Clavius, Christoph
,
Geometria practica
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LIBER OCTAVVS.
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ſecans diametrum in G, ad rectos angulos, iunganturque ad extrema diametri
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279
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387-01
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rectæ BC, BA. </
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">Dico tamangulos CBF, CBG,
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quam (producta F B, ad H,) angulos ABH,
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ABG, eſſe æquales. </
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<
s
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xml:space
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"> Quoniam enim
<
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">32. tertij.</
note
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C B F, angulo B A C, in alterno ſegmento æ-
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qualis eſt. </
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<
s
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"> & </
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<
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">angulus C B D, eidem
<
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b
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note-387-02a
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">27. tertij.</
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B A C, æqualis, ob arcus æquales CB, CD; </
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<
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c
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note-387-03
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note-387-03a
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xml:space
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">8. ſexti.</
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(vel etiam angulus CBG, angulo BAC, æqua-
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lis eſt; </
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<
s
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echoid-s16773
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">quod BG, in triangulo rectangulo AB-
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C, ad baſem AC, perpendicularis ſit) erunt an-
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guli CBF, CBG, inter ſe quoque æquales.
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</
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<
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">Producta autem CB, ad I, ſi ex rectis angulis
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ABC, ABI, tollantur æquales CBG, HBI,
<
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note-387-04
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">15. primi.</
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(cum enim CBF, æqualis ſit angulo H B I, ad
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verticem: </
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<
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">& </
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<
s
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">angulus CBG, angulo CBF, o-
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ſtenſus æqualis; </
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<
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">erit quo que angulus C B G,
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angulo H B I, æqualis.) </
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<
s
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">erunt quo que reliqui
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anguli ABG, ABH, inter ſe æquales. </
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<
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primum.</
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<
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ducatur recta FN, ſecans circu-
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lum in K, L, ductiſque rectis KGO, LGM, per
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G, iungantur tam rectæ K C, K A, quam L C,
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L A, ad extrema diametri. </
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">Dico rurſus, tam angulos CLF, CLG, quam ALG,
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ALN: </
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">Item tam CKF, CKG, quam AKG, AKL, eſſe æquales. </
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">Ductis enim ex
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centro rectis EB, EK; </
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<
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"> erit angulus EBF, rectus: </
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<
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"> Igitur erit FB, media
<
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">18. tertij.</
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tionalis inter EF, FG: </
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<
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"> Ideoque rectangulum ſub EF, FG, quadrato ex FB,
<
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">coroll. 8.
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ſexti.</
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quale erit; </
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<
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"> Eſt autem eidem quadrato æquale quo que rectangulum ſub LF, FK. </
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<
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">Igitur rectangulum ſub EF, FG, rectangulo ſub L F, F K, æquale erit: </
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<
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<
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xml:space
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">17. ſexti.</
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>
pro inde erit vt EF, prima ad FK, ſecundam, ita LF, tertia ad FG, quartam. </
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<
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">Qua-
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">36. tertij.</
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re cum triangula EFK, LFG, habeant latera circa communem angulum F, pro-
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">16. ſexti.</
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portionalia; </
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<
s
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"> erunt anguli FEK, FLG, homologis lateribus FK, FG,
<
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k
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xlink:label
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xml:space
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">6. ſexti.</
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æquales. </
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<
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"> Eſt autem angulus FEK, in centro anguli CIK, ad
<
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">20. tertij.</
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>
(cum habeãt eandem baſem C K,) duplus. </
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<
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">Igitur & </
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">angulus FLG, eiuſdem an-
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guli C L K, duplus erit; </
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<
s
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">ac proinde angulus F L G, ſectus erit bifariam à recta
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LC, hoc eſt, anguli CLF, CLG, æquales erunt. </
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<
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">Producta autem CL, ad P, ſi ex
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rectis angulis ALC, ALP, demantur æquales anguli CLG, P L N, (Cum enim
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CLF, oſtenſus ſit æqualis angulo CLG, & </
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<
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">CLF, & </
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<
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">æqualis ſitangulo
<
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">15. primi.</
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ad verticem, erit quoque CLG, eidem angulo PLN, æqualis.) </
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<
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">erunt quoq; </
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<
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liquianguli ALG, ALN, æquales. </
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<
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xml:space
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">Rurſus quia anguli CLK, CLM, oſtenſi ſunt
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<
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xlink:label
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xml:space
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">26. tertij.</
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æquales; </
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<
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"> erunt arcus CK, CM, æquales. </
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<
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"> Igitur anguli CGK, CGM: </
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">ſchol. 29.
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tertij.</
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& </
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<
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">anguli A G O, AGL, ad verticem æquales erunt: </
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<
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"> Ac proinde arcus etiam AO, AL, æquales erunt: </
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<
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"> ideoque & </
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<
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">anguli AKO, AKL, erunt æquales. </
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<
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<
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">15 primi</
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>
ducta autem AK, ad Q, ſi ex rectis angulis CKA, CKQ, auferantur æquales AKG,
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<
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">ſchol. 29.
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tertij.</
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FKQ, (Cum enim angulus AKG, angulo AKL, oſtenſus ſit æqualis: </
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<
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"> hic autem angulo FKQ, ad verticem ſit æqualis; </
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<
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xml:space
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">erit quoque angulus AKG, angulo FKQ.
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</
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<
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<
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">27. tertij.</
note
>
æqualis.) </
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>
<
s
xml:id
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">erunt etiam reliqui anguli CKG, CKF, inter ſe æquales. </
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<
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">Quæ omnia
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<
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">15. primi.</
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demonſtranda erant.</
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