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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<
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xml:space
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">Vel potius ſex ſe midiameſtris addatur {1/5} dicti lateris qua-
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drati inſcripti ut habeatur recta æqualis peripheriæ toti.</
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<
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III.
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. XII.</
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style
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xml:space
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ſumere.</
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<
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xml:space
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">Eſto datus circumferentiæ arcus C D, primum quadrante mi-
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xml:space
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">TAB. XXXIX.
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Fig. 3.</
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nor, cui rectam æqualem ſumere oporteat. </
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<
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xml:space
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cus C D bifariam in E, ſitque ſubtenſæ C D æqualis recta F G.
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</
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<
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xml:space
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">Duabus vero C E, E D, quæ ſubtendunt arcus dimidios,
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æqualis F H. </
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<
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Erit tota F I arcui C D æqualis ferè: </
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<
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xml:space
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">adeo ut unâ ſui particulâ,
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qualium 1200 continet, aucta, major futura ſit, etiamſi arcus
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C D quadranti æqualis detur. </
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<
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xml:space
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minor erit differentia. </
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<
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xml:space
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">Nam ſi fuerit datus non major peri-
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pheriæ ſextante, linea inventa minus quam {1/6000} ſui parte à ve-
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ra arcus longitudine deficiet. </
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<
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xml:space
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">Et minores quidem eſſe arcu-
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bus rectas eo modo inventas conſtat ex Theoremate 7. </
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De quantitate autem differentiæ eſt oſtendendum.</
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</
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<
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xml:space
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">Primum itaque ponendo arcum C D quadranti peripheriæ
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æqualem, erit C D recta, hoc eſt, F G, latus quadrati
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circulo inſcripti, & </
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<
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xml:space
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">minor proinde quam partium 141422,
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qualium radius circuli 100000. </
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xml:space
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">C E autem vel E D latus in-
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ſcripti octogoni, ideoque major quam 76536. </
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xml:space
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plæ E D æqualis F H. </
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<
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xml:space
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<
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xml:space
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re exceſſus G H major quam 11650: </
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<
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xml:space
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major quam 3883. </
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<
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xml:space
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">Ideoque tota F I major quam 156955.
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</
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<
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xml:space
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quam 157080. </
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<
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partibus 125, qualium ipſa eſt 156955. </
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<
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xml:space
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efficiunt quam {1/1200} ipſius F I.</
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<
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xml:space
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">Si vero ſextans peripheriæ ſit arcus C D, erit recta C D,
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hoc eſt, F G, latus hexagoni inſcripti, ideoque partium
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10000, & </
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