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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135
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DE PERSPECT.
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quam iudicio. </
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<
s
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xml:space
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">Tibi quoque conſiderandum relinquo; </
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<
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xml:space
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">cum rationabilis degrada-
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tio eſſe debeat, qua ratione neceſſarium ſit, vt diſtantiæ reſq́ue, in vna &
<
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eadem
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pro-
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portione cum altitudine oculi ad rem degradatam exiſtant? </
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<
s
xml:id
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xml:space
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">Cum poſtea degrada-
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uerit
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, is ſcriptor, in figura
<
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>.d.b.c.e.</
var
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eum bene & ex perſpectiuæ optimis
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legibus degradatum fuiſſe probare nititur; </
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<
s
xml:id
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xml:space
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<
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>.d.e.</
var
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æqualem eſſe ipſi
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E.h.</
var
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<
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type
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<
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>.E.h.</
var
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<
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type
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ipſum eſt degra datio lateris
<
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var
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&
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cum
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type
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ſuperius dixerit, ſetria
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quadrati plana degradauiſſe, quia
<
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degradat
<
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var
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et
<
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>.E.h.</
var
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degradat
<
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>.c.g.</
var
>
et
<
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>.f.
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h.</
var
>
degradat
<
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>.f.g.</
var
>
nec quidem de lateribus
<
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>.b.d.</
var
>
et
<
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>.c.e.</
var
>
loquitur, quia ſi
<
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>.c.g.</
var
>
<
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perfecti, degradatum eſt in
<
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>
: et
<
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>.d.e.</
var
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rectè protracta exiſtit, cum ſit æqua-
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lis ipſi
<
var
>.E.h.</
var
>
cum etiam
<
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>.b.d.</
var
>
et
<
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>.c.e.</
var
>
rectè protractæ eſſe debeant: </
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>
<
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xml:id
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xml:space
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">qua de cau-
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ſa ipſis
<
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>.b.E.</
var
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et
<
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>.f.h.</
var
>
quæ, ex ipſo, ſunt degradationes
<
var
>.b.c.</
var
>
et
<
var
>.f.g.</
var
>
æquales eſſe non de-
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bent? </
s
>
<
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xml:space
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">Poſſet is mihi quidem reſpondere,
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hoc pacto nulla ſuperficies clauderetur.
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</
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<
s
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xml:space
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">Ergo tria latera
<
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>.b.c</
var
>
:
<
var
>c.g.</
var
>
et
<
var
>.g.f.</
var
>
<
reg
norm
="
non
"
type
="
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">nõ</
reg
>
benè ſunt degradata,
<
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norm
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eiusque
"
type
="
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">eiusq́;</
reg
>
<
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proportionalitates
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type
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">ꝓportionalitates</
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>
ma
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lè intellectæ nil probant. </
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<
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xml:id
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xml:space
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">quia ſi dictæ proportionalitates, nobis tutò promitterent
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degradationes, ab eo primum effectas, in linea
<
var
>.b.f.</
var
>
eſſe bonas, ergo duæ
<
var
>.b.d.</
var
>
et
<
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>.e.c.</
var
>
<
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falſæ exiſterent, quarum quælibet maior eſt
<
var
>.b.E.</
var
>
et
<
var
>.f.h.</
var
>
ex .18. primi Eucli. </
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>
<
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xml:id
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xml:space
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">Omitta-
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mus etiam quod vbi is ſcribit eam eſſe rationem, aut comparationem ab
<
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>.A.d.</
var
>
ad
<
var
>.b.
<
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/>
E.</
var
>
quæ eſt ab
<
var
>.d.c.</
var
>
ad
<
var
>.b.c.</
var
>
eandemq́ue eſſe ab
<
var
>.E.h.</
var
>
ad
<
var
>.c.g.</
var
>
quæ eſt ab
<
var
>.A.E.</
var
>
ad
<
var
>.A.c.</
var
>
nil
<
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/>
probet; </
s
>
<
s
xml:id
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xml:space
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preserve
">nec ſimilitudinem triangulorum, nec aliquam propoſitionem Eucli. citans.
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</
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<
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xml:space
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">In quo excuſari non poteſt, quòd non ſoleat Euclidem, aut alium quemuis autorem
<
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citare, cum vel in ipſo operis principio capite .3. primæ partis, A pollonium
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<
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<
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">Euclidemq́;</
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, & ſi etiam præter rem, citet. </
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<
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xml:space
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">Deinde
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idem probare vult
<
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var
>
æqua
<
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lem eſſe ipſi
<
var
>.E.h.</
var
>
eandem inquit eſſe proportionem
<
var
>.a.b.</
var
>
ad
<
var
>.a.d.</
var
>
quæ eſt ipſius
<
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>.A.c.</
var
>
<
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/>
ad
<
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>.A.E.</
var
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quod & ſi verum ſit, hic tamen modus ratiocinandi nullo ordine nititur,
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quia rectius dixiſſet pro clariori intelligentia ipſius
<
var
>.a.c.</
var
>
ad
<
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>.a.e.</
var
>
eandem proportio-
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nem eſſe, quæ eſt
<
var
>.A.c.</
var
>
ad
<
var
>.A.E.</
var
>
propter ſimilitudinem, quæ inter duos triangulos
<
var
>.A.
<
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c.a.</
var
>
et
<
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>.E.c.e.</
var
>
intercedit, cum
<
var
>.E.e.</
var
>
ſupponatur parallela ipſi
<
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>.A.a.</
var
>
quod etiam vt de-
<
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monſtraretur longiori oratione ei opus fuiſſet ſi voluiſſet intellectum eorum, qui pa
<
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rum ſunt exercitati, perduci ad
<
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idem planè futurum de
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ad
<
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>.a.e.</
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>
vt
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eſt ipſius
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>.A.c.</
var
>
ad
<
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>.A.E.</
var
>
in hunc modum, ideſt probando primùm duos triangulos
<
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>.A.
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c.a.</
var
>
et
<
var
>.E.c.e.</
var
>
æquiangulos eſſe, mediante .29. primi Eucli. cum
<
var
>.A.a.</
var
>
et
<
var
>.E.e.</
var
>
inuicem
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ſint parallelæ. </
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>
<
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xml:space
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">Vnde ex .4. ſexti. idem extitiſſet de
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ad
<
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>.E.c.</
var
>
vt
<
var
>.a.c.</
var
>
ad
<
var
>.e.c.</
var
>
et. ex
<
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16. quinti idem de
<
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>.A.c.</
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>
ad
<
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>.a.c.</
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>
vt ipſius
<
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>.E.c.</
var
>
ad
<
var
>.e.c.</
var
>
& ex .19. eiuſdem de
<
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>.A.E.</
var
>
ad
<
var
>.a.
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e.</
var
>
vt ipſius
<
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>.A.c.</
var
>
ad
<
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>.a.c.</
var
>
& ex .16. iam dicta de
<
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>.A.E.</
var
>
ad
<
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>.A.c.</
var
>
vt ipſius
<
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>.a.e.</
var
>
ad
<
var
>.a.c.</
var
>
ideſt
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ipſius
<
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>.A.c.</
var
>
ad
<
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>.A.E.</
var
>
vt eſt ipſius
<
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>.a.c.</
var
>
ad
<
var
>.a.e</
var
>
: Aut hoc alio modo, qui breuior eſt pro-
<
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cedendum, incipiendo ſcilicet à ſecunda ſexti Eucli. dicendo
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exiſtente
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>
paral
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lela ipſi
<
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>.A.a</
var
>
: ex dicta .2. lib. 6. erit idem de
<
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>.c.E.</
var
>
ad
<
var
>.E.A.</
var
>
vt de
<
var
>.c.e.</
var
>
ad
<
var
>.e.a.</
var
>
vnde ex
<
num
value
="
18
">.
<
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18.</
num
>
quinti innotuiſſet ſtatim quod de
<
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>.c.A.</
var
>
ad
<
var
>.E.A.</
var
>
vt de
<
var
>.c.a.</
var
>
ad
<
var
>.e.a.</
var
>
extitiſſet. </
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>
<
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xml:space
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">Nunc
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mediantibus ſupradictis duabus propoſitionibus ideſt .29. primi, & 4. ſexti, cogno-
<
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/>
ſcitur idem planè eſſe de
<
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>.b.c.</
var
>
ad
<
var
>.d.e.</
var
>
quod ipſius
<
var
>.a.c.</
var
>
ad
<
var
>.a.e.</
var
>
& ex eiſdem idem eſſe
<
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de
<
var
>.c.g.</
var
>
ad
<
var
>.E.h.</
var
>
quod ipſius
<
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>.A.c.</
var
>
ad
<
var
>.A.E.</
var
>
vnde ex .11. quinti bis repetita idem erit de
<
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<
var
>b.c.</
var
>
ad
<
var
>.d.e.</
var
>
quod de
<
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>.c.g.</
var
>
ad
<
var
>.E.h.</
var
>
ſed cum ex ſuppoſito
<
var
>.c.g.</
var
>
ſit æqualis ipſi
<
var
>.c.b.</
var
>
idem
<
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erit de
<
var
>.c.g.</
var
>
ad
<
var
>.e.d.</
var
>
quod ipſius
<
var
>.c.b.</
var
>
ad eandem ex .7. quinti, vnde ex .11. idem erit de
<
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/>
<
var
>c.g.</
var
>
ad
<
var
>.E.h.</
var
>
quod eiuſdem
<
var
>.c.g.</
var
>
ad
<
var
>.e.d.</
var
>
ex .9. igitur eiuſdem
<
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>.d.e.</
var
>
æqualis erit ipſi
<
var
>.E.
<
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h.</
var
>
atque hic verus eſt modus ducendi intellectum parum exercitatum in cognicio-
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nis campum. </
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<
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xml:space
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">quem quidem mihi obſeruandum proponerem ſi onus ſcribendi ſu-
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ſciperem ijs, qui in ſcientijs parum verſati ſunt, quos tanquam puerulos manu du- </
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