Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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THEOR. DE QUADRAT.
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<
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VIII.</
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arcus ad duas tertias rectæ ſibi ſubtenſæ hanc ra-
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tionem, quam ſemidiameter ad eam, quæ ex centro
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ducitur ad ſectoris centrum gravitatis.</
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">Eſto primùm ſemicirculus A B C, deſcriptus centro D,
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Fig. 3.</
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ſectuſque bifariam rectâ B D, in qua centrum gravitatis
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ſemicirculi ſit E . </
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A C, ſicut B D ad D E. </
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tur, ut ſemicirculus ad triangulum A B C, ſic ſunt duæ ter-
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tiæ B D ad D E , eſt enim B D æqualis diametro
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nis reliquæ. </
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gulus habens baſin æqualem arcui A B C & </
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<
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">altitudinem B D,
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ad A B C triangulum, ita eſt arcus A B C ad A C re-
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ctam; </
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">ergo ut arcus A B C ad A C, ita ſunt duæ tertiæ
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B D ad D E, & </
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B D, ita A C ad D E, ſive ita {2/3} A C ad {2/3} D E, unde rur-
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ſus permutando, ut arcus A B C ad {2/3} A C, ita {2/3} B D ad {2/3}
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D E, ſive ita, B D ad D E.</
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<
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Fig. 4.</
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ſectus rectâ D B, in qua ſectoris centrum gravitatis ponatur
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E punctum, & </
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A B C ad duas tertias rectæ A C eam habere rationem,
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quam B D ad D E. </
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circuli ſit diameter K D B, quæ producatur in Q, ut fiat
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Q F, ad B F, ſicut portio A C B ad A B C triangulum,
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& </
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<
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ni A C B æqualis. </
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anguli A C D, & </
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Q F, ita ſit H D ad D R.</
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triangulum A B C, id eſt, ut Q F ad B F, ita {2/3} K F ad
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D H , erit rectangulum ſub Q F, D H, æquale
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