Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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CHRISTIANI HUGENII
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ſimul A G, A B; </
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<
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xml:space
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">hoc eſt, minor quam C A cum dimidia
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A G. </
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<
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xml:space
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diâ A G. </
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<
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xml:space
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<
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xml:space
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">Ergo ſi adda-
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tur A C ad A G, erit tota C G major quam tripla ipſius
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C H. </
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<
s
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xml:space
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">Quia autem ut H G ad G E, ita eſt E D ad D K;
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</
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<
s
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xml:space
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">ut autem G E ad G C, ita L D ad D E: </
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<
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">Erit ex æquo in
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proportione turbata ut H G ad G C, ita L D ad D K. </
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<
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">Et
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per converſionem rationis & </
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<
s
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xml:space
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">dividendo, ut G C ad C H,
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ita D K ad K L. </
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<
s
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xml:space
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">Ergo etiam D K major quam tripla K L. </
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<
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Erat autem D K exceſſus ipſius E B ſupra E G. </
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<
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">Ergo K L
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minor eſt triente dicti exceſſus. </
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<
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xml:space
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">K B autem æqualis eſt ipſi
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E B ſubtenſæ. </
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<
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xml:space
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">Ergo K B unà cum K L, hoc eſt, tota
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L B omnino minor erit arcu B E . </
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<
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xml:space
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">Quod erat
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xlink:label
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">per 7. huj.</
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dum.</
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<
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">Perpenſo autem Theoremate præcedenti, liquet non poſſe
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ſumi punctum aliud in producta B A diametro, quod minus
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à circulo diſtet quam punctum C, eandemque ſervet proprie-
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tatem, ut nimirum ductâ C L fiat tangens intercepta B L
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ſemper minor arcu abſciſſo B E.</
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</
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<
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<
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xml:space
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">Porro uſus hujus Theorematis multiplex eſt, cum in inve-
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niendis triangulorum angulis quorum cognita ſint latera, id-
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que citra tabularum opem, tum ut latera ex angulis datis
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inveniantur, vel cuilibet peripheriæ arcui ſubtenſa aſſigne-
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tur. </
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<
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">Quæ omnia à Snellio in Cyclometricis diligenter pertra-
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ctata ſunt.</
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<
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XIV.
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. XVII.</
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Ortionis circuli centrum gravitatis diametrum
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portionis ita dividit, ut pars quæ ad verticem
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reliquâ major ſit, minor autem quam ejuſdem ſeſ-
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quialtera.</
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<
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<
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xml:space
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">Eſto circuli portio A B C, (ponatur autem ſemicirculo
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<
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">TAB. XL.
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Fig. 2.</
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minor, quoniam cæteræ ad propoſitum non faciunt) & </
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meter portionis ſit B D, quæ bifariam ſecetur in E. </
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