Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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Iſoperimetr{as},
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quæ plur{es} an-
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gulos, ſeu late-
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ra continet, il-
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la maior eſt.</
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plures continet angulos, pluraue latera.</
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duæ figuræ regulares iſoperimetræ ABC, DEF, habeatque plura late-
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ra, ſiue angulos figura ABC, quam DEF. </
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Deſcribatur enim circa figuras circuli, à quorum centris G, H, ducantur ad BC,
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EF, perpendiculares GI, HK, quæ diuident rectas BC, EF, bifariam. </
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igitur figura ABC, plura habet latera, quam DEF, ſibi iſoperimetra, efficitur, vt
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latus BC, ſæpius repetitum metiatur ambitum figuræ ABC, quam latus EF, am-
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bitum figuræ DEF. </
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">Quare latus B C, minus erit latere EF, ideo que BI, medietas
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lateris B C, minor, quàm EK, medietas lateris EF. </
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ducantur rectæ LH, HE, HF, GB, GC. </
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æquales, quòd & </
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">erit recta E F, ita ſubmul-
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tiplex ambitus figuræ D E F, vt arcus E F, ſubmultiplex eſt circumferen-
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tiæ circuli D E F: </
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rectæ B C, ſicut multiplex eſt circumferentia A B C, arcus B C. </
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ſexti.</
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arcus EF, ad circumferentiam circuli DEF, ita eſt angulus EHF, ad quatuor re-
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ctos; </
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tum figuræ ABC, illi æqualem, ita angulus EHF, ad quatuor rectos: </
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ambitus figuræ ABC, ad rectam BC, ita eſt circumferentia circuli ABC, ad arcum
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BC, hoc eſt, ita quatuor rectiad angulum B G C. </
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ſexti.</
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ad rectam BC, hoc eſt, vt recta EK, ad rectam BI, hoc eſt, ad rectam KL, ita an- gulus EHF, ad angulum BGC, hoc eſt, ita angulus EHK, ad angulum B G I. </
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Eſt autem maior proportio rectæ EK, ad rectam KL, quam anguli EHK, ad an-
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gulum KHL. </
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BGI, quam eiuſdem anguli EHK, ad angulum KHL; </
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lus KHL, quam angulus B G I. </
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pote recti; </
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angulus K L M, æqualis angulo G B I; </
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cum KH, producta vltra H, in puncto M. </
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guli GBI, ęquales ſunt duobus angulis L, K, trianguli MLK, & </
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qualia, erunt rectæ GI, MK, ęquales. </
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