Clavius, Christoph
,
Geometria practica
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[Figure 294]
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GEOMETR. PRACT.
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atque inter AB, AE, media proportionali A G; </
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proportionali AH; </
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<
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">ducantur EI, GK, HL, lateri BC, parallelæ@ quas dico trian-
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gulum partiriin 4. </
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<
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xml:space
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"> Quoniam enim triangulum ABC,
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ſexti.</
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lo AEI, ſimile eſt; </
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<
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"> erit triangulum ABC, ad triangulum AEI, vt A B, ad A D, quod tres A B, A E, A D, ſint continuè pro portionales. </
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<
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ſexti.</
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parsipſius AB. </
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<
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<
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aliter oſtendemus, eſſetriangulum A B C, ad triangulum A G K,
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ſexti.</
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AB, ad AE, quod etiam tres AB, AG, AE, ſint continue proportionales. </
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cum AE, contineat {2/4}. </
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guli A B C: </
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">eadem ratione erit triangulum A B C, ad trian-
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gulum AHL, vt AB, ad AF, quod etiam tres AB, AH, AF, ſint continue propor-
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tionales: </
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admodum AF, continet {3/4}. </
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ductam in duas partes æquales diuidere.</
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">Ex puncto D, extra triangulum AB C, dato ducenda ſit linea diuidens tri-
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angulum bifariam. </
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in E: </
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E, ſit ſegmentum CE, maius, cui ducatur parallelaDF, occurrens lateri AC, pro-
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ducto in F. </
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ta proportionalis CH; </
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"> Eritque rectangulum ſub DF, CH, æquale rectangulo ſub B C, C G; </
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B C, C A, duplum ſit rectanguli ſub B C, C G. </
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inuenta L, media proportionaliinter F C, C H, vt qua- dratum ex L, æquale ſitrectangulo ſub FC, CH, adiũ-
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gaturipſi CH, recta H@, vtrectangulum ſub tota CI, & </
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adiuncta HI, ęquale ſit quadrato exL, ſiue rectangulo
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ſub F C, C H, quemadmodum ad finem ſcholij pro-
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poſ. </
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ſecans BC, in K. </
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KI, IKC, æquales. </
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æquale eſt rectangulo ſub CF, CH, erit vt CI, ad CF, ita CH, ad IH; </
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aũt IF, ad CI, ita eſt FD, ad CK. </
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permutando.</
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{pue}inde rectangulũ ſub FD, CH æquale erit rectangulo ſub CK, CI: </
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ctangulũ ſub FD, CH, per conſtructionẽ æquale ſemiſsirectanguli ſub BC, CA.
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<
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<
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Igitur & </
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<
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C A. </
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<
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angulum CKI, ad triangulum ABC. </
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