Apian, Petrus
,
Instrvmentvm Sinvvm, sev primi mobilis
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<
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0063
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63
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TABVLARVM SINVVM PER PET. APIANVM.
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complementi declinationis minoris. </
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<
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<
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<
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<
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<
s
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<
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</
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<
s
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<
s
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<
s
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xml:space
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">cõplementũ ipſius erit 71. </
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<
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<
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<
s
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<
s
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">ſinus atit 94570. </
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<
s
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echoid-s4401
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xml:space
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">ꝓductũ ex hac multiplicati
<
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<
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xlink:label
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note-0063-01
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xlink:href
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note-0063-01a
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<
emph
style
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it
">Per latera.</
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<
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<
emph
style
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it
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<
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<
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<
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<
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<
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</
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one diuido in ſinũ totũ, & </
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<
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<
s
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">arcus eſt 48. </
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<
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">gra. </
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<
s
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echoid-s4405
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">altiudo illa poli quæſita
<
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/>
in loco intronizationis. </
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>
<
s
xml:id
="
echoid-s4406
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xml:space
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preserve
">Quid ſi aũt contingat, ut alter terminus eclypticæ ſit in medie-
<
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tate eclypticæ ſeptentrionali, alter uero in meridionali? </
s
>
<
s
xml:id
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xml:space
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">tunc ſanè duc ſinum differentiæ
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aſcenſionũ in ſinũ cõplementi de clinationis Borealis, ꝓducto diuiſo in ſinũ totum, quo
<
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tiens dabit inuentũ primũ. </
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>
<
s
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xml:space
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">Sinũ cõplementi huius inuenti propone tibi, & </
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<
s
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="
echoid-s4409
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xml:space
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">ſimul ſinũ de-
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clinationis Borealis, minorem duc in totum, & </
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<
s
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xml:space
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">productũ diuide in maiorẽ, arcui quoti-
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entis adde arcũ declinationis Auſtrinæ, & </
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<
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xml:space
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">collectũ hoc uocabit̃ inuentũ ſecundũ. </
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<
s
xml:id
="
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xml:space
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">Poſtea
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duc ſinũ complementi primi inuenti in ſinũ cõplem enti ſecundi inuenti, productũ diui-
<
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/>
de in ſinũ totum, quotientis arcu ex 90. </
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>
<
s
xml:id
="
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xml:space
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">ſubtracto, reſidui ſinũ ſeorſim colloca unà cum ſi-
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nu inuenti primi, minorẽ duc in totũ, productum in maiorem diuide, & </
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<
s
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xml:space
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">quotientem ex di
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uiſione prouenientem rurſus duc in ſinum cõplementi declinationis Auſtrinæ, & </
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>
<
s
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ctum diuide cum ſinu toto, tunc arcus quotientis arguet altitudinem poli quam optabas
<
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ſcire, nec eſt. </
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>
<
s
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xml:space
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">ꝙ hic inſuper expectes exemplum, quum neceſſarium non uideatur.</
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</
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</
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<
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<
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<
s
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">Cognito antea & </
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<
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">ſimul perſpecta amplitudine ortiua
<
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aſcendentis, altitudinem poli inde perquirere.</
s
>
<
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</
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<
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<
s
xml:id
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xml:space
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">Iam ſupra præmonuimus, ubi declinatio tanta eſt quanta amplitudo, in ea ciuitate
<
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nullã eſſe eleuationẽ poli, q̊d ſanè omnibus cõtingit ſub æquatore habitãtibus, nequit e-
<
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<
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note-0063-02
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<
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">Amplitude</
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<
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<
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<
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style
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<
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<
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<
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<
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<
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<
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<
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<
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<
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<
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</
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nim amplitudo eſſe declinatione minor, ſed bene maior, ſi igitur maior illa fuerit, quære
<
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angulũ quẽ facit eclyptica cũ meridiano iuxta gradũ medij cœli ꝑ 26. </
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">& </
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<
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<
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">ꝓnuncia
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ta, angulus ille ſi fuerit quadrãte minor, tunc erit ad hanc operationẽ adcõ modatus. </
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<
s
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autem maior extiterit, ſubtrahe eũ à ſemicirculo, & </
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<
s
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">remanebit numerus quo uteris in hac
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conſideratione loco anguli. </
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<
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xml:space
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">Sinum arcus illius ſeorſim pone unà cũ ſinu cõplementi am-
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plitudinis ortiuæ, ſicut per 12. </
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<
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">pronunc. </
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<
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">inueniſti, minorẽ exijs duc in totũ, productum
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diuide in maiorem, & </
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<
s
xml:id
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xml:space
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">arcus quotientis tibi dabit arcũ à medio cœli uſ ad gradũ horo-
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ſcopi numerãdo ſecũdũ ordinẽ ſignorũ. </
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>
<
s
xml:id
="
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xml:space
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">At hoc uerum eſt ſi angulus medij cœli minor
<
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/>
fuerit quadrante, fit aũt id, quando gradus eclypticæ aſcendens eſt in ſignis meridionali
<
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/>
bus. </
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>
<
s
xml:id
="
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xml:space
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">Si autẽ angulus meridiani & </
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>
<
s
xml:id
="
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xml:space
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">eclypticæ maior ſit recto, q̊d fit, quũ aſcendens eſt in
<
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<
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<
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<
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>
</
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>
ſignis ſeptentrionalibus, arcũ quotiẽtis minue de ſemicirculo, & </
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>
<
s
xml:id
="
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xml:space
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">reliquus manebit arcus
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eclypticæ à medio cœli uſ ad caput horoſcopi. </
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>
<
s
xml:id
="
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xml:space
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">Porrò etiã tibi propone ſinũ amplitudi
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nis ortiuæ & </
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>
<
s
xml:id
="
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xml:space
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">ſinum declinationis aſcendentis, minorẽ duc in ſinũ totum, & </
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>
<
s
xml:id
="
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xml:space
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">ꝓductum di-
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<
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<
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style
="
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">Per aream</
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>
</
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>
uide in maiorem. </
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<
s
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="
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xml:space
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">arcus à 90. </
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>
<
s
xml:id
="
echoid-s4441
"
xml:space
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">ſubtractus, relinquet altitudinem poli eius loci in quo am-
<
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plitudinem obſeruaſti. </
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>
<
s
xml:id
="
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xml:space
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">Potes idem diuerſa paulo operatione ſic exequi, ſinum ampli
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tudinis ortiuæ & </
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>
<
s
xml:id
="
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xml:space
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">ſinũ cõplementi tibi propone, ſimul etiã ſinum complementi arcus in-
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ter medium cœli & </
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>
<
s
xml:id
="
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xml:space
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">aſcendentis gradum, minorem duc in totum, productum in maiorem
<
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diuide, & </
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<
s
xml:id
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xml:space
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">quotiens dabit diſtantiã medij cœli à 90. </
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<
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xml:id
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xml:space
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">gradu ab aſcendente, ad eã diſtantiã
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adde declinationem medij cœli, ſi Borealis fuerit, uel ſubtrahe, ſi Auſtrina extiterit, quic
<
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/>
<
note
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="
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xlink:label
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note-0063-05
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xlink:href
="
note-0063-05a
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<
emph
style
="
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">Per latera.</
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>
</
note
>
quid inde ꝓuenerit, erit altitudo poli quæſita, ſed hic quo exemplum non negabimus
<
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<
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xlink:label
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xml:space
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PLVM
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<
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<
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pi.</
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>
</
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tibi. </
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<
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<
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<
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<
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<
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">gra. </
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<
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<
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xml:id
="
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">mi. </
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<
s
xml:id
="
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xml:space
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">♈ in medio cœli fuiſſe hora & </
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>
<
s
xml:id
="
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xml:space
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">lo-
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co factæ intronizationis, angulũ quo eclypticæ & </
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>
<
s
xml:id
="
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xml:space
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">meridiani iuxta illum gradum eſſe
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112. </
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>
<
s
xml:id
="
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">gra. </
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<
s
xml:id
="
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xml:space
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">37. </
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<
s
xml:id
="
echoid-s4459
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xml:space
="
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">mi. </
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<
s
xml:id
="
echoid-s4460
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">cognoui ꝑ 26. </
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>
<
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="
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">27. </
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>
<
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xml:id
="
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xml:space
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">& </
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<
s
xml:id
="
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xml:space
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">28. </
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>
<
s
xml:id
="
echoid-s4464
"
xml:space
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">ꝓnunciata, & </
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>
<
s
xml:id
="
echoid-s4465
"
xml:space
="
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">quia angulus hic maior eſt qua-
<
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/>
drãte, ſubtraxi eũ de ſemicirculo, & </
s
>
<
s
xml:id
="
echoid-s4466
"
xml:space
="
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">remanſerunt 67. </
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>
<
s
xml:id
="
echoid-s4467
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xml:space
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">gra. </
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>
<
s
xml:id
="
echoid-s4468
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xml:space
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">23. </
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>
<
s
xml:id
="
echoid-s4469
"
xml:space
="
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">mi ſinus eorũ uoco nume℞
<
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introitualem. </
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>
<
s
xml:id
="
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"
xml:space
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">ſ. </
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>
<
s
xml:id
="
echoid-s4471
"
xml:space
="
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">92309. </
s
>
<
s
xml:id
="
echoid-s4472
"
xml:space
="
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">At quum ſinus cõplementi amplitudinis aſcendentis 87405.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4473
"
xml:space
="
preserve
">minimus fuerit, nume℞ illum duxi in totũ, ꝓductũ diuiſi in ſinum introitualem, & </
s
>
<
s
xml:id
="
echoid-s4474
"
xml:space
="
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">in quo
<
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/>
tiente ꝓdierunt 94687. </
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>
<
s
xml:id
="
echoid-s4475
"
xml:space
="
preserve
">arcus eius eſt 71. </
s
>
<
s
xml:id
="
echoid-s4476
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4477
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s4478
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4479
"
xml:space
="
preserve
">quibus à ſemicirculo ſubtractis, re-
<
lb
/>
manent 108. </
s
>
<
s
xml:id
="
echoid-s4480
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4481
"
xml:space
="
preserve
">43. </
s
>
<
s
xml:id
="
echoid-s4482
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4483
"
xml:space
="
preserve
">arcus ille eclypticæ à medio cœli uſ ad gradum aſcendentis,
<
lb
/>
tantũ quo ſi numeres â 16. </
s
>
<
s
xml:id
="
echoid-s4484
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4485
"
xml:space
="
preserve
">40. </
s
>
<
s
xml:id
="
echoid-s4486
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4487
"
xml:space
="
preserve
">♈, iuxta uerum ſignorũ ordinem, numerus tan
<
lb
/>
get 5. </
s
>
<
s
xml:id
="
echoid-s4488
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4489
"
xml:space
="
preserve
">25. </
s
>
<
s
xml:id
="
echoid-s4490
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4491
"
xml:space
="
preserve
">♌, & </
s
>
<
s
xml:id
="
echoid-s4492
"
xml:space
="
preserve
">ſic quidẽ gradũ aſcendentẽ adhuc diuerſo â ſuꝑioribus modo in-
<
lb
/>
ueni. </
s
>
<
s
xml:id
="
echoid-s4493
"
xml:space
="
preserve
">Inſuper ſi ꝑ 5. </
s
>
<
s
xml:id
="
echoid-s4494
"
xml:space
="
preserve
">ꝓnunc. </
s
>
<
s
xml:id
="
echoid-s4495
"
xml:space
="
preserve
">quæro declinationẽ, inuenio uti 18. </
s
>
<
s
xml:id
="
echoid-s4496
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4497
"
xml:space
="
preserve
">58. </
s
>
<
s
xml:id
="
echoid-s4498
"
xml:space
="
preserve
">mi ſinum eius
<
lb
/>
declinationis. </
s
>
<
s
xml:id
="
echoid-s4499
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s4500
"
xml:space
="
preserve
">32501. </
s
>
<
s
xml:id
="
echoid-s4501
"
xml:space
="
preserve
">quia minorem duco in ſinũ totũ, & </
s
>
<
s
xml:id
="
echoid-s4502
"
xml:space
="
preserve
">productũ diuido in ſinũ </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>
