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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132
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0132
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0132
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<
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<
s
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xml:space
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">Pro cuius rei ſpeculatione imaginemur in figura corporea .A:
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eſſe figuram re-
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ctangulam
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orizontalemque
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type
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ad degradandam ſuper aliquod planum perpendiculare
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orizonti, & cum eo primum coniunctam in linea
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>.q.d.</
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cuius plani triangulum
<
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>
<
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pars erit, ſit autem oculus reſpicientis
<
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>.o.</
var
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cuius altitudo
<
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>.o.p.</
var
>
ab orizonte, qui
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quidem
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type
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context
">quidẽ</
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>
<
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conſpicit rectangulum dictum orizontale
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>.q.a.</
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in pyramide
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>.o.q</
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:
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>o.u</
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:
<
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>o.a.</
var
>
et
<
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>.o.d.</
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<
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/>
terminata quatuor triangulis
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>.o.q.u</
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:
<
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>o.u.a</
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>
:
<
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>o.a.d.</
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>
et
<
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>.o.d.q.</
var
>
ſit verò primum ita
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collocatus pes
<
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>.p.</
var
>
eius qui reſpicit, vt linea
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>.p.l.</
var
>
perpendicularis ipſi
<
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>.u.a.</
var
>
lateri re-
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ctanguli, medio loco poſita ſit, inter
<
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>.a.n.</
var
>
et
<
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>.u.s</
var
>
. </
s
>
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xml:id
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xml:space
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<
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Idque
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type
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simple
">Idq́;</
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primum nobis erit exem-
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plum.</
s
>
</
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>
<
p
>
<
s
xml:id
="
echoid-s1496
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xml:space
="
preserve
">Imaginemur nunc lineas
<
var
>.u.q.</
var
>
et
<
var
>.a.d.</
var
>
indefinitè productas eſſe, quæ in ſuperficie-
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bus duorum triangulorum
<
var
>.o.u.q.</
var
>
et
<
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>.o.a.d.</
var
>
& rectanguli orizontalis
<
var
>.q.a.</
var
>
ex
<
ref
id
="
ref-0018
">prima
<
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vndecimi Euclid.</
ref
>
poſitæ erunt. </
s
>
<
s
xml:id
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xml:space
="
preserve
">Imaginemur etiam lineam
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var
>.p.s.n.</
var
>
perpendicula-
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/>
rem ipſi
<
var
>.p.l.</
var
>
quæ etiam cum duabus
<
var
>.u.q.s.</
var
>
et
<
var
>.a.d.n.</
var
>
ex .34. primi Euclid. angulos
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rectos conſtituet, cum ex .28. duæ
<
var
>.u.q.s.</
var
>
et
<
var
>.a.d.n.</
var
>
ſint parallelæ ipſi
<
var
>.p.l.</
var
>
et
<
var
>.s.n.</
var
>
ipſi
<
var
>.u.
<
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/>
a.</
var
>
& quia ſupponitur
<
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>.o.p.</
var
>
perpendicularis plano orizontali, Angulus ergò
<
var
>.o.p.l.</
var
>
re-
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/>
ctus erit ex ſecunda definitione .11. Euclid. </
s
>
<
s
xml:id
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xml:space
="
preserve
">Imaginemur quoque ductas eſſe
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/>
duas
<
var
>.o.s.</
var
>
et
<
var
>.o.n.</
var
>
vnde
<
var
>.l.p.</
var
>
ei ſuperficiei, in qua ſunt duæ lineæ
<
var
>.o.p.</
var
>
et
<
var
>.s.n.</
var
>
ex .4.
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/>
11. perpendicularis erit, & ſuperficies orizontalis
<
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>.a.s.</
var
>
perpendicularis erit cum dicta
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/>
<
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>o.s.n.</
var
>
ex .18. eiuſdem lib. vnde ex dicta definitione
<
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>.o.s.u.</
var
>
et
<
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>.o.n.a.</
var
>
erunt anguli recti
<
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/>
et
<
var
>.o.s.</
var
>
et
<
var
>.o.n.</
var
>
ex communi ſcientia, in ſuperficiebus duorum triangulorum
<
var
>.o.u.q.</
var
>
et
<
var
>.
<
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o.a.d.</
var
>
erunt, ſi noluerimus cogere aduerſarium ad confitendum duas lineas rectas in-
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cludere ſuperficiem, quemadmodum cogere-
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<
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fig-0132-01
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xlink:href
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fig-0132-01a
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number
="
179
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file
="
0132-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0132-01
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</
figure
>
tur facere, ſi opinaretur duas alias rectas per
<
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/>
eadem puncta
<
var
>.o.s.n.</
var
>
tranſire, quæſunt in di-
<
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ctis ſuperficiebus. </
s
>
<
s
xml:id
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"
xml:space
="
preserve
">Vnde
<
var
>.o.s.</
var
>
et
<
var
>.o.n.</
var
>
communes
<
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erunt ſectiones duarum dictarum
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ſuperficierum
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>
<
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cum ſuperficie
<
var
>.o.s.n</
var
>
. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">Imaginemur nunc has
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duas ſuperficies
<
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>.o.u.</
var
>
et
<
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>.o.a.</
var
>
quarum commu-
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nis ſectio ſit
<
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>.o.t.</
var
>
(quæ erit linea recta ex .3. lib.
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II.) quæ erunt perpendiculares ſuperficiei
<
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>.o.s.
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n.</
var
>
ex .4. et .14. iam dictis. </
s
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<
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xml:space
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">& ex .19. eiuſdem
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<
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>
perpendicularis eidem ſuperficiei
<
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>.o.s.n.</
var
>
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erit, & ex .6. eiuſdem hæc linea
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>.o.t.</
var
>
duabus
<
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>.u.
<
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q.s.</
var
>
et
<
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>.a.d.n.</
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>
parallela exiſter, & ex .9. eiuſdem
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hæc linea
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>.o.t.</
var
>
duabus
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>.u.q.s.</
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>
et
<
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>.a.d.n.</
var
>
parallela
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exiſtet, & ex eadem .9. erit parallela ipſi
<
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>.p.l.</
var
>
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Imaginemur nunc planum, ſuper quod deſide
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remus videre quadrangulum orizontale, quod
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planum, exempli gratia, ſit primo, vt iam dixi-
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mus, locatum in linea
<
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>.q.d.</
var
>
ad angulos rectos
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cum plano orizontali, cuius communes ſectio
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nes cum ſuperficiebus
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>.s.t.</
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>
et
<
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>.n.t.</
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>
viſionis la-
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terum
<
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>.u.q.</
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>
et
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>.a.d.</
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>
ſint
<
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>.i.q.</
var
>
et
<
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>.i.d.</
var
>
& com-
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munis ſectio trianguli
<
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>.o.u.a.</
var
>
ideſt viſionis
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lateris
<
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>.a.u.</
var
>
cum dicto plano, ſit
<
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>.r.e</
var
>
. </
s
>
<
s
xml:id
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xml:space
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">Vnde ex
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communi ſcientia rectangulum orizontale,
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oculo
<
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>.o.</
var
>
ſeipſum patefaciet in plano
<
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>.i.q.d.</
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>
ſe- </
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