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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DE PERSPECT.
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0135
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xlink:href
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aliud eſt, quàm punctum, varijs ſectionibus commune, & huiuſmodi punctum, ocu
<
lb
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lus non eſt, quemadmodum multi Pictores, Sculptores, Architecti, & Perſpectiui
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ignari, ipſum punctum, oculum appellando, falsò crediderunt, quaſi
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type
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per-
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ſpectiuæ oculus eſſet.</
s
>
</
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<
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<
s
xml:id
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xml:space
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">In ſupradictis igitur figuris manifeſte eluceſcit cauſa diminutionis obiectorum,
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& altitudinis trianguli æqualis ei, quæ eſt oculi à plano orizontali, vt etiam diſtantię
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var
>.
<
lb
/>
p.l.p.x.</
var
>
& cuiuſuis tandem rei. </
s
>
<
s
xml:id
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xml:space
="
preserve
">Sed vt huius effectus ſcientia magis in vniuerſum pa-
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retur. </
s
>
<
s
xml:id
="
echoid-s1524
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xml:space
="
preserve
">Volo duas hic ſubſcriptas figuras
<
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>.D.</
var
>
corpoream, &
<
var
>.D.</
var
>
ſuperficialem à vo-
<
lb
/>
bis conſiderari, in quarum corporea, linea
<
var
>.p.l.</
var
>
ſit extra duas
<
var
>.u.s.</
var
>
et
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var
>.a.n.</
var
>
vt in figu-
<
lb
/>
ra
<
var
>.B.</
var
>
locata, ita tamen vt planum trianguli
<
var
>.i.q.d.</
var
>
diſiunctum ſit à rectangulo ſuper-
<
lb
/>
ficiali, ideſt, vt ſeparatum exiſtat à linea
<
var
>.q.d.</
var
>
latere ipſius rectanguli, & ſit etiam obli
<
lb
/>
quum, reſpectu ipſius rectanguli, ideſt vt communis ſectio dicti plani cum ſuperficie
<
lb
/>
<
var
>a.s.</
var
>
orizontalis ipſi
<
var
>.u.a.</
var
>
parallela non ſit, ſed ſit obliqua, ſi tamen idem planuni per-
<
lb
/>
pendiculare dictæ ſuperficiei orizontali
<
var
>.a.s.</
var
>
erit: </
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>
<
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xml:id
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xml:space
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preserve
">& dicta communis ſectio exprima
<
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/>
tur characteribus .q.ω.α.d.x. nunc in figura corporea habebimus figuram
<
var
>.e.r.c.m.</
var
>
<
lb
/>
in plano, quod viſualem pyramidem ſecat, medio cuius figuræ
<
var
>.e.r.c.m.</
var
>
oculus po-
<
lb
/>
ſitus in
<
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>.o.</
var
>
rectangulum orizontale conſpicit. </
s
>
<
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xml:id
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xml:space
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">Volentes vero nunc in figura
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>.D.</
var
>
ſuper-
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ficiali eam deſcribere, faciem us
<
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>.p.x.</
var
>
ſuperficialem, æqualem corporeæ, eiq́ue
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/>
addemus
<
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>.x.l.</
var
>
æqualem corporeæ, aut ſumemus
<
var
>.p.l.</
var
>
eidem corporeæ
<
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norm
="
aequa- lem
"
type
="
simple
">ęqua-
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/>
lem</
reg
>
, quam ſecabimus in puncto
<
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>.x.</
var
>
eodem planè modo, quo corporea reperi-
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/>
tur diuiſa; </
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>
<
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xml:id
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xml:space
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">erigemus deinde
<
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>.p.o.</
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>
et
<
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>.x.i.</
var
>
æquales corporeis. </
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>
<
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xml:id
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xml:space
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">Secabimus deinde
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>.x.q.</
var
>
<
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/>
æqualem corporeæ, & ducemus
<
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>.q.i.</
var
>
et
<
var
>.l.o.</
var
>
vnde habebimus triangulos
<
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>.o.p.l.</
var
>
et
<
var
>.i.x.
<
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/>
q.</
var
>
ſimiles & æquales corporeis ex .4. primi Eucli. </
s
>
<
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xml:id
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xml:space
="
preserve
">Secabimus deinde
<
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>.q.x.</
var
>
in pun-
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/>
cto
<
var
>.d.</
var
>
eadem ratione, qua ſecta fuit corporea, & ducemus lineam
<
var
>.d.i.</
var
>
vnde habebi-
<
lb
/>
mus triangulos
<
var
>.i.d.q.</
var
>
et
<
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>.i.d.x.</
var
>
ſimiles corporeis. </
s
>
<
s
xml:id
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xml:space
="
preserve
">& mediante triangulo
<
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>.i.q.d.</
var
>
hu-
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/>
<
figure
xlink:label
="
fig-0135-01
"
xlink:href
="
fig-0135-01a
"
number
="
184
">
<
image
file
="
0135-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0135-01
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<
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xml:space
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">CORPOREA.</
caption
>
</
figure
>
cuſque habebimus ſitus duorum laterum figurę
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/>
rectanguli degradati, ideſt ſitus ipſius
<
var
>.e.m.</
var
>
et
<
var
>.r.
<
lb
/>
c.</
var
>
etiam ſi adhuc neſciatur in qua parte ipſius
<
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>.i.
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/>
q.</
var
>
& ipſius
<
var
>.i.d.</
var
>
eſſe
<
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type
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. </
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<
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xml:id
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xml:space
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">Quod ſi ſcire volue
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rimus
<
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ſecabitur
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type
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">ſecabit̃</
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>
.
<
var
>p.l.</
var
>
in
<
reg
norm
="
puncto
"
type
="
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">pũcto</
reg
>
<
var
>.g.</
var
>
ſimilis corporeæ,
<
lb
/>
ſi in ipſa tamen corporea prius protraxerimus
<
lb
/>
lineam
<
var
>.q.d.</
var
>
latus rectanguli vſque ad
<
var
>.p.l.</
var
>
in pun
<
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/>
cto
<
var
>.g</
var
>
. </
s
>
<
s
xml:id
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xml:space
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">Ducetur deinde linea
<
var
>.o.g.</
var
>
ſuperficialis,
<
lb
/>
quæ ſecabit lineam
<
var
>.i.x.</
var
>
in puncto
<
var
>.f.</
var
>
linea vero
<
var
>.
<
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/>
o.l.</
var
>
in puncto
<
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>.z.</
var
>
punctis ſitis in
<
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>.i.x.</
var
>
ſuperficiali,
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/>
pręcisè vt in corporea,
<
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norm
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type
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quilibet
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ex ſe facilè cognoſcere poteſt. </
s
>
<
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xml:id
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xml:space
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">Deinde in cor
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porea, in ſuperficie orizontali ducatur
<
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>.p.q.</
var
>
et
<
lb
/>
<
figure
xlink:label
="
fig-0135-02
"
xlink:href
="
fig-0135-02a
"
number
="
185
">
<
image
file
="
0135-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0135-02
"/>
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xml:space
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