in 2. parte quinræ propoſitionis ediſerit, & per conſequens
<
lb
/>
2. corollarij falſitatem oſtendit, vt eam quoque, quæ in 6. propoſitione latet. </
s
>
<
s
xml:id
="
echoid-s1783
"
xml:space
="
preserve
">quia
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
</
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>