Apian, Petrus
,
Instrvmentvm Sinvvm, sev primi mobilis
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0026
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GENVINVS VSVS
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<
head
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xml:space
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">Sequuntur nunc canones uſum ſiue ingreſſum iſtarum
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tabularum lucidiſsime declarantes.</
head
>
<
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>
<
s
xml:id
="
echoid-s598
"
xml:space
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preserve
">QVando arcus propoſiti ſinum ex tabulis ſupputare deſideras, primo conſidera an
<
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maior aut minor quadrãte exiſtat. </
s
>
<
s
xml:id
="
echoid-s599
"
xml:space
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preserve
">fit interdum ut arcus quarta circuli parte ſit mi
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<
note
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xlink:label
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note-0026-01
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xlink:href
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note-0026-01a
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<
emph
style
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it
">Cuiuslibet</
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<
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<
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>
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<
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<
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">inuenias.</
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</
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nor, aliquando maior, & </
s
>
<
s
xml:id
="
echoid-s600
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xml:space
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">tamen ſemicirculo minor, hoc eſt gra. </
s
>
<
s
xml:id
="
echoid-s601
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xml:space
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">180. </
s
>
<
s
xml:id
="
echoid-s602
"
xml:space
="
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">nonnunquam etiam
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maior illo, & </
s
>
<
s
xml:id
="
echoid-s603
"
xml:space
="
preserve
">adhuc minor gradibus 270. </
s
>
<
s
xml:id
="
echoid-s604
"
xml:space
="
preserve
">quæ tres quartæ ſunt circuli unius, quibus etiã
<
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/>
arcus dari poteſt maior, & </
s
>
<
s
xml:id
="
echoid-s605
"
xml:space
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">tamẽ toto circulo minor. </
s
>
<
s
xml:id
="
echoid-s606
"
xml:space
="
preserve
">Quicquid aũt ſit, facile huiuſmo
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/>
di arcus ſinum inuenire poteris in hunc modum. </
s
>
<
s
xml:id
="
echoid-s607
"
xml:space
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">Si arcus 90. </
s
>
<
s
xml:id
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xml:space
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">gra. </
s
>
<
s
xml:id
="
echoid-s609
"
xml:space
="
preserve
">fuerit minor, tabulam
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/>
<
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left
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xlink:label
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note-0026-02
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xlink:href
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note-0026-02a
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<
emph
style
="
it
">Propoſiti</
emph
>
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/>
<
emph
style
="
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">arcus qud-</
emph
>
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/>
<
emph
style
="
it
">drãte maio-</
emph
>
<
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/>
<
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style
="
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">ris, nec non</
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>
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/>
<
emph
style
="
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">ſemiãr culo</
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>
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<
emph
style
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">minoris</
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>
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/>
<
emph
style
="
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">quõ ſinus</
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>
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/>
<
emph
style
="
it
">quærẽdg ſit</
emph
>
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/>
<
emph
style
="
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">Vbi ſing nu</
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>
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/>
<
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style
="
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">merũ ſupat</
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>
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/>
<
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style
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">100000. ue</
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>
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/>
<
emph
style
="
it
">luti arcg eig</
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>
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<
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style
="
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">ſit inuenicn</
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>
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<
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style
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">dus.</
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>
</
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>
præſcriptam ingredere, in eius capite quære gradus cum minutisiuxta lineam primam
<
lb
/>
manus ſiniſtræ deſcendẽdo, & </
s
>
<
s
xml:id
="
echoid-s610
"
xml:space
="
preserve
">inuenies in angulo communi ſinũ arcus propoſiti. </
s
>
<
s
xml:id
="
echoid-s611
"
xml:space
="
preserve
">Sin
<
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/>
autẽ arcus gra. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">90. </
s
>
<
s
xml:id
="
echoid-s613
"
xml:space
="
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">maior fuerit, & </
s
>
<
s
xml:id
="
echoid-s614
"
xml:space
="
preserve
">tamen adhuc minor gradibus 180. </
s
>
<
s
xml:id
="
echoid-s615
"
xml:space
="
preserve
">ſubtrahe hinc 90.
<
lb
/>
</
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s617
"
xml:space
="
preserve
">cum reſiduo tabulam ingreſſus, inuenies etiã ſinum arcus quem quærebas. </
s
>
<
s
xml:id
="
echoid-s618
"
xml:space
="
preserve
">Si porrò
<
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/>
arcus maior fuerit gradibus 180. </
s
>
<
s
xml:id
="
echoid-s619
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s620
"
xml:space
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">tamen 270. </
s
>
<
s
xml:id
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"
xml:space
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">minor, ſubtractis inde 180. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">ingredere
<
lb
/>
tabulam cũ reſiduo, & </
s
>
<
s
xml:id
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echoid-s623
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xml:space
="
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">inuenies quod optas. </
s
>
<
s
xml:id
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echoid-s624
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xml:space
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">Similiter operare quum arcus maior eſt
<
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gra. </
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>
<
s
xml:id
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xml:space
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">270. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">& </
s
>
<
s
xml:id
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"
xml:space
="
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">tamen minor 360. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Quando & </
s
>
<
s
xml:id
="
echoid-s629
"
xml:space
="
preserve
">hoc fit nõ raro, ut dati ſinus recti arcũ ſcire
<
lb
/>
cupias, tunc ita ſinum illum quære in tabulis præſcriptis in area aliqua, ſi non præciſe
<
lb
/>
attamen quàm potes rectiſsime proximum illum accipiendo, qui nec magnus, nec nimi
<
lb
/>
um ſit paruus, & </
s
>
<
s
xml:id
="
echoid-s630
"
xml:space
="
preserve
">tunc ab iſto digitum directe ad ſiniſtram educendo, inuenies in prima
<
lb
/>
linea numeros minutorum, & </
s
>
<
s
xml:id
="
echoid-s631
"
xml:space
="
preserve
">ſi directe ſurſum ab eo ſinu tendas, inuenies in capite ta-
<
lb
/>
bulæ etiam gradus, quos ubi minutis coniunxeris, habebis arcũ quæſitum. </
s
>
<
s
xml:id
="
echoid-s632
"
xml:space
="
preserve
">Quid ſi au
<
lb
/>
tem tot fuerint ſinus ij, ut in tabula inuenire nequeant? </
s
>
<
s
xml:id
="
echoid-s633
"
xml:space
="
preserve
">tunc ſanè ſubtrahe ab eo ſinu
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lb
/>
100000. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s635
"
xml:space
="
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">cum reſiduo quære arcum ut ſupra. </
s
>
<
s
xml:id
="
echoid-s636
"
xml:space
="
preserve
">Quod ſi arcus propoſiti ſinũ uerſum
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0026-03
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xlink:href
="
note-0026-03a
"
xml:space
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">
<
emph
style
="
it
">Vt inuenia</
emph
>
<
lb
/>
<
emph
style
="
it
">tur ſing uer</
emph
>
<
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/>
<
emph
style
="
it
">ſus ꝓ ppoſiti</
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>
<
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<
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style
="
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">arcus.</
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>
</
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>
inueſtigare uolueris, & </
s
>
<
s
xml:id
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xml:space
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">hic minor fuerit 90. </
s
>
<
s
xml:id
="
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xml:space
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">cuius reſidui ſinum ſtatim rectum inquire, ip
<
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/>
ſum´ à ſinu toto ubi ſubtraxeris, remanebit ſinus uerſus quem quæſiſti. </
s
>
<
s
xml:id
="
echoid-s639
"
xml:space
="
preserve
">Sin aũt arcus 90
<
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/>
maior fuerit, & </
s
>
<
s
xml:id
="
echoid-s640
"
xml:space
="
preserve
">minor 180. </
s
>
<
s
xml:id
="
echoid-s641
"
xml:space
="
preserve
">ſubtrahe inde 90. </
s
>
<
s
xml:id
="
echoid-s642
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s643
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s644
"
xml:space
="
preserve
">cum reſiduo quære ſinũ rectũ, eũ ad-
<
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/>
de ad 100000. </
s
>
<
s
xml:id
="
echoid-s645
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s646
"
xml:space
="
preserve
">habebis ſinũ uerſum arcus ꝓpoſiti. </
s
>
<
s
xml:id
="
echoid-s647
"
xml:space
="
preserve
">Siuero habueris ſinũ uerſum, & </
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>
<
s
xml:id
="
echoid-s648
"
xml:space
="
preserve
">uis
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<
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position
="
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"
xlink:label
="
note-0026-04
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xlink:href
="
note-0026-04a
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">
<
emph
style
="
it
">Habito ſinu</
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>
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/>
<
emph
style
="
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">uerſu quõ</
emph
>
<
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/>
<
emph
style
="
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">arcus eiuſdê</
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>
<
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/>
<
emph
style
="
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">agnoſ@tur.</
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>
</
note
>
indagare arcum illius, conſidera ſi minor fuerit 100000. </
s
>
<
s
xml:id
="
echoid-s649
"
xml:space
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">ſubtrahe eum â 100000. </
s
>
<
s
xml:id
="
echoid-s650
"
xml:space
="
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">cũ eius
<
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/>
reſiduiſinu quærere arcũ illum, ſi ſubtraxeris à 90. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">remanebit arcus optatus. </
s
>
<
s
xml:id
="
echoid-s652
"
xml:space
="
preserve
">Sin uero
<
lb
/>
fuerit maior ſinu perſecto, inquiſiturus ſic quo arcum, ſubtrahe de ſinu uerſo 100000.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s653
"
xml:space
="
preserve
">eius reſidui quære arcum non ſecus ac ſi ſinus rectus eſſet. </
s
>
<
s
xml:id
="
echoid-s654
"
xml:space
="
preserve
">arcum illum adde ad grad. </
s
>
<
s
xml:id
="
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xml:space
="
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">90. </
s
>
<
s
xml:id
="
echoid-s656
"
xml:space
="
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">
<
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/>
<
note
position
="
left
"
xlink:label
="
note-0026-05
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xlink:href
="
note-0026-05a
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xml:space
="
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">
<
emph
style
="
it
">Chordã ꝓ-</
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>
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<
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style
="
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">poſiti arcus</
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>
<
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<
emph
style
="
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">ueluti de-</
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>
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<
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style
="
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">prehendas.</
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>
</
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>
& </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">tunc habebis arcũ ſinus quẽ quærebas. </
s
>
<
s
xml:id
="
echoid-s658
"
xml:space
="
preserve
">Si uero arcus propoſiti chordam inuenire
<
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/>
uolueris, eodem modo operare, ut inquirendo ſinum, niſi quòd arcum illum medium tan
<
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/>
tum accipere debes, eius arcus inuentus & </
s
>
<
s
xml:id
="
echoid-s659
"
xml:space
="
preserve
">duplicatus ſinus, chordam monſtrat quæſitã.
<
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/>
</
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">ſiquidẽ cũ Sinus, quod principio cõmemorauimus, nihil aliud eſt quàm arcus dati chor
<
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/>
<
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position
="
left
"
xlink:label
="
note-0026-06
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xlink:href
="
note-0026-06a
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xml:space
="
preserve
">
<
emph
style
="
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">Ad propo-</
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>
<
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/>
<
emph
style
="
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">ſitam chor-</
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>
<
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/>
<
emph
style
="
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">dam arcum</
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>
<
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/>
<
emph
style
="
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">ut ſdas</
emph
>
.</
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>
da media. </
s
>
<
s
xml:id
="
echoid-s661
"
xml:space
="
preserve
">Chordæ uero propoſitæ arcũ inuenies facillime, modo chordam mediaris,
<
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/>
& </
s
>
<
s
xml:id
="
echoid-s662
"
xml:space
="
preserve
">medij illius arcum quæſieris ex præmiſsis, arcum quo iſtum dehinc duplicaris, tunc
<
lb
/>
enim ſinum habebis quæſitum.</
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
"/>
</
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>
<
figure
number
="
7
">
<
image
file
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0026-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0026-01
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