Stevin, Simon
,
Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis
,
1605
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Figures
Content
Thumbnails
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 197
>
Scan
Original
71
71
72
72
73
73
74
74
75
75
76
76
77
77
78
79
80
81
81
82
82
83
83
84
84
85
85
86
86
87
87
88
88
89
89
90
90
91
91
92
92
93
93
94
94
95
95
96
96
97
97
98
98
99
99
100
100
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 197
>
page
|<
<
(75)
of 197
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div357
"
type
="
section
"
level
="
1
"
n
="
254
">
<
p
>
<
s
xml:id
="
echoid-s2459
"
xml:space
="
preserve
">
<
pb
o
="
75
"
file
="
527.01.075
"
n
="
75
"
rhead
="
*DE* S*TATICÆ PRINCIPIIS*.
"/>
ſolidi ex inſcriptis cylindris compoſiti à dato minus erit. </
s
>
<
s
xml:id
="
echoid-s2460
"
xml:space
="
preserve
">Itaque infinita hac in-
<
lb
/>
ſcriptione tandem eò adſcenditur ut ſolidum factitium à conoïdali abl
<
unsure
/>
it diffe-
<
lb
/>
rentiâ, quæ ſolido dato quocunque minor ſit, cui conſequens eſt AD dati co-
<
lb
/>
noïdalis gravitatis eſſe diametrum, itaque gravitas ſitus unius lateris à gravita-
<
lb
/>
te lateris alterius minus aberit, quam vel minimi ponderis differentiâ. </
s
>
<
s
xml:id
="
echoid-s2461
"
xml:space
="
preserve
">Quod
<
lb
/>
legittimo ſyllogiſmi judicio ita concludam.</
s
>
<
s
xml:id
="
echoid-s2462
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s2463
"
xml:space
="
preserve
">Ponderum ſitu gravium differentiâ minus pondus dari poteſt.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2464
"
xml:space
="
preserve
">Sed borum ſegmentorum ſitu gravium differentiâ pondus minus nullu dari poteſt. </
s
>
<
s
xml:id
="
echoid-s2465
"
xml:space
="
preserve
">
<
lb
/>
Itaque borum conoïdalis ſegmentorum ſitu gravium differentia nullaeſt.</
s
>
<
s
xml:id
="
echoid-s2466
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2467
"
xml:space
="
preserve
">Et AD gravitatis erit diameter. </
s
>
<
s
xml:id
="
echoid-s2468
"
xml:space
="
preserve
">C*ONCLVSIO*. </
s
>
<
s
xml:id
="
echoid-s2469
"
xml:space
="
preserve
">Quamobrem conoïda-
<
lb
/>
lis gravitatis centrum eſt in axe. </
s
>
<
s
xml:id
="
echoid-s2470
"
xml:space
="
preserve
">quod demonſtraſſe oportuit.</
s
>
<
s
xml:id
="
echoid-s2471
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div358
"
type
="
section
"
level
="
1
"
n
="
255
">
<
head
xml:id
="
echoid-head269
"
xml:space
="
preserve
">10 PROBLEMA. 23 PROPOSITIO.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2472
"
xml:space
="
preserve
">Conoïdalis gravitatis centrum invenire.</
s
>
<
s
xml:id
="
echoid-s2473
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2474
"
xml:space
="
preserve
">D*ATVM*. </
s
>
<
s
xml:id
="
echoid-s2475
"
xml:space
="
preserve
">ABC conoïdale, A vertex, AD axis.</
s
>
<
s
xml:id
="
echoid-s2476
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2477
"
xml:space
="
preserve
">Q*VAESITVM*. </
s
>
<
s
xml:id
="
echoid-s2478
"
xml:space
="
preserve
">Gravitatis centrum invenire.</
s
>
<
s
xml:id
="
echoid-s2479
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div359
"
type
="
section
"
level
="
1
"
n
="
256
">
<
head
xml:id
="
echoid-head270
"
xml:space
="
preserve
">CONSTRVCTIO.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2480
"
xml:space
="
preserve
">A D axis ſecetur in E ratione dupla videlicet ut ſegmentum vertici conter-
<
lb
/>
minum reliqui ſit duplum, ajo E eſſe centrum quæſitum cujus demonſtrario-
<
lb
/>
nem ſolers & </
s
>
<
s
xml:id
="
echoid-s2481
"
xml:space
="
preserve
">ſubtilis Mathematicus Fredericus Commandinus de ſolidorũ cen-
<
lb
/>
trobaricis propoſ. </
s
>
<
s
xml:id
="
echoid-s2482
"
xml:space
="
preserve
">29 exhibet, quæ noſtro more & </
s
>
<
s
xml:id
="
echoid-s2483
"
xml:space
="
preserve
">modo digeſta ita habet.</
s
>
<
s
xml:id
="
echoid-s2484
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div360
"
type
="
section
"
level
="
1
"
n
="
257
">
<
head
xml:id
="
echoid-head271
"
xml:space
="
preserve
">DEMONSTRATIO.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2485
"
xml:space
="
preserve
">Conoïdale ſecetur plano FG axem in H biſecante, baſiq́ue BC parallelo,
<
lb
/>
atque planiſecantis & </
s
>
<
s
xml:id
="
echoid-s2486
"
xml:space
="
preserve
">ſuperficiei ſectio eſto in I, K, deinde BCGF, IKLM
<
lb
/>
cylindri circa conoïdale circumſcribantur, quorum gravitatis centra N, O:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2487
"
xml:space
="
preserve
">præterea intra ipſum cylindri IKPQ inſcripti O itidem gravitatis erit centrũ. </
s
>
<
s
xml:id
="
echoid-s2488
"
xml:space
="
preserve
">
<
lb
/>
Cum per 20 prop. </
s
>
<
s
xml:id
="
echoid-s2489
"
xml:space
="
preserve
">1 lib. </
s
>
<
s
xml:id
="
echoid-s2490
"
xml:space
="
preserve
">Apoll. </
s
>
<
s
xml:id
="
echoid-s2491
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2492
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s2493
"
xml:space
="
preserve
">pr. </
s
>
<
s
xml:id
="
echoid-s2494
"
xml:space
="
preserve
">12. </
s
>
<
s
xml:id
="
echoid-s2495
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s2496
"
xml:space
="
preserve
">
<
lb
/>
<
figure
xlink:label
="
fig-527.01.075-01
"
xlink:href
="
fig-527.01.075-01a
"
number
="
122
">
<
image
file
="
527.01.075-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.075-01
"/>
</
figure
>
Eucl. </
s
>
<
s
xml:id
="
echoid-s2497
"
xml:space
="
preserve
">igitur ſit ut DA ad AH videlicet 2
<
lb
/>
ad 1, ſic circulus BC ad circulũ IK, etiam
<
lb
/>
cylindri BC ad cylindrum IL (propter æ-
<
lb
/>
qualĕ altitudinem) ratio dupla erit, quam
<
lb
/>
obrem ſi BG 2 librarum ſtatu@ur IL erit
<
lb
/>
1 libræ, ſed centra gravitatis ſunt N, O,
<
lb
/>
ideoq́ue NO jugo in R ſecto ut NR
<
lb
/>
radii RO duplus ſit, ipſum circumſcripto-
<
lb
/>
rum cylindrorum gravitatis erit centrum,
<
lb
/>
ſed & </
s
>
<
s
xml:id
="
echoid-s2498
"
xml:space
="
preserve
">O inſcripti cylindri eſt centrum, E verò ab O & </
s
>
<
s
xml:id
="
echoid-s2499
"
xml:space
="
preserve
">ab R eodem intervallo
<
lb
/>
diſtat, videlicet {1/12} totius AD. </
s
>
<
s
xml:id
="
echoid-s2500
"
xml:space
="
preserve
">Acſimilis erit cæterorum ſimilium paradigma-
<
lb
/>
r
<
unsure
/>
um eventus. </
s
>
<
s
xml:id
="
echoid-s2501
"
xml:space
="
preserve
">Verumenimverò quo res ſit manifeſtior, altero exemplo idem ex-
<
lb
/>
plicabimus.</
s
>
<
s
xml:id
="
echoid-s2502
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2503
"
xml:space
="
preserve
">Denuò iſta axis biſegmenta AH, HD, bifariam dividantur, unde tres cy-
<
lb
/>
lindri inſcribantur & </
s
>
<
s
xml:id
="
echoid-s2504
"
xml:space
="
preserve
">quatuor circumſcribantur, ut in ſecundo diagrammate
<
lb
/>
ubi AD conoïdalis axis ſit, centra verò cylindrorum I, K, L, M, AE verò
<
lb
/>
dupla ſit ipſius ED ut ſupra. </
s
>
<
s
xml:id
="
echoid-s2505
"
xml:space
="
preserve
">Itaque cum ſit ut AD ad AN (nempe ut 4 ad 3)
<
lb
/>
ſic circulus BC ad circulum OP, erit quoque cylindrus BF ad OQ in </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>