Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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in hexagono continet rectum cum parte tertia, hoc eſt, grad. </
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<
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<
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xml:space
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ſemidiameter ſecat angulum figuræ bifariam, vt conſtat ex demonſtratione
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propoſ. </
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<
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<
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<
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<
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ponatur ſinus totus, perpendicularis ſit Tangens ſemiſsis anguli figuræ, & </
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<
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diameter, Secans. </
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Vt lat{us} 100000, ſin{us} \\ tot{us}. # ad ſemiſſem \\ lateris: # ita Tangens ſemiſſis an- \\ guli, vel ſecans. # ad aliud,
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prodibit tam perpendicularis, quàm ſemidiameter in partibus lateris figuræ.
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</
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<
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xml:space
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">Verbi gratia, in Hexagono regulari, cuius vnum latus ſit 12. </
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<
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<
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nus totus ad 6. </
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<
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<
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<
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">tangens ſemiſsis anguli Hexagoni
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ad aliud, reperietur perpendicularis 10 {39230/100000}. </
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<
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">vel 10 {3923/10000}. </
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<
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xml:space
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">Item ſi fiat, vt
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100000. </
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<
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<
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<
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<
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xml:space
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">Secans ſemiſsis anguli
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liexagoni ad aliud, exibit ſemidiameter figuræ 12.</
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<
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ſi perpendicularis 10 {3923/10000}. </
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<
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<
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xagoni ex tribus lateribus conflatam, producetur area Hexagoni 374 {1228/10000}. </
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<
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374 {307/2500}. </
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<
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xml:space
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">Eodemque modo procedendum eſt in aliis figuris regularibus, in
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quibus angulorum ſemiſſes in tabula Tangentium, ac ſecantium accipi poſ-
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ſunt.</
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<
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<
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vero circa quamlibet figuram regularem circulus deſcribi
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poteſt, vt ex lib. </
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<
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<
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">conſtet, proponemus hic plurimarum figurarum regu-
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larium latera in partibus diametri circuli ambientis 20000000. </
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<
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xml:space
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tri, ſiue ſinus totius 10000000. </
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<
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xml:space
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">ex probatis auctoribus, vt earum areæ magis ex-
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<
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xml:space
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">Quare ex la-
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tere figuræ re-
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gularis dato
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non ſemper
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poſſit inueniri
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area, niſi figu-
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raipſa deſcri-
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pta ſit.</
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quiſitè inueniri poſsint per regulam Num. </
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<
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latere in aliqua menſura cognito aream inueſtigare velimus, quemadmodum in
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Hexagono factum eſt, occurrẽt multæ difficultates acmagnę, propterea quod
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ſemidiametri, perpendiculareſque ex ſinubus, Tangentibus, ac ſecantibus erui
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non poſſunt, niſi quando ſemiſsis anguli figuræ comprehendit pręcisè gradus,
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vel gradus cum minutis, vel gradus cumminutis & </
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cunda adſint, neceſſe ſit partem proportionalem adhibere) ſicut in Hexago-
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no paulo ante factum eſt, cuius anguli ſemiſsis continet grad. </
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<
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quam plurimis figuris non contingit. </
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7. </
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<
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<
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<
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<
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<
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nus angulus complectitur vnum rectum cum {3/7}. </
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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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Ter. </
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<
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<
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<
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<
s
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">ex qua ſemiſſe nequit Tangens pro perpendiculari, ne-
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que ſecans pro ſemidiametro per tabulas Tangentium, atque ſecantium excer-
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pi poteſt. </
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<
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<
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ſcientia inuenta eſſet conſtruendi omnes figuras regulares, ſuperari aliquo mo-
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do poſſet hæc diffi cultas: </
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<
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que partibus, cognoſci quoque poſſet tam perpendicularis, quam ſemidiame-
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ter in iiſdem partibus, beneficio inſtrumenti partium, vt lib. </
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<
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<
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<
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Num. </
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<
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<
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uimus intra circulum, areas plurimarum ignorari ncceſſe eſt. </
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<
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ſam nonnulli Geometræ, inter quos ſtrenuam operam nauauit Ludolphus,
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à Collen, ingenti labore latera figurarum, ſiue deſcriptæ eæ ſint, ſiue non, ex-
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plorarunt: </
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<
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