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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<div xml:id="echoid-div7" type="body" level="1" n="1">
<div xml:id="echoid-div308" type="chapter" level="2" n="2">
<div xml:id="echoid-div308" type="section" level="3" n="1">
<p>
<s xml:id="echoid-s1494" xml:space="preserve">Pro cuius rei ſpeculatione imaginemur in figura corporea .A:
<var>q.a.</var>
eſſe figuram re-
<lb/>
ctangulam
<reg norm="orizontalemque" type="simple">orizontalemq́;</reg>
<lb/>
orizonti, & cum eo primum coniunctam in linea
<var>.q.d.</var>
cuius plani triangulum
<var>.i.q.d.</var>
<lb/>
pars erit, ſit autem oculus reſpicientis
<var>.o.</var>
cuius altitudo
<var>.o.p.</var>
ab orizonte, qui
<reg norm="quidem" type="context">quidẽ</reg>
<lb/>
conſpicit rectangulum dictum orizontale
<var>.q.a.</var>
in pyramide
<var>.o.q</var>
:
<var>o.u</var>
:
<var>o.a.</var>
et
<var>.o.d.</var>
<lb/>
terminata quatuor triangulis
<var>.o.q.u</var>
:
<var>o.u.a</var>
:
<var>o.a.d.</var>
et
<var>.o.d.q.</var>
ſit verò primum ita
<lb/>
collocatus pes
<var>.p.</var>
eius qui reſpicit, vt linea
<var>.p.l.</var>
perpendicularis ipſi
<var>.u.a.</var>
lateri re-
<lb/>
ctanguli, medio loco poſita ſit, inter
<var>.a.n.</var>
et
<var>.u.s</var>
. </s>
<s xml:id="echoid-s1495" xml:space="preserve">
<reg norm="Idque" type="simple">Idq́;</reg>
primum nobis erit exem-
<lb/>
plum.</s>
</p>
<p>
<s xml:id="echoid-s1496" xml:space="preserve">Imaginemur nunc lineas
<var>.u.q.</var>
et
<var>.a.d.</var>
indefinitè productas eſſe, quæ in ſuperficie-
<lb/>
bus duorum triangulorum
<var>.o.u.q.</var>
et
<var>.o.a.d.</var>
& rectanguli orizontalis
<var>.q.a.</var>
ex
<ref id="ref-0018">prima
<lb/>
vndecimi Euclid.</ref>
poſitæ erunt. </s>
<s xml:id="echoid-s1497" xml:space="preserve">Imaginemur etiam lineam
<var>.p.s.n.</var>
perpendicula-
<lb/>
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
<lb/>
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.
<lb/>
a.</var>
& quia ſupponitur
<var>.o.p.</var>
perpendicularis plano orizontali, Angulus ergò
<var>.o.p.l.</var>
re-
<lb/>
ctus erit ex ſecunda definitione .11. Euclid. </s>
<s xml:id="echoid-s1498" xml:space="preserve">Imaginemur quoque ductas eſſe
<lb/>
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.
<lb/>
11. perpendicularis erit, & ſuperficies orizontalis
<var>.a.s.</var>
perpendicularis erit cum dicta
<lb/>
<var>o.s.n.</var>
ex .18. eiuſdem lib. vnde ex dicta definitione
<var>.o.s.u.</var>
et
<var>.o.n.a.</var>
erunt anguli recti
<lb/>
et
<var>.o.s.</var>
et
<var>.o.n.</var>
ex communi ſcientia, in ſuperficiebus duorum triangulorum
<var>.o.u.q.</var>
et
<var>.
<lb/>
o.a.d.</var>
<lb/>
<lb/>
</figure>
tur facere, ſi opinaretur duas alias rectas per
<lb/>
<var>.o.s.n.</var>
tranſire, quæſunt in di-
<lb/>
ctis ſuperficiebus. </s>
<s xml:id="echoid-s1499" xml:space="preserve">Vnde
<var>.o.s.</var>
et
<var>.o.n.</var>
communes
<lb/>
erunt ſectiones duarum dictarum
<reg norm="ſuperficierum" type="context">ſuperficierũ</reg>
<lb/>
cum ſuperficie
<var>.o.s.n</var>
. </s>
<s xml:id="echoid-s1500" xml:space="preserve">Imaginemur nunc has
<lb/>
duas ſuperficies
<var>.o.u.</var>
et
<var>.o.a.</var>
quarum commu-
<lb/>
nis ſectio ſit
<var>.o.t.</var>
(quæ erit linea recta ex .3. lib.
<lb/>
II.) quæ erunt perpendiculares ſuperficiei
<var>.o.s.
<lb/>
n.</var>
ex .4. et .14. iam dictis. </s>
<s xml:id="echoid-s1501" xml:space="preserve">& ex .19. eiuſdem
<lb/>
<var>o.t.</var>
perpendicularis eidem ſuperficiei
<var>.o.s.n.</var>
<lb/>
erit, & ex .6. eiuſdem hæc linea
<var>.o.t.</var>
duabus
<var>.u.
<lb/>
q.s.</var>
et
<var>.a.d.n.</var>
parallela exiſter, & ex .9. eiuſdem
<lb/>
hæc linea
<var>.o.t.</var>
duabus
<var>.u.q.s.</var>
et
<var>.a.d.n.</var>
parallela
<lb/>
exiſtet, & ex eadem .9. erit parallela ipſi
<var>.p.l.</var>
<lb/>
Imaginemur nunc planum, ſuper quod deſide
<lb/>
<lb/>
planum, exempli gratia, ſit primo, vt iam dixi-
<lb/>
mus, locatum in linea
<var>.q.d.</var>
<lb/>
cum plano orizontali, cuius communes ſectio
<lb/>
nes cum ſuperficiebus
<var>.s.t.</var>
et
<var>.n.t.</var>
viſionis la-
<lb/>
terum
<var>.u.q.</var>
et
<var>.a.d.</var>
ſint
<var>.i.q.</var>
et
<var>.i.d.</var>
& com-
<lb/>
munis ſectio trianguli
<var>.o.u.a.</var>
ideſt viſionis
<lb/>
lateris
<var>.a.u.</var>
cum dicto plano, ſit
<var>.r.e</var>
. </s>
<s xml:id="echoid-s1502" xml:space="preserve">Vnde ex
<lb/>
communi ſcientia rectangulum orizontale,
<lb/>
oculo
<var>.o.</var>
ſeipſum patefaciet in plano
<var>.i.q.d.</var>
ſe- </s>
</p>
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