Clavius, Christoph
,
Geometria practica
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GGOMETR. PRACT.
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K M, baſi K C, oſtenſa æqualis; </
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<
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"> erunt quo que anguli K B M, KBC, æquales.</
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">8. primi.</
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Itaque quoniam duo latera B H, B K, trianguli B H K, duo bus lateribus B L, B K,
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trianguli B L K, æqualia ſunt, æqualeſq; </
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<
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erunt & </
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<
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<
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<
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<
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ne rectus ſit, erit quo que L, rectus. </
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">Quare cum latera KH, KB, trianguli KBH,
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lateribus KL, KB, trianguli KBL, æqualia ſint, & </
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anguli BKH, BKL, æquales.</
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autem ex iis, quæ ad prop. </
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quatuor anguli quadrilateri BHKL, quatuor rectis ſunt æquales: </
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demptis duobus rectis H, L, duo HBL, HKL, duobus rectis æquales; </
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duobus angulis HBL, EBL, æquales, quod hi quo que duobus ſint rectis
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quales, ablato que communi HBL, reliquus HKL, reliquo EBL, æqualis erit:
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rectus H, recto E, ſit ęqualis, erit quo que reliquus H B K, in triangulo H B
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reliquo EDB, in triangulo EDB, æqualis; </
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quiangula erunt. </
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"> Quapropter erit vt DE, ad EB, ita BH, ad HK; </
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co ſi lineæ hę ad numeros contrahantur, erit numerus, qui fit ex D E, in H
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æqualis numero, qui fit ex EB, in BH. </
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<
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quadratus ex DE, ad productum ex DE, in HK, & </
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</
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<
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"> Sedita eſt quadratus ex D E, ad productum ex DE, in HK, vt DE, ad HK:</
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proptera quod DE, multiplicans DE, & </
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ductum ex D E, in H K. </
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EB, in BH, vt DE, ad HK. </
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<
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parallelæ ſint DE, HK, æquiangula erunt triangula AED, AHK, ex coroll. </
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"> Igitur erit vt AE, ad ED, ita AH, ad HK, & </
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<
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AE, ad AH, ita ED, ad HK. </
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ctum ex EB, in BH, vt AE, ad AH. </
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<
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"> Qui ergo fit ex quadrato ipſius DE,
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AH, æqualis erit ei, qui fit AE, in productum ex EB, in BH. </
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qui ex producto ex quadrato ipſius D E, in A H, multiplicato in A H, gignitur,
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æqualis erit numero, qui ex producto ex AE, in productum ex EB, in BH, mul-
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tiplicato in eundem A H, procreatur. </
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<
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productus ex quadrato ipſius DE, in AH, & </
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EB, in BH, eundem numerum AH, multiplicant habebunt producti,
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numerus, qui ex producto ex quadrato ipſius DE, in AH, multiplicato in AH,
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gignitur, & </
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tiplicato in eundem A H, procreatur, eandem proportionem, quam multipli-
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cantes. </
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<
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<
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">illi producti æquales) hoc eſt, nu-
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merus productus ex AH, in AH, id eſt, quadratus ipſius AH, ductus in quadra-
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tum ipſius DE, (Per ſcholium enim propoſ. </
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que tres numeri inter ſe multiplicentur, idem ſemper numerus procreatur)
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æqualis erit numero, qui ex producto ex A E, in productum ex E B, in B H,
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nempe ex producto trium differentiarum A E, E B, B H, inter ſe multipli-
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catarum, ducto in A H, id eſt, in ſemiſſem laterum gignitur. </
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<
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to ipſius D E, in quadratum ipſius A H, producitur quadratus numerus areæ
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trianguli A B C, vt mox oſtendemus. </
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<
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ſuum A E, EB, B H, inter ſe multiplicatorum, ducto in A H, ſemiſſem late-
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rum A B, B C, A C, producitur idem quadratus numerus areæ @@ianguli A B C:</
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