Clavius, Christoph
,
In Sphaeram Ioannis de Sacro Bosco commentarius
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129
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Ioan. de Sacro Boſco.
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vna linea, deſcripto. </
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<
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xml:space
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">& </
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<
s
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xml:space
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">quadrato ex K M, M H, tanquam ex una linea deſcri-
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pto, hoc eſt, quadrato K H, vtriuſque ſimul. </
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<
s
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xml:space
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">Ablato ergo communi quadrato
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K H, erit quadratum ex F K, G H, tanquam ex una linea, deſcriptum maius
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quadrato ex B K, D H, tanquam ex una linea, deſcripto; </
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<
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xml:space
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">ideòque maiores e-
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runt rectæ linea F K, G H, ſimul rectis B K, D H, ſimnl: </
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<
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xml:space
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">Ac propterea, demptis
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communibus B K, G H, erit F B, reliqua maior quàm reliqua D G. </
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<
s
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xml:space
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">Eſt autem
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& </
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<
s
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xml:space
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">K C, maior quàm H C, eò quòd tota A C, cuius dimidium eſt K C, maior
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ponitur, quam tota C E,
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<
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31
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129-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/129-01
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cuius dimidium eſt H C.
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</
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<
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">Qua propter rectangulũ
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ſub F B, K C, contentum,
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maius erit rectangulo
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ſub D G, H C, contẽto. </
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<
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Et quoniam triangulum
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F B C, dimidium eſt re,
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ctanguli ſub F B, K C, con
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tenti; </
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<
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xml:space
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">(Nam ſi ſuper F B,
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conſtituatur rectangu--
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lum altitudinem habens
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K C, ita ut triangulum,
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& </
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<
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">rectangulum inter eaſ-
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dem ſint parallelas; </
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xml:space
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">41. primi.</
note
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triangulum parallelo--
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grammi dimidium. </
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quidem parallelogram-
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mum idem eſt, quod re-
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ctangulum ſub F B, K C,
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contentum, ut conſtat.
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</
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<
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">Triangulum uero D G C, dimidium eſt rectanguli contenti ſub, D G, H C; </
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<
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enim ſuper D G, conſtituatur rectangulum altitudinem habens H C, ita vt
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triangulum, & </
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<
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rallelogrammi dimidium. </
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note
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rectangulum ſub D H, H C, contentum, ut conſtat. </
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<
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xml:space
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">(erit quoque triangulum
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FBC, maius triangulo D G C, ac propterea duplum trianguli F B C, nimirũ
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rectilineum A F C B A, maius erit duplo trianguli D G C, ut pote rectilineo
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erunt triangula A F C, C G E, utraque ſimul maiora triangulis A B C, C D E,
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utriuſque ſimul. </
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<
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xml:space
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">Duo ergo triangula Iſoſcelia ſimilia ſuper inæqualibus baſi-
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bus conſtituta, &</
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rimetras fi-
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guras ęqua-
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lia numero
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habentes la
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tera maxi-
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ma & æqui
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latera eſt,
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& æquian-
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gula.</
note
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<
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bentium maxima & </
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<
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figura quotcunq; </
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">laterum ABCDEF, maxima inter omnes totidem
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laterum ſibi iſoperimetras; </
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<
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">ita ut maior dari non poſſit. </
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<
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terã, & </
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">Sit enim, ſi fieri poteſt, primũ nõ æquilatera, ſed ſint </
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