Ghetaldi, Marino
,
Marini Ghetaldi Promotvs Archimedis sev de varijs corporum generibus grauitate & magnitudine comparatis
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of handwritten notes
<
1 - 3
[out of range]
>
<
1 - 3
[out of range]
>
page
|<
<
(69)
of 89
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div83
"
type
="
section
"
level
="
1
"
n
="
45
">
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1542
"
xml:space
="
preserve
">
<
pb
o
="
69
"
file
="
0081
"
n
="
81
"
rhead
="
ARCHIMEDES.
"/>
mas eadem eſt differentia, propterea quod omnes grauitates in tabu-
<
lb
/>
la procedunt per æqualem exceſſum, vel defectum, vt inferius de-
<
lb
/>
monſtrabitur. </
s
>
<
s
xml:id
="
echoid-s1543
"
xml:space
="
preserve
">Inueniatur quoque differentia inter eandem gra-
<
lb
/>
uitatem proxime minorem & </
s
>
<
s
xml:id
="
echoid-s1544
"
xml:space
="
preserve
">inter grauitatem auri propoſiti quam
<
lb
/>
babet in aqua, quæ quidĕ eſt Gran. </
s
>
<
s
xml:id
="
echoid-s1545
"
xml:space
="
preserve
">7 {627/1767}, & </
s
>
<
s
xml:id
="
echoid-s1546
"
xml:space
="
preserve
">fiat vt 14 {1374/1767},
<
lb
/>
ad 1, ita 7 {637/1767}, ad alium numerum & </
s
>
<
s
xml:id
="
echoid-s1547
"
xml:space
="
preserve
">inuenietur bæc fractio
<
lb
/>
{1/2}, eademque adijcienda erit ad denominatorem 20, partium, vt
<
lb
/>
componatur totus denominator auripropoſiti partium 20 {1/2}, & </
s
>
<
s
xml:id
="
echoid-s1548
"
xml:space
="
preserve
">eo-
<
lb
/>
dem modo inueniendus erit denominator cuiuſcunq; </
s
>
<
s
xml:id
="
echoid-s1549
"
xml:space
="
preserve
">alterius auri,
<
lb
/>
cuius grauitas in aqua, in tabula non reperitur.</
s
>
<
s
xml:id
="
echoid-s1550
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1551
"
xml:space
="
preserve
">Ceterum qui volet contentus eſſe partibus vigeſimis quartis de-
<
lb
/>
nominatorum auri, is multo breuius aſſequetur quod quæritur, per
<
lb
/>
tabellam partis proportionalis. </
s
>
<
s
xml:id
="
echoid-s1552
"
xml:space
="
preserve
">illic enim vnico ingreſſu offendet
<
lb
/>
partem proportionalem, quam quærit, vt in eodem exemplo apparet,
<
lb
/>
in quo differentia grauitatum auri erat Gran. </
s
>
<
s
xml:id
="
echoid-s1553
"
xml:space
="
preserve
">7 {687/1767}, quæ in
<
lb
/>
tabella partis proportionalis babetur præcisè è regione particularum
<
lb
/>
12. </
s
>
<
s
xml:id
="
echoid-s1554
"
xml:space
="
preserve
">V nde concluditur, denominatorem auri propoſiti eſſe partium
<
lb
/>
20 {12/24}, vel quod idem es
<
unsure
/>
t partium 20 {1/2}, vt prius. </
s
>
<
s
xml:id
="
echoid-s1555
"
xml:space
="
preserve
">Quando vero
<
lb
/>
differentia grauitatum in tabella partis proportionalis non babetur
<
lb
/>
præcisè. </
s
>
<
s
xml:id
="
echoid-s1556
"
xml:space
="
preserve
">accipiatur alia ipſi propinquior & </
s
>
<
s
xml:id
="
echoid-s1557
"
xml:space
="
preserve
">particula illi in latere
<
unsure
/>
<
lb
/>
reſpondens addatur denominatori auri ex primaria tabula extr a-
<
lb
/>
cti. </
s
>
<
s
xml:id
="
echoid-s1558
"
xml:space
="
preserve
">ſic enim ſaltem non errabitur in vna particula vigeſimaquarta
<
lb
/>
vnius partis denominatoris auri.</
s
>
<
s
xml:id
="
echoid-s1559
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1560
"
xml:space
="
preserve
">Denique ſi proponatur aurum non vnius libræ ſed vel plurium,
<
lb
/>
vel ſolum aliquot vnciarum. </
s
>
<
s
xml:id
="
echoid-s1561
"
xml:space
="
preserve
">R educenda erit eius grauitas quam
<
lb
/>
babet in aqua, ad grauitatem quam haberet ſi eßet vnius libræ, id
<
lb
/>
quod abſoluetur per proportionis ratiocinationem, ſi pro termino
<
lb
/>
primo ponatur vera grauitas auri propoſiti, pro ſecundo, e iuſdem
<
lb
/>
grauitas in aqua, & </
s
>
<
s
xml:id
="
echoid-s1562
"
xml:space
="
preserve
">pro tertio lib. </
s
>
<
s
xml:id
="
echoid-s1563
"
xml:space
="
preserve
">1, quartus enim terminus indic a-
<
lb
/>
bit grauitatem in aqua reſpondentem vni libræ auri propoſiti. </
s
>
<
s
xml:id
="
echoid-s1564
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1565
"
xml:space
="
preserve
">
<
lb
/>
bac inuenta reliqua expedientur vt prius.</
s
>
<
s
xml:id
="
echoid-s1566
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1567
"
xml:space
="
preserve
">Exemplum buius caſus bic non affero, quod per ſe res ſit clara.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1568
"
xml:space
="
preserve
">Sed illud tantum obiter aduertere placet, quod videtur pertinere. </
s
>
<
s
xml:id
="
echoid-s1569
"
xml:space
="
preserve
">
<
lb
/>
ad commodiorem vſum tabulæ, videlicet vt ijs in caſibus in quibus
<
lb
/>
neceßarius est calculus, fractiones granorum ommittantur quando
<
lb
/>
minus valent quam {1/2}, & </
s
>
<
s
xml:id
="
echoid-s1570
"
xml:space
="
preserve
">quando valent plus, eorum loco, addatur
<
lb
/>
vnum granum reliquis granis, & </
s
>
<
s
xml:id
="
echoid-s1571
"
xml:space
="
preserve
">ſi quando accidat binc procreari
<
lb
/>
grana 24. </
s
>
<
s
xml:id
="
echoid-s1572
"
xml:space
="
preserve
">tunc etiam grana ommittantur addita prius vnitate ad
<
lb
/>
ſcrupula in tabula inuenta. </
s
>
<
s
xml:id
="
echoid-s1573
"
xml:space
="
preserve
">bac enim ratione calculus erit expedi-
<
lb
/>
tior & </
s
>
<
s
xml:id
="
echoid-s1574
"
xml:space
="
preserve
">error qui binc oborietur erit inſenſibilis.</
s
>
<
s
xml:id
="
echoid-s1575
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>