Clavius, Christoph
,
In Sphaeram Ioannis de Sacro Bosco commentarius
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Ioan. de Sacro Boſco.
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au em augulus D A C, dimidiũ anguli E D C; </
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<
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D C A, æquales ſunt, & </
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E D C. </
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æqualis angulo interno D A C; </
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">cadetq́ue D F, recta ſupra rectam D B, æqui-
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diſ
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tabit q́ue rectæ A C. </
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<
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">Producatur D F, donec cum A B protracta conueniat
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in F, du caturq́; </
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ſunt@tr i angulum autem A F C, maius eſt triangulo A B C; </
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<
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trian gulum A D C, triangulo A B C. </
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perim etorum eandem habentium baſim, &</
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">IN ſimilibus triangulis rectangulis quadratum à lateribus, quæ an-
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duorũ trian
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gulorum re
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ct angulorũ
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ſimilium.</
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gulis rectis ſubtenduntur, tanquam ab una linea, deſcriptum æquale eſt
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quadratis duobus ſimul, quæ à reliquis homologis lateribus, tanquam ex
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duabus lineis, ita ut quælibet duo latera homologa conficiant unam lineam
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rectam, deſcribitur.</
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triangula rectangula ſimilia A B C, D E F, ita ut anguli B, & </
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ſint recti, anguli uero C, & </
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æqua les: </
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B C, E F, & </
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D F, tan quam ex linea una, deſcriptum æqua-
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le eſſe duobus quadratis, quorũ unum ex A B,
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D E, tanquam ex una linea, alterum uero ex
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BC, E F, tanquam ex vna quoque linea, deſcri-
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bitur. </
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matur E G, æqualis rectæ A B, & </
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recta æquidiſtans rectę E F, donec cum D F,
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producta conueniat in puncto H; </
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F, ducatur recta F I, æquidiſtans rectæ E G.
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</
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triangulo D E F, hoc eſt, triangulo ABC: </
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angulus F I H, æqualis eſt angulo G, & </
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qualis angulo D E F, hoc eſt, angulo B: </
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gulus uero H, æqualis eſt angulo D E F, hoc
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eſt, angulo C; </
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gulo A; </
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</
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<
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rectæ A B, ſumpta fuit æqualis. </
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B C, I H, item A C, F H, æqualia inter ſe e-
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runt. </
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D F; </
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cta æqualis ſit rectæ EF. </
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<
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rectarum D G, G H, ſimul, conſtat verum eſſe, quod proponitur. </
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<
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igitur triangulis rectangulis quadratum à
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lateribus, quæ angulis rectis ſubten-
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duntur, &</
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