Cardano, Geronimo, Opvs novvm de proportionibvs nvmerorvm, motvvm, pondervm, sonorvm, aliarvmqv'e rervm mensurandarum, non solùm geometrico more stabilitum, sed etiam uarijs experimentis & observationibus rerum in natura, solerti demonstratione illustratum, ad multiplices usus accommodatum, & in V libros digestum. Praeterea Artis Magnae, sive de regvlis algebraicis, liber vnvs abstrvsissimvs & inexhaustus planetotius Ariothmeticae thesaurus ... Item De Aliza Regvla Liber, hoc est, algebraicae logisticae suae, numeros recondita numerandi subtilitate, secundum Geometricas quantitates inquirentis ...

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<archimedes>
<text>
<body>
<chap>
<p type="main">
<s id="id002398">
quadrati 2 quod eſt 12 exit 1/4 detrahe ex 2 fit 1 3/4 cuius cubus eſt 5 23/64
<lb/>
differentia eſt 23/64 diuide per triplum quadrati 1 3/4 quòd eſt 9 3/16 exit
<lb/>
23/588 detrahe ex 1 3/4
<expan abbr="relinquũtur">relinquuntur</expan>
1 107/147 cuius cubus eſt 5 504449/3176523 Ita diuides
<lb/>
hunc exceſſum ſi placet per triplum quadrati 1 107/147 & eſt fermè 9 exit
<lb/>
56050/3176523 quaſi detrahe ex 1 107/147 relinquuntur 323159/453789.</s>
</p>
<p type="main">
<s id="id002399">Tertius modus eſt ſubtilior, tu ſcis, q̊d duo decima denominatio
<lb/>
<lb/>
autem eſt inter
<expan abbr="tertiã">tertiam</expan>
& ſextam ſecunda quantitas in continua pro­
<lb/>
portione: ergo inuenta <02> numeri propoſiti & <02> radicis inuentæ
<lb/>
<expan abbr="reducã">reducam</expan>
ad unam denominationem, et inter numeratores collo cabo
<lb/>
duas quantitates, quod facile erit ſenſim procedendo, & habebo <02>
<lb/>
cu. </s>
<s id="id002400">quæſitam, ſcilicet minorem ex duabus intermedijs. </s>
<s id="id002401">Et ſimiliter
<lb/>
pro relata prima, capiam ſexaginta denominationes, & ſcis, quòd
<lb/>
quinta decima eſt <02> <02> ſexageſimę, & decima eſt <02> cu. </s>
<s id="id002402"><02> ſexageſimę,
<lb/>
& duodecima <02> relata prima ſexageſimæ per eandem inuenta, er­
<lb/>
go <02> numeri propoſiti tanquam ille ſit ſexageſima denominatio,
<lb/>
<lb/>
quia duodecima quantitas quæ eſt <02> relata prima numeri eſt
<lb/>
ſecunda, quatuor intermediarum inter ponam inter <02> quadra­
<lb/>
<lb/>
continua proportione, & ſecundus ex minoribus erit <02> relata
<lb/>
prima numeri propoſiti. </s>
<s id="id002403">Exemplum cubicæ uolo <02> cu: 5 habui <02>
<lb/>
quadratam eius 2 5/21 ſed uolo proximiorem diuidendo 4/441 per 4,
<lb/>
quod eſt fermè duplum 2 5/21 exit 1/441 detraho ex 2 5/21 relinquitur ualde
<lb/>
proxima <02> 5. 2 104/441 huius igitur radix quadrata, primo inuenta eſt 1 1/2
<lb/>
ſecunda proximior eſt 1 41/84 reduco ad eandem denominationem fi­
<lb/>
ent 284/9261 2 416/1764 & 1 861/1764 inter 3944, & 2625, inueniemus duos nume­
<lb/>
ros in continua proportione, ut uides, & erit ſecunda quantitas
<lb/>
<lb/>
3006/7641, quod eſt 167/98 proximum ad 1 5/7, <02> cubica. </s>
<s id="id002404">5.
<lb/>
<expan abbr="">nam</expan>
eius cubus eſt 5. 13/343 at exactiſsima eſt ergo 1 69/98.
<lb/>
ut liquet. </s>
<s id="id002405">Pro relata prima ergo ponamus, ut ue­
<lb/>
lim <02> relatam
<expan abbr="primã">primam</expan>
25, accipio 5 <02> 25 cuius <02> eſt, ut uiſum eſt, 2 104/441
<lb/>
ſimiliter <02> cu: 5 fuit 1 69/98 igitur reducam ad unam denominationem,
<lb/>
& inueniam quatuor numeros in
<expan abbr="cõtinua">continua</expan>
proportione inter illos,
<lb/>
& ſecundus poſt minimum ex illis erit <02> relata prima propinquiſ­
<lb/>
ſima 25. Quomodo uerò inueniantur facillimè illi termini, do­
<lb/>
cui in ſexto libro operis perfecti.</s>
</p>
<p type="main">
<s id="id002406">Quarta regula eſt utilior, licet minus uideatur nobilis, & eſt fun­
<lb/>
data in hoc, quod ſi a b ſit maior c & eis ad dantur b e, & d f æqua­
<lb/>
les dico, quod erit minor proportio a c ad c f, quam a b ad c d, & ex
<lb/>
conſequenti per
<expan abbr="uiã">uiam</expan>
fracti maior pars unius erit c f ipſius a e, quàm </s>
</p>
</chap>
</body>
</text>
</archimedes>