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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ad A G, ita B C ad C F, propter triangulos ſimiles D A G,
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B C F. </
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<
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<
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.</
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<
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">Eſto linea B C diviſa æqualiter in R; </
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<
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">inæqualiter in F,
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Fig. 5.</
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ſitque ſegmentum majus F C; </
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<
s
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xml:space
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">fiat B O æqualis utrique
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ſimul B C, C F; </
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<
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xml:space
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">B M vero utrique B C, C R. </
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<
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jorem eſſe rationem R B ad B F, quam triplicatam ejus,
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quam habet O B ad B M. </
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<
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xml:space
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">Sumatur enim ipſi O M æqualis
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utraque harum M L, L P. </
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<
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xml:space
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">Quoniam igitur M O ipſi R F
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æqualis eſt, (nam hoc ex conſtructione intelligitur) erit P O
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tripla ipſius F R. </
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<
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">Sed & </
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<
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">B M tripla eſt B R. </
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<
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xml:space
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">Ergo ut B R
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ad B M, ita F R ad P O. </
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xml:space
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">Et permutando ut B R ad F R,
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ſic B M ad P O. </
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">Major autem eſt B O quam B M. </
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">Ergo
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major erit ratio B O ad O P, quam B R ad R F: </
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converſionem rationis minor O B ad B P, quam R B ad
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B F. </
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">Porro quoniam æquales ſunt O M, M L, major erit
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ratio B O ad O M, quam B M ad M L: </
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<
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nem rationis minor O B ad B M, quam M B ad B L. </
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<
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dem modo minor adhuc oſtendetur ratio M B ad B L, quam
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L B ad B P. </
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<
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">Itaque omnino ratio triplicata ejus quam ha-
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bet O B ad B M minor erit quam compoſita ex rationibus
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O B ad B M, B M ad B L, & </
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<
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">B L ad B P, hoc eſt,
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quam ratio O B ad B P. </
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<
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quam O B ad B P. </
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<
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">Ergo omnino major erit ratio R B ad
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B F, quam triplicata rationis O B ad B M. </
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<
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poſitum.</
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<
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. XI.
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. XIV.</
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<
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Mnis circuli circumferentia minor eſt minore
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duarum mediarum proportionalium inter peri-
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metros polygonorum ſimilium, quorum alterum or-
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dinate circulo inſcriptum ſit, alterum </
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