Clavius, Christoph
,
Geometria practica
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LIBER OCTAVVS.
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pla continuerunt proportionalia, quadratum videlicet FGHI, octogonum A-
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KBCDA, & </
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gurarum octauæ partes, vtliquet. </
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<
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">Octogonum igitur medio loco proportiona-
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le eſt inter quadrata FGHI, ABCD, quod demonſtrandum erat.</
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alterius quadrati, cuius diameter eſt linea, quæ relinquitur, ſi latus in-
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uentum bis ex diametro prioris quadrati auferatur; </
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<
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inuentum ex prioris quadrati latere tollatur.</
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diametro BD, quadrati ABCD, abſcindatur recta BE, lateri AB, æqualis,
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& </
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">ex eadem diametro dematur reliqua DE, bis vſque ad F, ita vt EF, ſit ipſi DE,
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æqualis: </
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<
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">vel (quod idem eſt) reliqua DE, ſiue EF, illi æqualis ex latere AB, hoc
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eſt, ex BE, auferatur. </
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<
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</
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">Ductis enim per F, rectis GH, IK, parallelis ipſis AD, AB; </
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ſecundi.</
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diametrum quadrata. </
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ſe lateri B G, quadrati G K, cuius diameter B F, reliqua fuit
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poſt detractionem D E, bis ex diametro B D. </
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<
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primi.</
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nim quadratum ex D F, duplum eſt quadrati ex I F, ſiue ex
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A G, & </
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cundi.</
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ponatur 4. </
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</
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<
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primi.</
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Eſt autem & </
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<
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"> Igitur erit vt re- cta A G, ad rectam EF, ita recta BF, ad rectam BG; </
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rum proportionalia ſunt, habentia nimirum proportionem duplam. </
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B L, ipſi BF, æqualis ita vt reliqua LA, reliquæ FE, æqualis ſit. </
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">AG, ad AL, vt BF, ſiue BL, ad BG; </
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">Et diuidendo GL, ad LA, vt GL, ad BG. </
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circa AL, ſiue EF, & </
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<
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nem, latitudinemue conſtituere.</
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<
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<
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ad altitudinem datam AB, conſtruendum
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octogonum æquilaterum, & </
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<
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<
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ſcripto ex AB, quadrato ABCD, ductiſque diame-
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tris AC, BD, ſe in E, ſecantibus bifariam, & </
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<
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gulos rectos; </
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<
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">abſcindantur ad interuallum EA, ex
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quatuor angulis quadratirectæ æquales A F, A G;
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</
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<
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">rectæ HK,
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G M, L I, N F. </
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eſſe æquilaterum, & </
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<
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enim rectæ A H, A K; </
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D F, D N, relinquuntur poſt </
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