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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328
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IO. BAPT. BENED.
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340
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file
="
0340
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0340
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zonte; </
s
>
<
s
xml:id
="
echoid-s3983
"
xml:space
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preserve
">cogitemus etiam lineam
<
var
>.A.t.i.x.</
var
>
illud coni latus eſſe, qu od à ſummitate ver
<
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/>
ſus baſim tranſit per medium latitudinis ipſius gnomonis, concipiamus etiam mente
<
lb
/>
<
var
>e.a.</
var
>
communem ſectionem eſſe trianguli ſupra dicti cum azimut horæ, necnon pun-
<
lb
/>
ctum
<
var
>.K.</
var
>
eſſe commune radio Solis
<
var
>.o.a.</
var
>
& ſuperficiei conicæ, quod quidem eſt illud
<
lb
/>
quod quæritur, hoc ſcilicet modo. </
s
>
<
s
xml:id
="
echoid-s3984
"
xml:space
="
preserve
">Primum cognoſcimus angulum
<
var
>.p.A.t.</
var
>
vt medie
<
lb
/>
tas anguli totius coni, & angulum
<
var
>.p.</
var
>
rectum, vnde
<
var
>.t.</
var
>
tam intrinſecus, quam extrinſe-
<
lb
/>
custrianguli
<
var
>.A.p.t.</
var
>
nobis cognitus erit. </
s
>
<
s
xml:id
="
echoid-s3985
"
xml:space
="
preserve
">Nunc cum angulus
<
var
>.A.t.o.</
var
>
cognoſcatur, ſi
<
lb
/>
gnomon
<
var
>t.o.</
var
>
fixus fuerit in ſuperficie conica, ita qd cum latere
<
var
>.A.t.</
var
>
eſſiciat
<
reg
norm
="
angulum
"
type
="
context
">angulũ</
reg
>
<
lb
/>
<
var
>A.t.o.</
var
>
& lateraliter faciat angulosrectos cum ſuperficie conica, ad quod efficiendum
<
lb
/>
nulla eſt difficultas, cognoſcendo deinde
<
var
>.A.t.</
var
>
ſimul cum angulis
<
var
>.A.</
var
>
et
<
var
>.t.</
var
>
intrinſecis
<
lb
/>
trianguli ortogonij
<
var
>.A.p.t.</
var
>
cognoſcemus
<
var
>.p.t.</
var
>
et
<
var
>.A.p.</
var
>
vnde etiam tota
<
var
>.o.p.</
var
>
ſed cogno
<
lb
/>
ſcendo
<
var
>.o.p.</
var
>
cum angulo
<
var
>.p.o.e.</
var
>
(angulus enim
<
var
>.p.o.e.</
var
>
cognoſcitur ex hypotheſi cum
<
lb
/>
ſit inter azimut Solis & azimut gnomonis) cum angulo
<
var
>.o.p.e.</
var
>
recto cognoſcemus
<
var
>.p.
<
lb
/>
e.</
var
>
et
<
var
>.o.e.</
var
>
</
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>
<
s
xml:id
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xml:space
="
preserve
">deinde cum nobis nota ſit
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>.o.e.</
var
>
cum angulo altitudinis Solis
<
var
>.e.o.a.</
var
>
& angu-
<
lb
/>
lo
<
var
>.o.e.a.</
var
>
recto cognoſc emus longitudinem azimutalis
<
var
>.e.a.</
var
>
necnon quantitatem
<
var
>.a.o.</
var
>
<
lb
/>
Imaginata poſtea
<
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>.a.q.</
var
>
æquidiſtante
<
var
>.e.p.</
var
>
habebimus
<
var
>.p.q.</
var
>
æqualem
<
var
>.a.e.</
var
>
ex .34. primi
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Eucli. </
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>
<
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xml:id
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xml:space
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">Vnde duabus
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>.o.p.</
var
>
et
<
var
>.p.q.</
var
>
mediantibus,
<
reg
norm
="
cognitiſque
"
type
="
simple
">cognitiſq́;</
reg
>
cum angulo recto
<
var
>.p.</
var
>
cogno
<
lb
/>
ſcemus
<
var
>.o.q.</
var
>
nec non angulum
<
var
>.o.q.
<
lb
/>
p.</
var
>
quo mediante, necnon median-
<
lb
/>
te angulo
<
var
>.q.A.t.</
var
>
et
<
var
>.A.q.</
var
>
cognita, co
<
lb
/>
<
figure
xlink:label
="
fig-0340-01
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xlink:href
="
fig-0340-01a
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number
="
363
">
<
image
file
="
0340-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0340-01
"/>
</
figure
>
gnoſcemus
<
var
>.A.i.</
var
>
et
<
var
>.q.i.</
var
>
quę
<
var
>.q.i.</
var
>
dem
<
lb
/>
pta à
<
var
>.q.o.</
var
>
relinquet nobis
<
reg
norm
="
cognitam
"
type
="
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">cognitã</
reg
>
<
lb
/>
<
var
>i.o</
var
>
. </
s
>
<
s
xml:id
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xml:space
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">Et quia
<
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et
<
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var
>
ſemper
<
lb
/>
ſunt in eadem ſuperficie ſecante co
<
lb
/>
num, quæ etiam ſecat ſuperficiem
<
lb
/>
trianguli
<
var
>.A.q.x.</
var
>
ad rectos ex .18. vn
<
lb
/>
decimi, cum linea
<
var
>.u.n.</
var
>
perpendicu
<
lb
/>
laris ſit ſuperficiei trianguli
<
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>.A.q.i.</
var
>
<
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/>
ex .8. dicti, quia parallela eſt
<
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>.l.p.</
var
>
quę
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/>
perpendicularis eſt ſuperficiei
<
reg
norm
="
trian- guli
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type
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guli</
reg
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<
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var
>
ex .4. eiuſdem, ſequitur,
<
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/>
quod talis ſectio ( quæ intelligatur
<
lb
/>
per
<
var
>.u.K.i.n.</
var
>
) ſemper erit elliptica,
<
lb
/>
vel parabole, ſeu hyperbole,
<
reg
norm
="
prout
"
type
="
simple
">ꝓut</
reg
>
<
lb
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linea
<
var
>.o.i.q.</
var
>
ſecabit latus coni, oppo
<
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/>
ſitum lateri
<
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>.A.i.</
var
>
diſtento in ipſa ſuperficie conica, ſeu ad ſuperiorem partem produ
<
lb
/>
ctum, velipſi parallelum.</
s
>
</
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<
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<
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xml:id
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xml:space
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">Supponamus nunc dictam lineam
<
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>.o.q.</
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>
ſecare dictum oppoſitum latus lateri
<
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>.A.i.</
var
>
<
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verſus baſim, vnde ſectio
<
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>.u.K.i.n.</
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>
erit elliptica. </
s
>
<
s
xml:id
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xml:space
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preserve
">quod facile cognitu eſt
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norm
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mediante
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type
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">mediãte</
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>
com
<
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/>
paratione angulorum
<
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>.A.q.i.</
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>
et
<
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>.q.A.i.</
var
>
interſe, eo quod ſi eſſent ęquales, dicta ſect o
<
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/>
barabola eſſet ex .27. primi Eucli. et .11. primi Pergei, ſed ſi angulus
<
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>.A.q.i.</
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>
maior eſ-
<
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ſet angulo
<
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>.q.A.i.</
var
>
ſectio eſſet ellipſis, ex ultimo poſtulato primi Euclid. </
s
>
<
s
xml:id
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xml:space
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">& ex .13. pri-
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mi Pergei, ſed ſi dictus angulus
<
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>
minor eſſet angulo
<
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>.A.</
var
>
tunc ſectio eſſet hyper-
<
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bole ex dicto poſtulato & ex .12. primi Pergei. </
s
>
<
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xml:id
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xml:space
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">Sit ergo primum vt
<
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eſt, hoc
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eſt, quod ſectio eſſet oxygonia, ideſt elliptica, ſeu defectio (quod idem eſt,) ſepa-
<
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/>
ratim oportebit nos ellipſim deſignare
<
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norm
="
ſimilem
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type
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">ſimilẽ</
reg
>
<
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norm
="
ęqualemque
"
type
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">ęqualẽq́;</
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>
ei, quæ eſt
<
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var
>
<
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norm
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quod
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type
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">qđ</
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<
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norm
="
quidem
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type
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>
<
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difficile non erit, quotieſcunque ſuos axes inuenerimus, maiorem ſcilicet, & mino- </
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