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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IO. BAPT. BENED.
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xml:space
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">NOTABILES ERRORES ORONTII
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& Tartaleæ.</
head
>
<
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style
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xml:space
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">Cornelio Bitonto.</
head
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<
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error non fuit, vt putabat Orontius, quodanguli triangulorum
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æquicrurium inuicem æqualium, baſibus oppoſiti, ijſdem baſibus propor
<
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tionales eſſent, cuius opinionis cauſa fuit quod nunquam viderit vel me
<
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minerit eius quod Ptolomeus ſcripſit lib. primo Almageſti, vbi de diſpro
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portionalitate chordarum
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type
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tractat, vel quod ſcribit Vitellio lib. primo pro
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poſitione .35. ſeu lib. quarto, propoſitione .21. quod idem eſt. </
s
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<
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xml:space
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">Sed nec ego tibi pro
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ponam id quod ſcribit Nicolaus Tartalea diuiſioni .28. quinti capitis quartæ partis
<
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ſuorum tractatuum, eo quod non exactè ſcientificè ſcripſerit, nec vniuerſaliter,
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type
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uis</
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talis propoſitio poſſit ſcientificè ſcribi, accipiendo
<
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var
>
in eius figura, pro latere
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octagoni, vnde angulus
<
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var
>
duplum foret angulo
<
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var
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collocato poſtea
<
var
>.b.c.</
var
>
in
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arcu
<
var
>.a.b.</
var
>
punctum
<
var
>.c.</
var
>
medium fuiſſet dicti arcus, et
<
var
>.e.c.</
var
>
diuideret
<
var
>.a.b.</
var
>
per æqualia,
<
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/>
ex quinta primi, nec non ad rectos ex .3. tertij, vnde ex .18. primi, clare vidiſſemus
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non eſſe proportionem
<
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var
>
ad
<
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var
>
vt anguli ad angulum. </
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>
<
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xml:space
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">Sed vniuerſaliori modo
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poſſumus hoc ſpeculari. </
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<
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xml:space
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">Nam manifeſtè ſcimus, eandem eſſe proportionem circun
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ferentiæ ad diametrum in omnibus circulis tam maioribus, quam minoribus.
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</
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<
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xml:space
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">Sint igitur duo anguli
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var
>
et
<
var
>.c.e.b.</
var
>
cuiuſuis amplitudinis, quorum latera
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var
>.e.a</
var
>
:
<
var
>e.b</
var
>
:
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/>
et
<
var
>.e.c.</
var
>
ſint inuicem æqualia, protrahatur
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>.b.a.</
var
>
et
<
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>.b.c</
var
>
. </
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>
<
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xml:space
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">Tunc dico maiorem proportio
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/>
nem eſſe anguli
<
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>.a.e.b.</
var
>
ad angulum
<
var
>.b.e.c.</
var
>
quam
<
var
>.a.b.</
var
>
ad
<
var
>.c.b.</
var
>
ducatur enim
<
var
>.b.g.</
var
>
ita
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norm
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type
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reg
>
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/>
faciat angulum
<
var
>.g.b.c.</
var
>
æqualem angulo
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var
>.e.b.a.</
var
>
protracta poſtea
<
var
>.c.g.</
var
>
quæ idem faciat
<
lb
/>
in puncto
<
var
>.c.</
var
>
vnde
<
var
>.g.b.</
var
>
et
<
var
>.g.c.</
var
>
æquales inuicem erunt ex .6. primi, & quia angulus
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var
>.a.</
var
>
<
lb
/>
æqualis eſt angulo
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var
>e.b.a.</
var
>
ex quinta eiuſdem, ideo ex .32. dicti, et .4. ſexti, horum
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duorum triangulorum latera, erunt inuicem proportionalia. </
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<
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xml:space
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">Conſtituto deinde
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>.g.</
var
>
<
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/>
centro, & ſecundum ſemidiametrum
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var
>.g.b.</
var
>
vel
<
var
>.g.c.</
var
>
quod idem eſt, deſcripto circu-
<
lb
/>
lo
<
var
>.b.i.c.</
var
>
necnon circulo
<
var
>.b.c.a.</
var
>
circa centrum
<
var
>.e.</
var
>
ope ſemidiametri
<
var
>.e.b.</
var
>
et
<
var
>.e.a.</
var
>
vn
<
lb
/>
de iſte circulus eritillo maior, cum
<
var
>.e.b.</
var
>
maior ſit
<
var
>.g.b.</
var
>
ex .14. quinti. cum ex .14. tertij
<
lb
/>
<
var
>a.b.</
var
>
longior ſit
<
var
>.c.b.</
var
>
ſed ex vltima definitione tertij, arcus
<
var
>.b.i.c.</
var
>
et
<
var
>.b.c.a.</
var
>
erunt in-
<
lb
/>
uicem ſimiles, hoc eſt proportio totius cir-
<
lb
/>
cunferentiæ circuli
<
var
>.b.i.c.</
var
>
ad arcus
<
var
>.b.i.c.</
var
>
ea-
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dem erit, quæ totius circunferentiæ circuli
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<
var
>b.c.a.</
var
>
ad arcus
<
var
>.b.c.a.</
var
>
ſed proportio diame-
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tri ad circunferentiam eſt vt diametri ad cir
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cunferentiam, vt ſupra diximus; </
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<
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xml:space
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">Quare ex
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proportionum æqualitate, vt ſemidiametri
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ad circunferentiam erit, vt ſemidiametri
<
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/>
ad circunferentiam, & per eandem propor
<
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tionum ęqualitatem, proportio
<
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var
>
ad
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reg
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<
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<
var
>b.c.a.</
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>
erit, vt
<
var
>.g.b.</
var
>
ad arcum
<
var
>.b.i.c.</
var
>
& per ean
<
lb
/>
dem æqualitatem, ita erit
<
var
>.a.b.</
var
>
chordæ ad ar
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/>
cum
<
var
>.b.c.a.</
var
>
vt
<
var
>.c.b.</
var
>
chordæ ad arcum
<
var
>.b.i.c.</
var
>
<
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/>
& permutando, ita erit chordæ
<
var
>.a.b.</
var
>
ad chor
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dam
<
var
>.c.b.</
var
>
vt arcus
<
var
>.b.c.a.</
var
>
ad arcum
<
var
>.b.i.c.</
var
>
ſed
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lb
/>
arcus
<
var
>.b.i.c.</
var
>
maior eſt arcu
<
var
>.b.d.c.</
var
>
ex commu </
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