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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anguli E B F. </
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xml:space
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B F C. </
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<
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xml:space
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quam quadruplum. </
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<
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<
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. II.
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. II.</
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<
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xml:space
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">Si fuerit circuli portio, ſemicirculo minor, & </
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<
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per eadem baſi triangulum, cujus latera portio-
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nem contingant; </
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<
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xml:space
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">ducatur autem quæ contingat por-
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tionem in vertice: </
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<
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lum abſcindet majus dimidio maximi trianguli in-
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tra portionem deſcripti.</
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<
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">Eſto circuli portio ſemicirculo minor A B C, cujus vertex
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xml:space
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">TAB. XXXVIII.
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Fig. 2.</
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B. </
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<
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">Et contingant portionem ad terminos baſis rectæ A E,
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C E, quæ conveniant in E: </
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<
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">convenient enim quia portio ſe-
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micirculo minor eſt. </
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<
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">Porro ducatur F G, quæ contingati-
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pſam in vertice B; </
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<
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itaque, triangulum F E G majus eſſe dimidio trianguli
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A B C. </
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<
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xml:space
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">Conſtat triangula A E C, F E G, item A F B,
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B G C æquicruria eſſe, dividique F G ad B bifariam. </
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<
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que autem ſimul F E, E G, major eſt quam F G; </
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<
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E F major quam F B, vel quam F A. </
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<
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xml:space
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quam dupla F E. </
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">Quare triangulum F E G majus erit quarta
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parte trianguli A E C. </
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<
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xml:space
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">Sicut autem F A ad A E, ita eſt al-
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titudo trianguli A B C ad altitudinem trianguli A E C, & </
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baſis utrique eadem A C. </
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<
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xml:space
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">Ergo, quum F A ſit minor quam
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ſubdupla totius A E, erit triangulum A B C minus dimi-
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dio triangulo A E C. </
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<
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">Hujus vero quarta parte majus erat
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triangulum F E G. </
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<
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xml:space
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">Ergo triangulum F E G majus dimidio
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trianguli A B C. </
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<
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<
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. III.
<
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. III.</
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<
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<
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">OMnis circuli portio, ſemicirculo minor, ad ma-
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ximum triangulum inſcriptum majorem ratio-
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nem habet quam ſeſquitertiam.</
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