Clavius, Christoph
,
Geometria practica
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LIBER SEXTVS.
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nerefertiſſimus. </
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<
s
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xml:space
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">Idem verò poſtea argumentum alia via aggreſſus eſt,
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& </
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<
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">meo certè iudicio, faciliori & </
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<
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">magis generali, Simon Steuinius
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Brugenſis: </
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<
s
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xml:space
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">ſed in qua aliquid deſiderari videatur, vt omnibus ſuper-
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ficiebus rectilineis (quodipſe velle videtur) conuenire poſſit. </
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<
s
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xml:space
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">quod
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facilè iudicabunt, qui illius problemata Geometrica attentè perlege-
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rint. </
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<
s
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xml:space
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">Res enim propoſita nulla ratione confici poteſt, niſi prius duæ
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propoſitiones demonſtrentur, quarum priorem ipſe ſine demonſtra-
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tione aſſumit pro principio, poſterioris verò ne meminit quidem,
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cum tamen admodum ſit neceſſaria, & </
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<
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xml:space
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">quam Machometus Bagdedi-
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nus demonſtrauit paulò aliter, quam nos. </
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<
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xml:space
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">Has ergo duas propoſitiones
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ad initium huius lib. </
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<
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xml:space
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">demonſtrabimus, & </
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<
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xml:space
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">poſteriorem quidem longè
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generalius, quam à Machometo factum eſt. </
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<
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xml:space
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">quod beneuolo Lecto-
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ri iudicandum relinquo. </
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<
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xml:space
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">Deindè
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ſuperficierum rectilinearum diui-
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ſionem aggrediemur, inſiſtentes eiuſdem Steuinii veſtigiis, niſi quan-
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do generalius rem oportebit demonſtrare. </
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<
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">Nihil autem deratione Ma-
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chometi, & </
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<
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">Federici Commandini dicemus: </
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<
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xml:space
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">tum quia libellus ipſo-
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rum in manibus omnium eſt, ac propterea eum, quicunque vo-
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let, legere poterit: </
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<
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xml:space
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">tum quia propoſita aliqua figura multorum an-
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gulorum, non ſine difficultate, ac labore eam ſtudioſus diuidet, ni-
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ſi diuiſionis omnium præcedentium figurarum memor ſit, quod in
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noſtra ratione non accidit: </
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<
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">tum denique quia illorum ratio ſolum fi-
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guris ordinariis conuenit, quæ videlicet omnes angulos habent intror-
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ſum, tot nimirũ, quotlatera figura ipſa continet, noſtra autem via figuras
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etiamillas complectitur, quæ angulos habent partim introrſum, & </
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tim extrorſum vergentes.</
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">SI magnitudo in quotuis partes ſecetur vtcunque, & </
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<
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">alia quæpiam ma-
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gnitudo in totidem partes ordine illis proportionales: </
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">habebunt
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quotlibet partes prioris magnitudinis ſimul ad reliquas omnes par-
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tes ſimul eandem proportionem, quam totidem partes poſterioris
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magnitudinis ſimul ad reliquas omnes partes ſimul. </
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">Et ſi quælibet
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pars prioris magnitudinis ſecetur in duas partes vtcunque, ſecetur
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autem & </
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<
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xml:space
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">pars poſterioris magnitudinis illi parti reſpondens in alias
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duas partes
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duabus illis proportionales: </
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<
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">erunt quoque ibidem to-
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tæ magnitudines ſectæ proportionaliter.</
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magnitudo A B, ſecta in quotuis partes vtcunque A C, C D, D E, EF,
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F B: </
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">& </
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<
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">alia magnitudo qualiſcunque G H, etiamſi diuerſi ſit generis, ſecta </
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