Ghetaldi, Marino
,
Marini Ghetaldi Promotvs Archimedis sev de varijs corporum generibus grauitate & magnitudine comparatis
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ARCHIMEDES.
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mas eadem eſt differentia, propterea quod omnes grauitates in tabu-
<
lb
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la procedunt per æqualem exceſſum, vel defectum, vt inferius de-
<
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monſtrabitur. </
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<
s
xml:id
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echoid-s1543
"
xml:space
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preserve
">Inueniatur quoque differentia inter eandem gra-
<
lb
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uitatem proxime minorem & </
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>
<
s
xml:id
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echoid-s1544
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xml:space
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">inter grauitatem auri propoſiti quam
<
lb
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babet in aqua, quæ quidĕ eſt Gran. </
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<
s
xml:id
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xml:space
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">7 {627/1767}, & </
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>
<
s
xml:id
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echoid-s1546
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xml:space
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">fiat vt 14 {1374/1767},
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ad 1, ita 7 {637/1767}, ad alium numerum & </
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>
<
s
xml:id
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echoid-s1547
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xml:space
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">inuenietur bæc fractio
<
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{1/2}, eademque adijcienda erit ad denominatorem 20, partium, vt
<
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componatur totus denominator auripropoſiti partium 20 {1/2}, & </
s
>
<
s
xml:id
="
echoid-s1548
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xml:space
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">eo-
<
lb
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dem modo inueniendus erit denominator cuiuſcunq; </
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>
<
s
xml:id
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echoid-s1549
"
xml:space
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preserve
">alterius auri,
<
lb
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cuius grauitas in aqua, in tabula non reperitur.</
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>
<
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xml:id
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xml:space
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</
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<
s
xml:id
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echoid-s1551
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xml:space
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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
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echoid-s1552
"
xml:space
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preserve
">illic enim vnico ingreſſu offendet
<
lb
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partem proportionalem, quam quærit, vt in eodem exemplo apparet,
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in quo differentia grauitatum auri erat Gran. </
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<
s
xml:id
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echoid-s1553
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xml:space
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">7 {687/1767}, quæ in
<
lb
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tabella partis proportionalis babetur præcisè è regione particularum
<
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/>
12. </
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>
<
s
xml:id
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echoid-s1554
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xml:space
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">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
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echoid-s1556
"
xml:space
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">accipiatur alia ipſi propinquior & </
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>
<
s
xml:id
="
echoid-s1557
"
xml:space
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">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
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">ſic enim ſaltem non errabitur in vna particula vigeſimaquarta
<
lb
/>
vnius partis denominatoris auri.</
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>
<
s
xml:id
="
echoid-s1559
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xml:space
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</
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>
<
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<
s
xml:id
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echoid-s1560
"
xml:space
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preserve
">Denique ſi proponatur aurum non vnius libræ ſed vel plurium,
<
lb
/>
vel ſolum aliquot vnciarum. </
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>
<
s
xml:id
="
echoid-s1561
"
xml:space
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">R educenda erit eius grauitas quam
<
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/>
babet in aqua, ad grauitatem quam haberet ſi eßet vnius libræ, id
<
lb
/>
quod abſoluetur per proportionis ratiocinationem, ſi pro termino
<
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/>
primo ponatur vera grauitas auri propoſiti, pro ſecundo, e iuſdem
<
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grauitas in aqua, & </
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>
<
s
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echoid-s1562
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">pro tertio lib. </
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<
s
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echoid-s1563
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xml:space
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">1, quartus enim terminus indic a-
<
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bit grauitatem in aqua reſpondentem vni libræ auri propoſiti. </
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<
s
xml:id
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echoid-s1564
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">& </
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>
<
s
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="
echoid-s1565
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">
<
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/>
bac inuenta reliqua expedientur vt prius.</
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>
<
s
xml:id
="
echoid-s1566
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xml:space
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"/>
</
p
>
<
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style
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<
s
xml:id
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"
xml:space
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">Exemplum buius caſus bic non affero, quod per ſe res ſit clara.
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</
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<
s
xml:id
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echoid-s1568
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xml:space
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">Sed illud tantum obiter aduertere placet, quod videtur pertinere. </
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>
<
s
xml:id
="
echoid-s1569
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<
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/>
ad commodiorem vſum tabulæ, videlicet vt ijs in caſibus in quibus
<
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neceßarius est calculus, fractiones granorum ommittantur quando
<
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/>
minus valent quam {1/2}, & </
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>
<
s
xml:id
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echoid-s1570
"
xml:space
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">quando valent plus, eorum loco, addatur
<
lb
/>
vnum granum reliquis granis, & </
s
>
<
s
xml:id
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"
xml:space
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">ſi quando accidat binc procreari
<
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grana 24. </
s
>
<
s
xml:id
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echoid-s1572
"
xml:space
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">tunc etiam grana ommittantur addita prius vnitate ad
<
lb
/>
ſcrupula in tabula inuenta. </
s
>
<
s
xml:id
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echoid-s1573
"
xml:space
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">bac enim ratione calculus erit expedi-
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tior & </
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<
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">error qui binc oborietur erit inſenſibilis.</
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