Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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HYPERB. ELLIPS. ET CIRC.
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B D G, quoniam in ea ſunt centra gravitatis utriusque fi-
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guræ circumſcriptæ ; </
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<
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">igitur magnitudinis ex dictis
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xml:space
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">Theor. 3. h.</
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compoſitæ centrum grav. </
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<
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xml:space
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">eſt ipſum punctum F. </
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<
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xml:space
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tem fuit L punctum centrum gravitatis ejus magnitudinis quæ
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ex portione A B C & </
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<
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xml:space
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">K F H triangulo componitur; </
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<
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tur magnitudinis reliquæ, compoſitæ ex duobus reſiduis,
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quæ in figuris circumſcriptis remanent, erit centr. </
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<
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">grav. </
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<
s
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xml:space
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">in
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producta L F, ubi ea ſic terminatur, ut pars adjecta habeat
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ad F L eandem rationem quam portio A B C ſimul cum
<
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K F H triangulo ad dicta duo reſidua : </
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<
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xml:space
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">is autem
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">8
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. lib. 1.
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Archine. d e
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Æquipond</
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nus eſt N; </
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<
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">itaque N punctum eſt centrum gravitatis duo-
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rum reſiduorum. </
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<
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<
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xml:space
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">Nam ſi per N ducatur
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recta baſi K H parallela, erunt ab una parte ſpatia omnia è
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quibus utrumque reſiduum conſtat. </
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>
<
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xml:space
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">Non eſt igitur L pun-
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ctum centrum gravitatis magnitudinis ex portione A B C & </
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<
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K F H triangulo compoſitæ. </
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<
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">Sed neque erit ab altera parte
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puncti F. </
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<
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xml:space
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">Namque hoc ſi dicatur, planè ſimili demonſtratio-
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ne eò devenietur ut duorum reſiduorum quæ demptâ portio-
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ne A B C & </
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">K F H triangulo, in circumſcriptis figuris ſu-
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pererunt, centrum gravitatis ſit ultra portionem A B C;
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</
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">quod eſt æquè abſurdum. </
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ctum F; </
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<
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VI.</
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<
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">OMnis hyperboles portio ad triangulum inſcri-
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ptum, eandem cum ipſa baſin habentem ean-
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demque altitudinem, hanc habet rationem; </
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<
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">quam
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ſubſeſquialtera duarum, lateris tranſverſi & </
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">dia-
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metri portionis, ad eam quæ ex centro ſectionis
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ducitur ad portionis centrum gravitatis.</
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</
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<
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<
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">inſcriptus ei, qualem diximus,
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<
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">TAB. XXXIV.
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Fig. 8.</
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triangulus A B C; </
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latus tranſverſum ſive diameter ſectionis B E, in cujus me-
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dio centrum ſectionis F. </
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