Apian, Petrus
,
Instrvmentvm Sinvvm, sev primi mobilis
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TABVLARVM SINVVM PER PET. APIANVM.
"/>
declinationis in ſinum diſtantiæ à meridiano, ꝓductũ diuide in totum, arcus quotientis
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note-0075-01
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note-0075-01a
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<
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">Inuentum</
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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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dicetur inuentũ primũ. </
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>
<
s
xml:id
="
echoid-s6018
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xml:space
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">Mox duc & </
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>
<
s
xml:id
="
echoid-s6019
"
xml:space
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">ſinũ minorẽ ex ſinu cõplementi huius primi inuenti
<
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& </
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>
<
s
xml:id
="
echoid-s6020
"
xml:space
="
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">ſinu declinationis ſtellæ uel propoſiti in totũ, ꝓductũ diuide in maiorẽ, & </
s
>
<
s
xml:id
="
echoid-s6021
"
xml:space
="
preserve
">arcũ quoti-
<
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entis ſubtrahe de 90. </
s
>
<
s
xml:id
="
echoid-s6022
"
xml:space
="
preserve
">reliquũ adde ad altitudinem poli tuæ regiõis, & </
s
>
<
s
xml:id
="
echoid-s6023
"
xml:space
="
preserve
">habebis inuentũ ſe
<
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/>
cundũ. </
s
>
<
s
xml:id
="
echoid-s6024
"
xml:space
="
preserve
">Deinde ducito ſinus utriuſ cõplementi in ſe, ꝓductũ diuide in totũ, arcum quoti
<
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/>
<
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position
="
right
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xlink:label
="
note-0075-02
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xlink:href
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note-0075-02a
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<
emph
style
="
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">Inuentum</
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>
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<
emph
style
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>
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<
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style
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<
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style
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>
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<
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style
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">ris.</
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>
</
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>
entis ſubduc de 90. </
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>
<
s
xml:id
="
echoid-s6025
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xml:space
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">& </
s
>
<
s
xml:id
="
echoid-s6026
"
xml:space
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">ſi ſecundũ inuentũ ſit minus ̈ 90. </
s
>
<
s
xml:id
="
echoid-s6027
"
xml:space
="
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">remanebit tibi inuentũ tertium,
<
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/>
ſi aũt plus 90. </
s
>
<
s
xml:id
="
echoid-s6028
"
xml:space
="
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">fuerit, adhuc adde arcũ quotientis, & </
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>
<
s
xml:id
="
echoid-s6029
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xml:space
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">habebis inuentũ tertium. </
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>
<
s
xml:id
="
echoid-s6030
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xml:space
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">Porrò ad-
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huc ꝓpone tibi ſinũ inuentorũ primi & </
s
>
<
s
xml:id
="
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xml:space
="
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">tertij, minorẽ exijs duc in totum, & </
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>
<
s
xml:id
="
echoid-s6032
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xml:space
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">productũ di-
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uide in maiorem, arcus q̊tientis dabit portionẽ circuli uerticalis inter uerticẽ capitis & </
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>
<
s
xml:id
="
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circulum poſitionis interceptũ quẽ quærebas. </
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>
<
s
xml:id
="
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xml:space
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">Sed ſi diſtantia puncti ꝓpoſiti uel ſtellæ à
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xlink:label
="
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xlink:href
="
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<
emph
style
="
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">Inuentum</
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>
<
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<
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style
="
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emph
>
<
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/>
<
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style
="
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">lateribus</
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>
<
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<
emph
style
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>
</
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>
meridiano præciſe fuerit 90. </
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>
<
s
xml:id
="
echoid-s6035
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xml:space
="
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">graduũ, tunc cõplementũ declinationis erit inuentũ primũ,
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& </
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>
<
s
xml:id
="
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xml:space
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">latitudo regionis inuentũ ſecundũ, tertiũ uero inuenies ut antea, ſimiliter & </
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>
<
s
xml:id
="
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xml:space
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">arcũ quæ-
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ſitum. </
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<
s
xml:id
="
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xml:space
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">Quod ſi qũt diſtantia à meridiano maior fuerit ̈ 90. </
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>
<
s
xml:id
="
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xml:space
="
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">ſubtrahe eam de ſemicirculo
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ſinum quo cõplementi duc in ſinum cõplementi declinationis, ꝓductũ diuide in ſinum
<
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/>
<
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position
="
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xlink:label
="
note-0075-04
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xlink:href
="
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<
emph
style
="
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">Introitus d</
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<
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<
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<
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>
</
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>
totũ, & </
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>
<
s
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xml:space
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">quotiens dabit inuentũ primũ, cuius cõplementũ ſimul & </
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>
<
s
xml:id
="
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xml:space
="
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">ſinũ declinationis ſtel-
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læ ſi tibi proponas, minorem uero nume℞ ducas in totum, diuidas aũt ꝓductum in maio
<
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/>
rem, & </
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>
<
s
xml:id
="
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xml:space
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">arcum quotientis ſubtrahas de 90. </
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>
<
s
xml:id
="
echoid-s6043
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xml:space
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">ſimiliter & </
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>
<
s
xml:id
="
echoid-s6044
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xml:space
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">reſiduũ de latitudine regiõis, rema-
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nebit inuentũ ſecundũ. </
s
>
<
s
xml:id
="
echoid-s6045
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xml:space
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">Mox ꝓcede hic, ut antea edoctus es, quãdo diſtãtia ſtellæ minor
<
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<
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position
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xlink:label
="
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<
emph
style
="
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">Inucntum</
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>
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<
emph
style
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>
<
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<
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style
="
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">latera ad-</
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>
<
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<
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style
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>
</
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>
erat ̈ 90. </
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>
<
s
xml:id
="
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xml:space
="
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">Operæpreciũ q̊ eſt ſcire, ꝙ qñ inuentũ ſecundũ maius eſt ̈ 90. </
s
>
<
s
xml:id
="
echoid-s6047
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xml:space
="
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">tunc etiã ter-
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tium erit amplius eo, at ſi ita contingat, tũc ſubtrahe inuentũ tertiũ de ſemicirculo, & </
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>
<
s
xml:id
="
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<
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inuentũ primũ etiã paulò diligẽtius cõſidera, numerũ´ minorẽ duc in totũ, & </
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>
<
s
xml:id
="
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xml:space
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">productũ
<
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xlink:label
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<
emph
style
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">Inuentum</
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>
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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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">Operatio</
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<
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<
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>
</
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diuide in maiorẽ, arcus quotientis dabit arcũ circuli uerticalis quæſitũ. </
s
>
<
s
xml:id
="
echoid-s6050
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xml:space
="
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">Fieri etiã poteſt, ut
<
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inuentũ ſecundũ ſit quadra circuli, & </
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>
<
s
xml:id
="
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xml:space
="
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">tũc quo inuentũ tertiũ erit quadra circuli, at ſic
<
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inuento primo habito, nõ eſt ꝙ amplius oꝑeris, ſiquidẽ illud ipſum inuentũ primũ eſt ar-
<
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/>
cus circuli uerticalis quæſitus. </
s
>
<
s
xml:id
="
echoid-s6052
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xml:space
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">Ethactenus ꝗdem diſſeruimus de ſtellis & </
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>
<
s
xml:id
="
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xml:space
="
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">punctis, quæ
<
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declinationẽ habent ſeptentrionalẽ, nunc reliquũ eſt & </
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>
<
s
xml:id
="
echoid-s6054
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xml:space
="
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">de ijsdicere quæ meridionalem
<
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habent declinationẽ, ibi tu duc ſinum declinationis ſtellæ in ſinũ diſtantiæ ſtellæ à meri-
<
lb
/>
<
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position
="
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xlink:label
="
note-0075-07
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xlink:href
="
note-0075-07a
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xml:space
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<
emph
style
="
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">De ſtellis et</
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>
<
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<
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<
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<
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style
="
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">bentibus de</
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>
<
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<
emph
style
="
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">clinationẽ</
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>
<
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/>
<
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="
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">meridionæ</
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>
<
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<
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">lem.</
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>
</
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>
diano, productũ diuide in ſinũ ꝑfectũ, arcus q̊tientis erit inuentũ primũ. </
s
>
<
s
xml:id
="
echoid-s6055
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xml:space
="
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">Deinde uter ſi-
<
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nus fuerit maior ex cõplemento huius inuenti & </
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>
<
s
xml:id
="
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xml:space
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">declinationis, ducatur in totum, & </
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>
<
s
xml:id
="
echoid-s6057
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xml:space
="
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">diui
<
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datur in alte℞. </
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>
<
s
xml:id
="
echoid-s6058
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xml:space
="
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">A cõplemẽto quotientis huius ſubtrahe latitudinẽ regiõis, & </
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>
<
s
xml:id
="
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xml:space
="
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">manebit in-
<
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/>
uentum ſecundũ. </
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>
<
s
xml:id
="
echoid-s6060
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xml:space
="
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">Vtriuſ huius inuẽti cõplementa duc in ſe, ꝓductũ in totũ ſinũ diuide,
<
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/>
& </
s
>
<
s
xml:id
="
echoid-s6061
"
xml:space
="
preserve
">cõplementũ huius quotientis oſtendit inuentũ tertiũ, ſi iam minorẽ ſinũ primi inuen-
<
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/>
ti & </
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>
<
s
xml:id
="
echoid-s6062
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xml:space
="
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">tertij ducas in totum, ꝓductũ uero diuidas in maiorẽ, arcus quotientis oſtendet arcũ
<
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<
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="
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xlink:label
="
note-0075-08
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xlink:href
="
note-0075-08a
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<
emph
style
="
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">Inuentum</
emph
>
<
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/>
<
emph
style
="
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">primum ꝑ</
emph
>
<
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/>
<
emph
style
="
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">areã inſpie</
emph
>
<
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/>
<
emph
style
="
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">ads.</
emph
>
</
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>
circuli uerticalis optatũ, & </
s
>
<
s
xml:id
="
echoid-s6063
"
xml:space
="
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">hactenus tam operoſe quæſitum. </
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>
<
s
xml:id
="
echoid-s6064
"
xml:space
="
preserve
">Si aũt declinatio nulla eſt
<
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/>
ſtellæ uel puncti ab æquinoctiali, tunc inuentũ primũ ſit tibi diſtantia ſtellæ uel puncti à
<
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/>
meridiano, & </
s
>
<
s
xml:id
="
echoid-s6065
"
xml:space
="
preserve
">inuentum ſecundũ erit cõplementũ altitudinis poli, tertium uero acquires,
<
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/>
ſi ſinum altitudinis poli ducas in ſinũ cõplementi diſtantiæ à meridiano, diuidas aũt in ſi-
<
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<
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xlink:label
="
note-0075-09
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xlink:href
="
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xml:space
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<
emph
style
="
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">Inuentũ ſe@</
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>
<
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/>
<
emph
style
="
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">cundum.</
emph
>
</
note
>
num ꝑfectũ, tunc tibi cõplementũ q̊tientis dabit inuentũ tertiũ. </
s
>
<
s
xml:id
="
echoid-s6066
"
xml:space
="
preserve
">Iam ſi minorem nurr e℞
<
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<
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position
="
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xlink:label
="
note-0075-10
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xlink:href
="
note-0075-10a
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<
emph
style
="
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">Inuentum</
emph
>
<
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/>
<
emph
style
="
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">tertim.</
emph
>
</
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>
ex inuento tertio & </
s
>
<
s
xml:id
="
echoid-s6067
"
xml:space
="
preserve
">diſtãtia à meridiano ducas in totũ, & </
s
>
<
s
xml:id
="
echoid-s6068
"
xml:space
="
preserve
">diuidas in maiorem, tunc arcus
<
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/>
quotientis ꝓducet arcũ circuli uerticalis inter zenith & </
s
>
<
s
xml:id
="
echoid-s6069
"
xml:space
="
preserve
">circulũ poſitionis, qui tranſit per
<
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/>
<
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position
="
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xlink:label
="
note-0075-11
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xlink:href
="
note-0075-11a
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xml:space
="
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">
<
emph
style
="
it
">De ſtellis ſi</
emph
>
<
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/>
<
emph
style
="
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">ue punctis</
emph
>
<
lb
/>
<
emph
style
="
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">declinatio-</
emph
>
<
lb
/>
<
emph
style
="
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">nem ab æꝗ</
emph
>
<
lb
/>
<
emph
style
="
it
">noctiali nõ</
emph
>
<
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/>
<
emph
style
="
it
">habẽtibus.</
emph
>
</
note
>
locum ſtellæ. </
s
>
<
s
xml:id
="
echoid-s6070
"
xml:space
="
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">?</
s
>
<
s
xml:id
="
echoid-s6071
"
xml:space
="
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">?Exempli loco quæram ecce in ipſo loco intronizatiõis arcum circuli
<
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/>
uerticalis inter zenith ſiue polum horizontis & </
s
>
<
s
xml:id
="
echoid-s6072
"
xml:space
="
preserve
">circulum poſitiõis, qui per locũ Solis du
<
lb
/>
citur, ad horã intronizatiõis, quæ ꝗa facta eſt hora 9 ante meridiẽ ſatis fœliciter, Sol tũc
<
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/>
fuit in 2. </
s
>
<
s
xml:id
="
echoid-s6073
"
xml:space
="
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">gra. </
s
>
<
s
xml:id
="
echoid-s6074
"
xml:space
="
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">26. </
s
>
<
s
xml:id
="
echoid-s6075
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s6076
"
xml:space
="
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">II, duco igit̃ ſinum cõplementi declinatiõis loci ☉(sun). </
s
>
<
s
xml:id
="
echoid-s6077
"
xml:space
="
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">ſ. </
s
>
<
s
xml:id
="
echoid-s6078
"
xml:space
="
preserve
">93544. </
s
>
<
s
xml:id
="
echoid-s6079
"
xml:space
="
preserve
">in ſinũ
<
lb
/>
diſtãtiæ ☉(sun) à meridie. </
s
>
<
s
xml:id
="
echoid-s6080
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s6081
"
xml:space
="
preserve
">70710. </
s
>
<
s
xml:id
="
echoid-s6082
"
xml:space
="
preserve
">ꝓductũ in totũ diuiſo, remanẽt 66145. </
s
>
<
s
xml:id
="
echoid-s6083
"
xml:space
="
preserve
">inuentũ illud pri-
<
lb
/>
mũ, cuius cõplementũ eſt 48. </
s
>
<
s
xml:id
="
echoid-s6084
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s6085
"
xml:space
="
preserve
">35. </
s
>
<
s
xml:id
="
echoid-s6086
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s6087
"
xml:space
="
preserve
">ſinus uero 74991. </
s
>
<
s
xml:id
="
echoid-s6088
"
xml:space
="
preserve
">Nunciã duco ſinũ declinatio
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0075-12
"
xlink:href
="
note-0075-12a
"
xml:space
="
preserve
">EXEM-
<
lb
/>
PLVM
<
lb
/>
<
emph
style
="
it
">de loco So</
emph
>
<
lb
/>
<
emph
style
="
it
">lis introni-</
emph
>
<
lb
/>
<
emph
style
="
it
">zationis</
emph
>
<
lb
/>
<
emph
style
="
it
">hora.</
emph
>
</
note
>
nis 35347. </
s
>
<
s
xml:id
="
echoid-s6089
"
xml:space
="
preserve
">ꝗa minorẽ in totũ, & </
s
>
<
s
xml:id
="
echoid-s6090
"
xml:space
="
preserve
">ꝓductum diuido in linũ cõplementi primi inuenti, ꝓue-
<
lb
/>
nient in q̊tiente 47135. </
s
>
<
s
xml:id
="
echoid-s6091
"
xml:space
="
preserve
">arcus eius eſt 28. </
s
>
<
s
xml:id
="
echoid-s6092
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s6093
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s6094
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s6095
"
xml:space
="
preserve
">is de 90. </
s
>
<
s
xml:id
="
echoid-s6096
"
xml:space
="
preserve
">ſubductus, relinꝗt 61. </
s
>
<
s
xml:id
="
echoid-s6097
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s6098
"
xml:space
="
preserve
">52
<
lb
/>
mi. </
s
>
<
s
xml:id
="
echoid-s6099
"
xml:space
="
preserve
">ijs addo altitudinem poli.</
s
>
<
s
xml:id
="
echoid-s6100
"
xml:space
="
preserve
">ſ.</
s
>
<
s
xml:id
="
echoid-s6101
"
xml:space
="
preserve
">48. </
s
>
<
s
xml:id
="
echoid-s6102
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s6103
"
xml:space
="
preserve
">20. </
s
>
<
s
xml:id
="
echoid-s6104
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s6105
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s6106
"
xml:space
="
preserve
">erit ſumma 110. </
s
>
<
s
xml:id
="
echoid-s6107
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s6108
"
xml:space
="
preserve
">12. </
s
>
<
s
xml:id
="
echoid-s6109
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s6110
"
xml:space
="
preserve
">dicetur´ in-
<
lb
/>
uentum ſecundum, q̊d ꝗa maius eſt ̈ 90. </
s
>
<
s
xml:id
="
echoid-s6111
"
xml:space
="
preserve
">ſubtraho de ſemicirculo, & </
s
>
<
s
xml:id
="
echoid-s6112
"
xml:space
="
preserve
">remanent 69. </
s
>
<
s
xml:id
="
echoid-s6113
"
xml:space
="
preserve
">gra.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6114
"
xml:space
="
preserve
">48. </
s
>
<
s
xml:id
="
echoid-s6115
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s6116
"
xml:space
="
preserve
">Cõplementũ eſt 20. </
s
>
<
s
xml:id
="
echoid-s6117
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s6118
"
xml:space
="
preserve
">12. </
s
>
<
s
xml:id
="
echoid-s6119
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s6120
"
xml:space
="
preserve
">cuius ſinum 34529. </
s
>
<
s
xml:id
="
echoid-s6121
"
xml:space
="
preserve
">duco in ſinum cõplementi in-
<
lb
/>
uenti primi 48. </
s
>
<
s
xml:id
="
echoid-s6122
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s6123
"
xml:space
="
preserve
">35. </
s
>
<
s
xml:id
="
echoid-s6124
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s6125
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s6126
"
xml:space
="
preserve
">74991. </
s
>
<
s
xml:id
="
echoid-s6127
"
xml:space
="
preserve
">ꝓductum diuido in totum, & </
s
>
<
s
xml:id
="
echoid-s6128
"
xml:space
="
preserve
">in q̊tiente, pdeũt 25904
<
lb
/>
arcus eius eſt 15. </
s
>
<
s
xml:id
="
echoid-s6129
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s6130
"
xml:space
="
preserve
">cue addo 90. </
s
>
<
s
xml:id
="
echoid-s6131
"
xml:space
="
preserve
">gradus(eo ꝙ inuentũ ſecundũ quadrãte maius eſt) </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>