Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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quadrantis, quorum alter tanto minor ſit arcu
<
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<
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xlink:label
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note-129-01
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xlink:href
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note-129-01a
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xml:space
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">Differentia
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inter ſinus
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duorũ ar-
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cuum, quo-
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rum alter
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tanto ſit
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minorarcu
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grad. 60.
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quãto alter
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maior eſt,
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ęqua@ ſinui
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arcus, quo
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alteruter di
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ctorũar@@ũ
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differt ab
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a@cu grad.
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60.</
note
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grad. </
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<
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<
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xml:space
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arcus, quo alteruter dictorũ arcuum ab arcu grad.
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</
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<
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<
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<
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<
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<
s
xml:id
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xml:space
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">IN quadrante ABC, ſit arcus CD, grad. </
s
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<
s
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<
s
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xml:space
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">arcus vero CE, eo tanto
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minor, quanto arcus CF, maior eſt: </
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<
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<
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xml:space
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ſinuum differẽtiam æqualem eſſe ſinui arcus DE, vel DF. </
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<
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xml:space
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drante, vna cum ſinubus EG, FH, ad I, K; </
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<
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æqualis, ita vt totus arcus
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129-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/129-01
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DCL, cõtineat grad. </
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</
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<
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xml:space
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<
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">arcus CI, CK,
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æquales ſunt arcubus CE,
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CF; </
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<
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">quòd per lemma in
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definitionibus poſitum re-
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cta BC, ſecet arcus ECI,
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FCK, bifariam, cum & </
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<
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ctas EI, FK, bifariam ſe-
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cet: </
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<
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">erunt quoque reliqui
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arcus LI, LK, reliquis ar
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cubus DE, DF, æquales.
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EM, FN, qui arcubus DE,
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DF, æquales ſint, ducan-
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tur chordæ LM, LN. </
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quoniam arcus FN, arcui
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LK, & </
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<
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xml:space
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">arcus EM, arcui
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LI, ęqualis eſt; </
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<
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munibus FL, MI, erit tam arcus NL, arcui FK, quàm arcus ML, arcui EI,
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æqualis: </
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<
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">ac proinde tan chorda NL, chordæ FK, quam chorda ML, chordæ
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<
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EI, æqualis. </
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</
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<
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">quanto arcus LN, eodem maior eſt; </
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darum LN, LM, chordæ DN, vel DM, æqualis; </
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">hoc eſt, recta k F, rectam
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IE, ſuperabit chorda DN, vel DM. </
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">Quare per antecedentem propoſ. </
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ſis HF, hoc eſt, ſinus arcus CF, ſuperabit ſemiſſem GE, id eſt, ſinum arcus CE,
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ſemiſſe chordæ DN, vel DM, hoc eſt, ſinu arcus DF, vel DE. </
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<
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monſtrandum erat.</
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<
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">& </
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<
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">arcus EF,
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EG, æquales, ac proinde arcus BF, tanto minor arcu BE, quanto arcus BG,
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eodem arcu BE, maior eſt: </
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<
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">ducanturq́ue FH, GI, ad BD, perpendiculares,
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quæ ſinus erunt arcuum BF, BG. </
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<
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">Ducta autem chorda FG, ſecet eam ſemi-
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diameter ducta DE, in L. </
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<
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quoque recta FG, bifariam ſecta in L, ex lemmate in definitionibus demon-
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ſtrato; </
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<
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<
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<
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<
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ſinus arcus EG. </
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<
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