Clavius, Christoph
,
In Sphaeram Ioannis de Sacro Bosco commentarius
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Comment. in I. Cap. Sphæræ
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tres lin eę AC, DF, FE, ita ſeſe
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habe bũt, vt quælibet duæ ſint
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reliq ua maiores. </
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<
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ipſis conficiatur triangulum
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A G C, effectum erit, quod
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proponitur. </
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<
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ra AG, GC, & </
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& </
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ribus AB, BC, ſimul ſumptis:
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</
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<
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">addito igitur communi A C,
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erunt triangula ABC, AGC,
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iſoperimetra. </
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<
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tur triangulo, cuius duo latera ſint inæqualia, ſupra reliquum latus triangulũ,
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&</
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<
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autem neceſſario punctum G, extra triangulum A B C: </
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deret in latus A B, ut ad punctum H, eßet ducta recta H C, minor quàm H B, B C, ſi-
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mul, & </
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trarium ex conſtructione eſt demonſtratum. </
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lto minus cadet punctum G, intra trian.</
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gu lum A B C. </
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<
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triangulorum iſoperimetrorum eandem habentium ba-
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triangulũ
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maius eſt
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triãgulo ſi
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bi Iſoperi-
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metro non
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@ſoſcele.</
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ſim, quorum unius duo latera ſint æqualia, alterius uero inæqualia; </
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erit i
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llud, cuius duo latera æqualia ſunt.</
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triangulum A B C, cuius latus A B, maius ſit latere B C, conſti-
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tuaturq́ue ſuper baſim A C, (per præcedentẽ
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propoſi.) </
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perimetrum A D C, habens latera A D, D C,
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æqualia & </
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mul ſumptis. </
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eſſe triangulo A B C. </
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ad partes D, ſitq́ue D E, æqualis ipſi A D, ſiue
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ipſi D C. </
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A E, hoc eſt, quàm A D, D C, ſimul hoc eſt,
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quàm A B, B C, ſimul; </
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<
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erit B E, maior quam BC. </
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<
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D B, trianguli E D B, æqualia ſunt lateribus
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C D, D B, trianguli C D B. </
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B E, baſe B C, maior ſit, erit angulus E D B,
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maior angulo C D B. </
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<
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maior eſt, quàm dimidium anguli E D C: </
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