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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">IN ſemicirculo & </
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<
s
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">quolibet circuli ſectore, habet
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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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<
s
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xml:space
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">Eſto primùm ſemicirculus A B C, deſcriptus centro D,
<
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<
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xml:space
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">TAB. XXXVI.
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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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<
s
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xml:space
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">Dico arcum A B C eſſe ad duas
<
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1
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xlink:label
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note-0028-02
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xml:space
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">Theor. 4. h.</
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A C, ſicut B D ad D E. </
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<
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">Jungantur enim A B, B C. </
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<
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">Igi-
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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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xml:space
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nis reliquæ. </
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<
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">Verùm etiam ut ſemicirculus, id eſt, ut trian-
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gulus habens baſin æqualem arcui A B C & </
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<
s
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xml:space
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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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<
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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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">permutando, ut arcus A B C ad duas tertias
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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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<
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">TAB. XXXVI.
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Fig. 4.</
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<
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">Sit deinde ſector D A B C, ſemicirculo minor, bifariam
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ſectus rectâ D B, in qua ſectoris centrum gravitatis ponatur
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E punctum, & </
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">ducatur ſubtenſa A C. </
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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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<
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">totius
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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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<
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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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<
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">Quia igitur ſicut portio A C B ſive triangulus A Q C ad
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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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