Clavius, Christoph
,
Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur
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LIBER PRIMVS.
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ipſorum ducuntur: </
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<
s
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xml:space
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">atque eodem modo paralleli ſingulorum graduum Eclipticæ inu ſtigari poſ-
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ſunt; </
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<
s
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echoid-s943
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xml:space
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">ſi nimirum circulus M P N Q, in ſingulos gra dus diſtribuatur, & </
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<
s
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xml:space
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">reliqua fiant, quæ prius.
<
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</
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<
s
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xml:space
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preserve
">Nam in vniuerſu@ rectæ, quæ ipſi P Q, parallelæ ſunt, abſcindunt ex Meridiano arcus declinatio-
<
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num eorum arcuum Eclipticæ, qui arcubus circuli M P N Q, ſi miles ſunt, ſicut & </
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<
s
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xml:space
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gna Zodiaci duodecim arcubus Q X, X Y, &</
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<
s
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xml:space
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">c. </
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<
s
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xml:space
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<
s
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xml:space
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">Quod quidem hac fere ratione cum
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Petro Nonio lib. </
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<
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xml:space
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">2. </
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<
s
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xml:space
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">de arte nauigandi demonſtrabimus.</
s
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<
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xml:space
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</
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<
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<
s
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xml:space
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">INTELLIGATVR circa E M, deſcriptus ſemicirculus Eclipticæ A M B, & </
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<
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xml:space
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">circa E H, ſe-
<
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<
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xlink:label
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xml:space
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">Demon ſtrati@
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deſcriptionis
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Analemmatis.
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</
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micirculus Aequatoris A H B, & </
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<
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xml:space
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">vtriuſque ſectio communis ſit recta A B; </
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<
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">ſitq́; </
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<
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xml:space
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">A, principium ♈,
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& </
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<
s
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xml:space
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">B, principium ♎. </
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<
s
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xml:space
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">Et quoniam M, eſt principium ♋, vel ♑, cum H M, portio Meridiani
<
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circuli ſit maxima declinatio ſolis; </
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>
<
s
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xml:space
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">diſtat autem vtrumque horũ ab æquinoctialibus punctis qua-
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xml:space
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drante integro; </
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<
s
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xml:space
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">erunt arcus A M, B M, quadrantes, atque adeo anguli A E M, B E M, recti. </
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<
s
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xml:space
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">Secet
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iam recta X R, in plano Meridiani per arcum H M, & </
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<
s
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xml:space
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">rectas E H, E M, M O, ducto rectã M O,
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in puncto φ, & </
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<
s
xml:id
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xml:space
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">rectam E M, in puncto C. </
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>
<
s
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xml:space
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">Intelligatur quoque per rectam X R, planũ duci Aequa-
<
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tori A H B, parallelum occurrens rectæ E M in C, (quoniam enim circulus M P N Q, cum in
<
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/>
Analemmate iaceat in plano Meridiani, ad Aequatorem rectus eſt, eſtq́; </
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>
<
s
xml:id
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xml:space
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">Q H P E, communis ſe-
<
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ctio Aequatoris & </
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<
s
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xml:space
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">eiuſdem pla
<
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ni Meridiani, & </
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>
<
s
xml:id
="
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xml:space
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">recta X R, di-
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ctæ ſectioni Q H P E, parallela,
<
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<
figure
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fig-0033-01
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number
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11
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file
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0033-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0033-01
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>
poterit per ipſam X R, duci
<
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planũ Aequatori æquidiſtans.)
<
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</
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<
s
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xml:space
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<
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xlink:href
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xml:space
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">20</
note
>
faciensq́; </
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>
<
s
xml:id
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xml:space
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">in Ecliptica quidem
<
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cõmunem ſectionem D K, re-
<
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ctam; </
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<
s
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xml:space
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">In Sphæra autem circu-
<
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<
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xml:space
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">3. vndec.</
note
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lum D γ k, ex propos. </
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<
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xml:space
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">1. </
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<
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<
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xml:space
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</
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<
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xml:space
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">Theod. </
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<
s
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xml:space
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">tranſeuntem per pun-
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ctum γ, in quo recta X R, arcũ
<
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Meridiani H M, ſecat. </
s
>
<
s
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xml:space
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">Quo-
<
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niam igitur eſt, vt M C, ad C E,
<
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<
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xlink:label
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xml:space
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">2. ſexti.</
note
>
ita M φ, ad φ O, erit & </
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<
s
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xml:space
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">compo
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nendo, vt M E, ad CE, ita M O,
<
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<
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">30</
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ad φ O; </
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<
s
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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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">permutando, vt M E, ſemidiameter Eclipticæ ad M O, ſemidiametrũ circuli M P Q,
<
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ita C E, ad φ O: </
s
>
<
s
xml:id
="
echoid-s981
"
xml:space
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">Eſt autem C E, æqualis ſinui arcus D A, hoc eſt, rectæ D F, ex D, ad A B, ad rectos
<
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<
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xlink:label
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xlink:href
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xml:space
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">34. primi.</
note
>
angulos ductæ (ſunt enim A B, D K, communes ſectiones planorum parallelorũ, nempe Aequa-
<
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<
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position
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xlink:label
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xlink:href
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xml:space
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">16. undec.</
note
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toris A H B, & </
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<
s
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xml:space
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">circuli D γ K, factæ ab Eclipticæ plano A M B, parallelæ nec non & </
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<
s
xml:id
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xml:space
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">C E, D F, pa-
<
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<
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xlink:label
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xml:space
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">28. primi.</
note
>
rallelæ) & </
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<
s
xml:id
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xml:space
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">φ O, eadem ratione ęqualis ſinui arcus Q X, hoc eſt, rectæ X ω, quæ ad Q E, perpendi-
<
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cularis eſt. </
s
>
<
s
xml:id
="
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xml:space
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">Igitur ſemidiametri M E, M O, eandem habent proportionem, quam ſinus D F, X ω,
<
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ac propterea arcus A D, Q X, ſimiles ſunt, vt mox lemmate ſequenti demonſtrabimus. </
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>
<
s
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xml:space
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">Oſtenden
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dum ergo eſt, arcum H γ, quem aufert parallela X R, ex Meridiano, æqualem eſſe arcui declina-
<
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tionis, quam habet Eclipticæ arcus A D, quem arcui Q X, circuli M P Q, ſimilem iam demonſtra
<
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uimus. </
s
>
<
s
xml:id
="
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xml:space
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">quod quidem facile præſtabimus hoc modo. </
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>
<
s
xml:id
="
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xml:space
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">Deſcripto per polos mundi, hoc eſt, per po-
<
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<
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position
="
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="
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xml:space
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">40</
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los parallelorum A H B, D γ K, & </
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<
s
xml:id
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xml:space
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">per D, punctum circulo maximo D G, erit arcus D G, arcus de-
<
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clinationis puncti D, cum intercipiatur inter ipſum punctum, & </
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<
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">Aequatorem. </
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<
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xml:space
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">Cum ergo arcus
<
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circulorum maximorum, qui per polos parallelorum deſcribuntur, inter ipſos parallelos interce-
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pti, ex propoſitione 15. </
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<
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<
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xml:space
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">2. </
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<
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xml:space
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">Theodoſii, æquales ſint; </
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<
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xml:space
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">Sint autem arcus H γ, D G, circulorum ma-
<
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ximorum per polos parallelorum A H B, D γ K, deſcriptorum, intercipianturq́; </
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>
<
s
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="
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xml:space
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">inter ipſos paral-
<
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lelos, æqualis erit arcus H γ, arcui D G. </
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>
<
s
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xml:space
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">Aufert igitur in Analemmate parallela X R, arcum H γ,
<
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æqualem arcui declinationis illius arcus Eclipticæ, qui arcui Q X, ſimilis eſt, qualis eſtarcus A D.
<
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</
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<
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xml:space
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">Idemq́ue dicendum eſt de reliquis parallelis Y S, Z T, & </
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<
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xml:space
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">α V. </
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<
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xml:space
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">Conſtat ergo arcus H γ, H β, H δ, & </
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<
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xml:space
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<
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H ε. </
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<
s
xml:id
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xml:space
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">æquales eſſe declinationibus reliquorum ſignorum Zodiaci inter ♋ & </
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<
s
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xml:space
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">♑, quandoqui-
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dem arcus ſignorũ in Ecliptica ſimiles ſunt arcubus Q X, X Y, &</
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<
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xml:space
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">c. </
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<
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xml:space
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">in circulo M P N Q. </
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<
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xml:space
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">tam enim
<
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<
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hi, quàm illi, duodecimæ partes ſunt ſuorum circulorum. </
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>
<
s
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xml:space
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">Quoniam verò ſectiones parallelorũ
<
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per ſignorum initia ductorum factæ à Meridiani plano parallelæ ſunt, liquido conſtat, parallelas
<
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illas per puncta M, β, γ, H, &</
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>
<
s
xml:id
="
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xml:space
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">c. </
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>
<
s
xml:id
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xml:space
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">ductas, eſſe diametros parallelorum, cum auferant ex circulo A B
<
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C D, arcus ſimiles illis, quos ex Meridiano ab@cindunt re uera diametri dictorum parallelorum,
<
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vt ante dictum eſt. </
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>
<
s
xml:id
="
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xml:space
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preserve
">Quòd ſi circulus A B C D, æqualis eſſet Meridiano in Sphæra, tranſirent om-
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nino per illas parallelas paralleli per initia ſignorum ducti. </
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>
<
s
xml:id
="
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xml:space
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">Idem prorſus demonſtrabimus, ſi pro
<
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Meridiano circulus A B C D, intelligatur quicunque alius circulus maximus per polos mundi
<
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ductus, qualis eſt Colurus ſolſtitiorum, vt ſupra in definitione Analemmatis diximus. </
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>
<
s
xml:id
="
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xml:space
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">Analemma
<
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ergo ad quamcunque poli altitudinem deſcripſimus. </
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<
s
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xml:space
="
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">Quod erat faciendum.</
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>
<
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</
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</
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"
n
="
16
">
<
head
xml:id
="
echoid-head19
"
xml:space
="
preserve
">LEMMA.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1015
"
xml:space
="
preserve
">QVAM proportionem habent ſinus toti, hoc eſt, ſemidiametri </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>