Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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priori: </
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<
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"> æqualia erunt ipſa parallelepipeda: </
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<
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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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<
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<
s
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<
s
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{1/2}. </
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<
s
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">areæ circuli maximi in {4/5}. </
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<
s
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<
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<
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intelligantur duo parallelepipeda, quorum vnius baſis æqualis ſit {2/3}.
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ſextæpartis.</
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areæ circuli maximi in ſphæra, & </
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<
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ſit {1/3}. </
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<
s
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">areæ maximi circuli, & </
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<
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<
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lepipedorum baſes cum altitudinibus reciprocantur: </
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ſit dupla baſis in poſteriori, quam altitudo in poſteriori altitudinis in priori:
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</
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<
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<
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<
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quale eſt ipſi ſphærę. </
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<
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<
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<
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">Ac proinde ſphæra ex dupla dia-
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metro in {1/3}. </
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<
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">areæ circuli maximi procreabitur. </
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<
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">quod ſexto loco eſt propo-
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ſitum.</
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<
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</
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<
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<
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quoque duo parallelepipeda, quorum vnius baſis con-
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ſeptimæ partis.</
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tineat {1/3}. </
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<
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">ſuperficiei ſphærę, & </
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<
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">altitudo {1/3}. </
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<
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<
s
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">alterius verò baſis compre-
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hendat {1/6}. </
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<
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">ſuperficiei, & </
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<
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">altitudo æqualis ſit diametro. </
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<
s
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xml:space
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">Et quoniam baſes cum
<
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altitudinibus ſunt reciprocę, quod ita ſit {1/3}. </
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<
s
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="
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xml:space
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">ſuperficiei baſis videlicet prioris
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parallelepipedi, ad {1/6}. </
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<
s
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xml:space
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">ſuperficiei, id eſt, ad baſem poſterioris, vt altitudo poſte-
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rioris, nempe diameter, ad prioris altitudinem, nimirum ad {1/2}. </
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>
<
s
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="
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">diametri, cum v-
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traque proportio ſit dupla: </
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<
s
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xml:space
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"> ipſa parallelepipeda æqualia erunt: </
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>
<
s
xml:id
="
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xml:space
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">Sed prius
<
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xlink:label
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="
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xml:space
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">34. vndec.</
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>
ſphærę, per 1. </
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>
<
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">partem huius 2. </
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>
<
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">regulæ æquale eſt. </
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<
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">Igitur, & </
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>
<
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">poſterius: </
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>
<
s
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">hoc eſt,
<
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ſphærę ſoliditas producetur ex diametro in ſextam partem ſuperficiei, quod eſt
<
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ſeptimum.</
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>
<
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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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concipiantur duo parallelepipeda, quorum vnius baſis ſit {1/3}.
<
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</
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<
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<
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xlink:label
="
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="
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xml:space
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">Demonſtratio
<
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octauæ partis.</
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>
ſuperficiei ſphæræ, & </
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>
<
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">altitudo ſemidiameter: </
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>
<
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">alterius autem baſis ſit {1/2}. </
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<
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ciei, & </
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<
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xml:id
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">altitudo {1/3}. </
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>
<
s
xml:id
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">diametri. </
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>
<
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xml:id
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">Quia verò baſes, & </
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>
<
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xml:id
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">altitudines recipro cantur, quod
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ita ſit {1/3}. </
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<
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xml:id
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">ſuperficiei ad {1/2}. </
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>
<
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xml:id
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">ſuperficiei, nimirũ baſis prioris parallelepipedi ad ba-
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ſem poſterioris, vt {1/3}. </
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>
<
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xml:id
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">diametriad {1/2}. </
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>
<
s
xml:id
="
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">diametri, altitudo videlicet poſterioris pa-
<
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rallelepipedi ad altitudinem prioris; </
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>
<
s
xml:id
="
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"> æqualia eruntipſa parallelepipeda. </
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>
<
s
xml:id
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<
note
symbol
="
d
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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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">34. vndec.</
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>
ergo, per 1. </
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<
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">partem huius 2. </
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<
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">regulæ, prius ſit ſphæræ æquale, eidem quo que po-
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ſterius æquale erit: </
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<
s
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xml:space
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">Ac propterea ſphæræ ſoliditas pro ducetur ex tertia part@
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diametri in ſemiſſem conuexæ ſuperficiei. </
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>
<
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">quod eſt o ctauum.</
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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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vero ex propoſ. </
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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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<
s
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">colliguntur quatuor ſe-
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quentes regulæ, per quas ſuperficies ſphæræ conuexa inuenitur tum maior
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quam vera, tum minor, tam ex circumferentia, quam ex diametro circuli ma-
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ximi.</
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<
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</
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<
head
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head
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<
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<
s
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xml:space
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">EX circumferentia circuli in ſphæra maximi ſuperficiem conuexam
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ſphęrę procreare vera maiorem.</
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<
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</
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<
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<
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<
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vt 223. </
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<
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<
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">ita quadratum ex circumferentia maximi circuli data de-
<
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<
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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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">Superfici{es}
<
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ſphæræmaior,
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quam vera.</
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>
ſcriptum ad aliud, pro dibitque ſphæræ ſuperficies maior quam vera. </
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>
<
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nim per propoſ. </
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<
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">4. </
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<
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">huius cap. </
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<
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xml:space
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">Num. </
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<
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xml:id
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xml:space
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">1. </
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>
<
s
xml:id
="
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xml:space
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">maior ſit proportio qua drati circumfe-
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rentiæ circuli maximi ad ſuperficiem ſphæræ, quam 223. </
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>
<
s
xml:id
="
echoid-s10474
"
xml:space
="
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">ad 71. </
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>
<
s
xml:id
="
echoid-s10475
"
xml:space
="
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">ſit autem qua-
<
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/>
dratum datæ circumferentiæ ad numerum procreatum, vt 223. </
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>
<
s
xml:id
="
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"
xml:space
="
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">ad 71. </
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>
<
s
xml:id
="
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xml:space
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">habebit
<
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quo que quadratum circumferentiæ datæ ad ſuperficiem ſphæræ ver@m, </
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