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]
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<
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xml:space
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">DE SPECVLATIONE
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REGVLAE FALSI.</
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<
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idem ferè mihi accidit, quod & Michaeli Stifelio, à quo
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cum Petreius Tipographus nuper totam ſuam Arithmeticam re
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cepiſſet, mox poſteà per literas petijt
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regulæ falſi.</
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</
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<
p
>
<
s
xml:id
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xml:space
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">Similiter poſt inciſas omnes ſuperiorum Theorematum figu-
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ras,
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opereque
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type
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>
Typographo commiſſo, amicus quidam omnium
<
lb
/>
ſcientiarum ornatiſſimus maxima neceſſitudine mecum coniun-
<
lb
/>
ctus monuit me, vt aliquid de regula falſi ſcribere vellem, cuius
<
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/>
ſuaſu hæc, quæ ſequuntur appendicis vice ponere libuit, nelector, quidpiam quod
<
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/>
ad hancrem pertinet iure merito à nobis deſiderare poſſet; </
s
>
<
s
xml:id
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xml:space
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">vt autem ad ipſam
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norm
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re- gulam
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type
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gulã</
reg
>
accedamus Ego ſicut, & in alijs multis, ita & in huiuſcæ regulę inuentione cum
<
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ipſo Stifelio maximè conuenio, putans regulam falſi, ſeu falſarum poſitionum in-
<
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uentam fuiſſe per paruos numeros in quæſtionibus facillimis & cognitis, eodem fer
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mè modo, quo ipſe monſtrat illis duobus exemplis, quæ quamuis ipſe appellet theo
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remata, nihilominus the oremata ego illa non vocarem, niſi adiuncta fuerit ſpecu-
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latio ab ipſo præterita, & non experientia tantummodo, vt ipſe fecit. </
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<
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exemplum eſt, quòd.</
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</
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<
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<
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xml:space
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">Quorumcumque
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duorum
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numerorum differentia, ſi fuerit multiplicata in aggre
<
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gatum eorum, producit ipſam differentiam, quæ eſt inter quadrata eorum.</
s
>
</
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<
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<
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xml:id
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xml:space
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">Secundum verò exemplum eſt, quod.</
s
>
</
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<
p
>
<
s
xml:id
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xml:space
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">Datis tribus numeris ſecundum progreſſionem arithmeticam diſpoſitis, facit mul
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tiplicatio medij in ſe,
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multiplicatio extremorum inter ſe cum multiplicatio
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ne differentiarum inter ſe.</
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</
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<
p
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<
s
xml:id
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xml:space
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">Talia enim exempla ipſe aliter non probat niſi experientia in aliquibus numeris,
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arbitratus ex eo inuentam eſſe regulam falſi, experientia tantummodo confirma-
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tam, quod quidem etiam & ego credo. </
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>
<
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xml:space
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preserve
">At experientia in philoſophia mathema-
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tica, aut
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nullam
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prorſus facit
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type
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>
, aut omnino ſuperfluus fuit Euclides in multis
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ſuis propoſitionibus, & præcipuè in eius ſecundo libro, ſi ſufficeret experientia. </
s
>
<
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xml:space
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">Id-
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circo quo magis ad euidentiam ipſius veritatis, quam profiteor, deuenire poſſim,
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<
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primò primum exemplum
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ipſius Stifelij hic ſuperius citatum,
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& pro numero maiori, in prima hic
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0115-01
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xlink:href
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ſubſcripta figura .AE. accipio
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>
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cuius quadratum ſit
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>
: pro minori
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vero numero capio
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ipſius
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cuius quadratum fit
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>
differen
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tia autem horum numerorum erit
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e.i.</
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>
reliqua pars ipſius
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>.a.i</
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>
: & differen
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tia ipſorum quadratorum erit gno-
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mon
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>.e.c.o</
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>
: Nunc autem protraho
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<
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i.c.</
var
>
latus quadrati maioris quouſque
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<
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>c.n.</
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>
æqualis ſit
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>
numero minori,
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rectangulum
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quod </
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