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
>
161
(149)
162
(150)
163
(151)
164
(152)
165
(153)
166
(154)
167
(155)
168
(156)
169
(157)
170
(158)
<
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
|<
<
(92)
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-div262
"
type
="
math:theorem
"
level
="
3
"
n
="
137
">
<
p
>
<
s
xml:id
="
echoid-s1199
"
xml:space
="
preserve
">
<
pb
o
="
92
"
rhead
="
IO. BAPT. BENED.
"
n
="
104
"
file
="
0104
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0104
"/>
ipſorum prochictorum per ſummam lucri hoc eſt per .60. vnde multiplicatio primi
<
lb
/>
producti erit .2190000. multiplicatio verò ſecundi producti erit .795000. tertij po
<
lb
/>
ſtca erit .247500. quarum multiplicationum vnaquæque diuidatur per ſummam
<
lb
/>
53875. productori
<
unsure
/>
t, & proueniet ex prima diuiſione .40.
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
fractis .35000. vnius in-
<
lb
/>
tegri diuiſi in partes .53875. quod erit lucrum primi, prouentus autem ſecundæ di-
<
lb
/>
uiſionis erit .14. cum fractis .41050. vnius integri diuiſi in partes .53875. lucrum
<
reg
norm
="
ſecu di.
"
type
="
context
">ſecũ
<
lb
/>
di</
reg
>
</
s
>
<
s
xml:id
="
echoid-s1200
"
xml:space
="
preserve
">prouentus verò quartæ diuiſionis erit .4. cum fractis .32000. vnius integri, vt ſu
<
lb
/>
pra diuiſi in partes .53875. hoc eſt lucrum tertij.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1201
"
xml:space
="
preserve
">Cuius rei ſpeculatio ex ſe in ſub ſcripta figura patet, vbi
<
var
>.a.q.</
var
>
ſignificat numerum
<
lb
/>
dierum totius anni pro primo mercatore
<
var
>.q.n.</
var
>
autem ſignificat numerum dierum ſe
<
lb
/>
cundi mercatoris
<
var
>.e.q.</
var
>
poſteà ſignificat numerum dierum tertij ſit etiam
<
var
>.s.a.</
var
>
pro nu-
<
lb
/>
mero denariorum primi, et
<
var
>.o.n.</
var
>
pro numero ſecundi, et
<
var
>.e.t.</
var
>
pro numero
<
lb
/>
tertij, productum autem
<
var
>.q.s.</
var
>
ſignificet valorem primi lucri, et
<
var
>.q.o.</
var
>
ſecundi,
<
lb
/>
et
<
var
>.q.t.</
var
>
tertij
<
var
>.x.y.</
var
>
autem ſignificet ſummam lucri omnium, et
<
var
>.x.i.</
var
>
ſignificet
<
lb
/>
partem primi, et
<
var
>.i.p.</
var
>
ſecundi, et
<
var
>.p.y.</
var
>
tertij. </
s
>
<
s
xml:id
="
echoid-s1202
"
xml:space
="
preserve
">vnde clarè patebit ex communi
<
lb
/>
ſcientia quòd eadem proportio erit
<
var
>.x.y.</
var
>
ad
<
var
>.x.i.</
var
>
quæ aggregati omnium producto-
<
lb
/>
rum
<
var
>.q.s</
var
>
:
<
var
>q.o.</
var
>
et
<
var
>.q.t.</
var
>
ad
<
var
>.q.s.</
var
>
& ita
<
var
>.x.y.</
var
>
ad
<
var
>.i.p.</
var
>
vt aggregati dictiad
<
var
>.q.o.</
var
>
et
<
var
>.x.y.</
var
>
ad
<
var
>.p.y.</
var
>
<
lb
/>
vt dicti aggregati ad
<
var
>.q.t</
var
>
. </
s
>
<
s
xml:id
="
echoid-s1203
"
xml:space
="
preserve
">Rectè igitur ex regula de tribus multiplicatio
<
var
>.q.s.</
var
>
in
<
var
>.x.y.</
var
>
<
lb
/>
diuiditur per aggregatum omnium
<
lb
/>
<
figure
xlink:label
="
fig-0104-01
"
xlink:href
="
fig-0104-01a
"
number
="
143
">
<
image
file
="
0104-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0104-01
"/>
</
figure
>
productorum, ita vt ſi aliquis dice-
<
lb
/>
ret, ſi ex dicto aggregato, prouenit
<
lb
/>
<
var
>x.y.</
var
>
quid proueniet vnicuique
<
reg
norm
="
illo- rum
"
type
="
context
">illo-
<
lb
/>
rũ</
reg
>
<
reg
norm
="
productorum
"
type
="
context
">productorũ</
reg
>
. </
s
>
<
s
xml:id
="
echoid-s1204
"
xml:space
="
preserve
">
<
reg
norm
="
Nam
"
type
="
context
">Nã</
reg
>
ſi numerus dena-
<
lb
/>
riorum
<
reg
norm
="
ſecundi
"
type
="
context
">ſecũdi</
reg
>
æqualis eſſet numero
<
lb
/>
<
var
>a.s.</
var
>
primi vt putà.
<
var
>n.b</
var
>
. </
s
>
<
s
xml:id
="
echoid-s1205
"
xml:space
="
preserve
">tunc eius
<
reg
norm
="
lucrum
"
type
="
context
">lucrũ</
reg
>
<
lb
/>
ſignificaretur à rectangulo
<
var
>.q.b.</
var
>
& ita
<
lb
/>
de tertio dico
<
reg
norm
="
quod
"
type
="
simple
">ꝙ</
reg
>
ſignificaretur à
<
reg
norm
="
re- ctangulo
"
type
="
context
">re-
<
lb
/>
ctãgulo</
reg
>
<
var
>.q.c.</
var
>
vel ſi ſi
<
unsure
/>
antibus
<
reg
norm
="
ijſdem
"
type
="
context
">ijſdẽ</
reg
>
<
reg
norm
="
denariorum
"
type
="
context
">denariorũ</
reg
>
quantitatibus
<
var
>.n.o.</
var
>
et
<
var
>.e.t.</
var
>
omnes ſuas pe-
<
lb
/>
cunias eodem tempore poſuiſſent, </
s
>
<
s
xml:id
="
echoid-s1206
"
xml:space
="
preserve
">tunc rectangula ſignificantia eorum lucra eſlent
<
lb
/>
<
var
>q.s.q.d.</
var
>
et
<
var
>.q.f.</
var
>
ſed cum nec eodem tempore, nec eandem quantitatem poſueruntr
<
unsure
/>
e
<
lb
/>
ctè eorum lucra ſignificantur à rectangulis
<
var
>.q.s.q.o.</
var
>
et
<
var
>.q.t.</
var
>
<
reg
norm
="
quod
"
type
="
simple
">ꝙ</
reg
>
ex prima .6. vel .18. aut
<
num
value
="
19
">.
<
lb
/>
19.</
num
>
ſeptimi ratiocinando clarè patebit.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div264
"
type
="
math:theorem
"
level
="
3
"
n
="
138
">
<
head
xml:id
="
echoid-head156
"
xml:space
="
preserve
">THEOREMA
<
num
value
="
138
">CXXXVIII</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1207
"
xml:space
="
preserve
">NIcolaus Tartalea in primo libro vltimæ partis numerorum ad .35. quæſitum
<
lb
/>
docet inuenire quantitatem laterum vnius propoſiti trianguli, cuius la-
<
lb
/>
r
<
unsure
/>
erum proportio nobis data ſit ſimul cum area ſuperſiciali ipſius trianguli, ſed quia
<
lb
/>
ipſe Tartalea vtiturregula algebræ, mihi viſum eſt breuiori methodo hoc idein fa
<
lb
/>
cere, & etiam vniuerſaliori via.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1208
"
xml:space
="
preserve
">Supp onamus igitur duo triangula, quorum vnum
<
var
>.u.n.i.</
var
>
ſit nobis
<
reg
norm
="
propoſitum
"
type
="
context
">propoſitũ</
reg
>
, &
<
lb
/>
cognitæ ſuperficiei, proportiones ſimiliter laterum
<
var
>.i.n.</
var
>
ad
<
var
>.n.u</
var
>
: et
<
var
>.u.n.</
var
>
ad
<
var
>.u.i.</
var
>
ſint no
<
lb
/>
bis datæ,
<
reg
norm
="
alterum
"
type
="
context
">alterũ</
reg
>
verò
<
reg
norm
="
triangulum
"
type
="
context
">triangulũ</
reg
>
ſit
<
var
>.a.o.u.</
var
>
à nobis tamen ita
<
reg
norm
="
confectum
"
type
="
context
">confectũ</
reg
>
, v
<
unsure
/>
latera ſint in
<
lb
/>
er ſe proportionata eodem modo, quo latera prioris trianguli, ſed hæc nobis
<
reg
norm
="
etiam
"
type
="
context
">etiã</
reg
>
<
lb
/>
cognita ſint,
<
reg
norm
="
quod
"
type
="
simple
">ꝙ</
reg
>
facillimum eſt. </
s
>
<
s
xml:id
="
echoid-s1209
"
xml:space
="
preserve
">Nunc vero ſi
<
reg
norm
="
demptum
"
type
="
context
">demptũ</
reg
>
fuerit
<
reg
norm
="
quadratum
"
type
="
context
">quadratũ</
reg
>
<
var
>.a.o.</
var
>
minimi
<
lb
/>
lateris, ex quadrato
<
var
>.o.u.</
var
>
maximi, relinquet nobis duplum producti
<
var
>.o.u.</
var
>
in
<
var
>.u.e.</
var
>
per
<
lb
/>
<
reg
norm
="
penultimam
"
type
="
context
">penultimã</
reg
>
.2. Eucli.
<
reg
norm
="
ſupponendo
"
type
="
context
">ſupponẽdo</
reg
>
<
var
>.a.e.</
var
>
perpendicularem ad
<
var
>.o.u.</
var
>
vnde tale productum
<
lb
/>
quòd fit ex
<
var
>.o.u.</
var
>
in
<
var
>.u.e.</
var
>
conſequenter nobis cognitum erit, & quia
<
var
>.o.u.</
var
>
nobis cogni- </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>