Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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tam Tetraedri ſuperficiem conficiet: </
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xml:space
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xml:space
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gularium cor
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porum & per-
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pendicular{es}
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baſium.</
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toti ſuperficiei Octaedri adæquabitur: </
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ſumptum ſuperficiei totitam Dodecaedri, quam Icoſaedri æquale erit. </
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<
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tem perpendicularis EF, in baſe cubi æqualis eſt ſemiſsilateris cubi AB, Quo- niam enim perpendicularis EF, ſecat latus AB, bifariam, eſt que ipſi AF, æqua- lis, quod anguli FAE, FEA, ſemirecti ſint; </
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<
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">conſtat EF, ſemiſsi lateris cubi eſſe ę-
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primi.</
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qualem. </
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ſemiſsis eſt ſemidiametri C D. </
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midiametri CD: </
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<
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">ita quadratum lateris dati AC, ad aliud, prodi-
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tertijdec.</
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bit quadratum ſemidiametri C D, cuius radix quadrata ipſam C D, indicabit, e-
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iuſque ſemiſsis perpendicularem DE, exhibebit. </
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in baſe Dodecaedrie ſemiſsis eſt ſummæ ex ſemidiametro AF, & </
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ni circuli ABD, collectæ, quodlatus decagoni cognoſcetur, vt ad finem Nume.
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<
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verò ſolidum, quod fit ex perpendiculari è centro cuius
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tijdec.</
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corporis regularis ad aliquam eius baſem ducta in tertiam partem ſuperficiei i-
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pſius corporis, ipſi corpori æquale eſt; </
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rumregulari-
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um aliter in-
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uentæ.</
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corporis regularis, vt proximè docuimus, atque in tertiam eius partem ducatur
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altitudo vnius pyramidum, in quas corpus ipſum per rectas è centro ipſius du-
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ctas diuiditur, (quæ altitudo reperietur, vt ſupra tradidimus) hoc eſt, perpendi-
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cularis è centro corporis in eius baſem demiſſa, procreabitur area, ſiue ſoliditas
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ipſius corporis. </
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">Quæ etiam obtinebitur, ſi dicta altitudo ducatur in totam ſu-
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perficiem conuexam, & </
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vt vides, tota difficultas in corporibus regularibus dimetien-
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dis conſiſtit fermè totain altitudine pyramidis baſem habentis eandem cũ cor-
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pore, verticem autem in centro ſphæræ, exquirenda: </
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<
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ometrica pernumeros moleſtiſsima eſt, propter radices ſurdas, & </
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ctos, quorum numeratores, denominatoreſq; </
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ræ pretium videatur eſſe eandem mechanicè explorare, vt adinitium Num. </
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</
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dimetienda adhibeatur. </
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<
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gularia, vt mechanicè eam altitudinem conſequi poſsimus, libetrationem quã-
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dam nouam, eamque facillimam hic præſcribere, qua ſine moleſtia illa numero-
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rum, eadem illa altitudo per lineas inueniatur, etiamſi corpus regulare </
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