Clavius, Christoph
,
Geometria practica
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LIBER QVINTVS.
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cularis in pentagono inclinato cum prædicto latere Dodecaedri efficit. </
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<
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">Ex quo
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fit punctum P, in plano ſupremæ baſis exiſtere, atque idcirco perpendicularem
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P Q, ad planum baſis per M N, ductum demiſſam, æqualem eſſe altitudini Do-
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decaedri; </
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<
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xml:space
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">eiuſque ſemiſſem R Q, altitudini vnius pyramidis pentagonæ eſſe æ-
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qualem. </
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<
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xml:space
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">Quæ omnia facil@ intelligentur, ſi Dodecaedrum aliquod materiale ad-
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hibeatur.</
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datum ſit Ico ſaedri latus a b, ſupra quod extruatur pentagonum
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æquilaterum, & </
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<
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xml:space
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">æquiangulum a b c d e, pro baſe pyramidis ex quin que baſibus
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Icoſaedri conflatæ. </
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<
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">Iuncta autem recta c e, ſeceturlatus a b, in ſ, bifariam, & </
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<
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xml:space
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cta ducaturſd, quæ vt in Dodecaedro oſtendimus proximè, perpendicularis e-
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rit ad vtramque a b, c e. </
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<
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xml:space
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">Fiat ſupra latus Icoſaedri c d, triangulum æquilaterum
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c d h, probaſe vna Icoſaedri; </
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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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">diuiſo latere c d, bifariam in k, iungatur recta h-
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k, quæ ad c d, erit perpendicularis. </
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xml:space
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">Præterea ſupra c e, fiat Iſoſceles c g e,
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Primi.</
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ius vtrum que laterum c g, e g, perpendicularihk, ſit æquale. </
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conſtituatur triangulum ſdl, cuius latus ſl, perpendiculari h k, & </
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<
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Icoſaedri a b, fit æquale. </
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<
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recta n o, perpendiculari h k, æqualis: </
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o p, lateri Icoſaedri a b, æqualis. </
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<
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xml:space
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">Dico perpendicularem p q, ad m n, demiſſam,
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eſſe altitudinem Icoſaedri, eiuſque ſemiſſem r q, altitudinem vnius pyramidis in
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">Altitudo py-
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ramidis Ico-
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ſaedri.</
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Icoſaedro. </
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<
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">Quia enim, vt ex Hypſicle ad finem Euclidis demonſtrauimus, an-
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gulus c g e, metitur in clinationem vnius baſis ad alteram, ſi m n, concipiatur eſ-
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ſe perpendicularis, quæ in baſe infima Icoſaedri ex angulo trianguli ad medium
<
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punctum lateris oppoſiti ducitur, reſpondebit n o, per pendiculari, quæ in trian-
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gulo ad illam baſem inclinato ex eodem medio pũcto ad angulum oppoſitum
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ducitur: </
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<
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xml:space
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">propterea quod angulum m n o, angulo inclinationis c g e, & </
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<
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n o, perpendiculari h k, æqualem fecimus: </
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<
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">Recta verò o p, referet latus Icoſae-
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dri inter angulum dicti trianguli inclinati, & </
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<
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">angulum ſupremæ baſis poſitum;
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</
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<
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">propterea quod recta o p, poſita eſt æqualis lateri Icoſaedri, & </
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angulo d l s: </
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<
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"> qui quidem æqualis eſt illi, quẽ dictum latus efficit cum
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">8. primi.</
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diculari ex angulo ſupradicti trianguli inclinati ad baſem, in medium punctum
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lateris oppoſiti ducitur. </
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">Eſt enim recta d s, æqualis perpendiculari ex angulo
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pentagoni ad latus oppoſitum ductæ, & </
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<
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