Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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iam ſit AB, latus Dodecaedri, ſupra quod extruatur pentagonum
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æquilaterum, & </
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<
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">æquiangulum ABCDE, pro baſe Dodecaedri. </
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<
s
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xml:space
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">Iuncta autem re-
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cta CE, quæ latus erit cubi in Dodecaedro, & </
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<
s
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xml:space
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">in eadem cumip ſo ſphæra
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xml:space
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">2. coroll. 17.
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@rtijdec.</
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pti, atque lateri AB, parallela: </
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<
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">ſecetur AB, bifariam in S, connectatur que recta S D. </
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<
s
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xml:space
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"> quæ angulum CDE, bifariam ſecabit: </
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<
s
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">d ac proinde & </
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<
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xml:space
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">rectam CE,
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xlink:label
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xml:space
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">coroll. 8.
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quintidec.</
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& </
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">ad angulos rectos diuidet: </
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<
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">anguli ad S, recti erunt. </
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xml:space
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">Fiat ſupra
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CE, Iſoſceles CGE, cuius vtrum que laterum CG, EG, perpendiculari SF, ſitæ-
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">ſchol. 12.
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quarti.</
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">4. primi.</
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/246-01
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quale. </
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<
s
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">Sumptis quo que FH, FI, ſemiſsi lateris AB, æqualibus, erigantur ad EC,
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perpendiculares HK, IL, quæ ex C, E, ad interuallum FD, ſecentur in K, L, iun-
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ganturq; </
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<
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">rectæ EL, CK. </
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">His paratis, fiat angulo CGE, æqualis angulus MNO,
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ponatur que N O, ipſi SD, æqualis: </
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<
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xml:space
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">Item angulo ELK, fiat æqualis angulus N-
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OP, ponaturque OP, lateri AB, æqualis: </
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<
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">ac tandem demittatur ex P, ad MN,
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perpendicularis PQ, quæ bifariam ſecetur in R. </
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<
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xml:space
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">Dico RQ, altitudinem eſſe py-
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ramidis vnius in Dodecaedro. </
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<
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">Nam quia, vt ad finem Euclidis ex Hypſicle de-
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monſtrauimus, angulus C G E, in clinationem vnius baſis ad alteram metitur, ſi
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MN, concipiatur eſſe perpendicularis, quæ in baſe infima ex angulo pentagoni
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ad medium punctum lateris oppoſiti ducitur, reſpondebit NO, perpendiculari,
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quæin pentagono ad illam baſem inclinato ex eodem medio puncto ad oppo-
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ſitum angulum ducitur: </
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<
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">propterea quod angulum M N O, angulo inclinatio-
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nis CGE, & </
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<
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">rectam NO, perpendiculari S D, æqualem poſuimus. </
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<
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xml:space
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">Recta autem
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OP, refert latus Dodecaedri inter angulum dicti pentagoni inclinati, & </
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lũ ſupremæ baſis poſitũ: </
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<
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">ꝓpterea ꝙ recta OP, poſita eſt æqualis lateri Dodeca-
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edri, & </
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>
<
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">angulus NOP, angulo ELK, qui quidem æqualis eſt illi, quem dictum la-
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tus efficit cum perpendiculari ex angulo ſupradicti pentagoni inclinatiad ba-
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ſemin medium punctum lateris oppoſiti ductæ, vt conſtat, ſi vna baſis cubi Do-
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decaedro inſcripti intelligatur dicto lateri Dodecaedri ſubſtrata, ita vt duo late-
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ra baſis cubi ſubtendant duos angulos duorum pentagonorũ, quorum vnum
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ad baſem Dodecaedri inclinatum eſt, alterum vero ò ſupremum in Dodecaedro.
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</
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<
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">Erit enim tuncrecta CE, æqualis rectæ duo puncta media duorum laterum di-
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ctorum baſis cubi connectenti. </
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>
<
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xml:space
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">Rectæ autem EL, CK, reſpondebunt rectis ex
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eiſdem punctis medijs laterum illorum baſis cubi, ad angulos prædictorũ pen-
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tagonorum ductis: </
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<
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">Ac proinde angulus ELK, æqualis erit ei, quem </
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