Clavius, Christoph
,
Geometria practica
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LIBER QVARTVS.
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ueniemus ei quadratum æquale, ſi, ducta perpendiculari F N, circa rectam ex
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F N, & </
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">ſemiſſe baſis E Z, conflatam ſemicirculus deſcribatur, &</
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<
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<
s
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xml:space
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">Sint ergo a, b,
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c, latera quadratorum trapeziis, ABCG, CDEG, & </
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<
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</
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<
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xml:space
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">quibus omnibus quadratis vnum ęquale exhibebimus hac arte. </
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rectus def, & </
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<
s
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xml:space
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">lateribus a, b, æquales ſumantur rectę ed, eg, eritque
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tum ductę rectę d g, quadratis rectarum ed, eg, hoc eſt, laterum a, b, æquale.
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</
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<
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xml:space
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">Capiatur rurſus e k, lateric, & </
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">recta e h, rectę d g, ęqualis; </
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s
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xml:space
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"> eritque rurſus
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dratum ex kh, ęquale quadratis ex k e, e h, id eſt ex c, eh, nimirum tribus ex a,
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b, c. </
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xml:space
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">Siigitur latus ex k h, menſuretur, & </
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s
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xml:space
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">in ſe ducatur, ginetur area figurę pro-
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poſitæ A B C D E F G.</
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<
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artificio, ſi plura ſint latera, inueniemus quadratum omnibus qua-
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dratis ęquale. </
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<
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xml:space
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">Vt ſi foret alterum latus q, acciperemus ei æqualem rectam
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e p. </
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xml:space
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">Item rectam ef, rectę k h, æqualem. </
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xml:space
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">Nam quadratum ex p f, quadratis ex
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e p, hoc eſt, ex q, & </
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<
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xml:space
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">ex ef, id eſt, ex a, b, c, erit ęquale, & </
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">Facilis ratio
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menſurandi
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trapezii irre-
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gularis.</
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<
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his colligitur facilis ratio metiendi trapezij irregularis, cuiuſmo di eſt in
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proxima figura trapezium A B C G. </
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">Nam ducta diametro B G, ſi ad eam duę
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perpendiculares demiſſę A L, CH, menſurentur, earumque aggregatum in me-
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dietatem diametri B G, multiplicetur, procreabitur area trapezij, vt demonſtra-
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tum eſt.</
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<
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octauo porrò lib. </
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">docebimus quo que, qua ratione datę figu-
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rę rectilineę rectangulum æquale conſtruatur. </
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<
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xml:space
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">quod ſi fiat hoc loco, effi cietur
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illi rectangulo quadratum ęquale, per vltimam propoſ. </
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<
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lo negotio, aut moleſtia.</
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">DE AREA MVLTILATERA-
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rum figurarum regularium.</
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<
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V.</
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<
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regulares figurę, quę ſcilicet ſunt & </
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& </
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<
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">æquiangulę, menſurari poſ@int, vt irregulares pręcedentis capi-
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tis, reſoluendo eas in triangula, &</
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<
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<
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culiaris regula, qua cuiuſque figurę regularis area inuenitur: </
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<
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">SEMISSIS ambit{us} figuræ multiplicetur in perpendicularem è centro figuræ ad
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vnum lat{us} cadentem. </
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<
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<
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vt lib. </
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<
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regularis.</
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figurę regularis ęqualis eſt rectangulo contento ſub perpendiculari à centro fi-
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gurę ad vnum latus ducta, & </
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<
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<
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porrò è centro figurę in vnum latus cadens,
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laris & ſemi-
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diameter fi-
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guræ regula-
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ris quo pacto
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inueniatur.</
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vna cum ſemidiametro circuli figuram ambientis ſic reperietur. </
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<
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rum, ſiue angulorum duplicetur, & </
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<
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<
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merus indicabit, quot rectis angulis omnes anguli figurę ęquiualeant, per ea,
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quę in ſcholio propoſ. </
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@us reliquus, videlicet, numerus angulorum rectorum, per numerum angulo-
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rum diuidatur, vt Quotiens vnius anguli figurę magnitudinem exhibeat, qui</
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