Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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">HOrologiorum motum temperare, addito ponde-
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re exiguo ſecundario, quod ſuper virga pen-
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duli, certa ratione diviſa, ſurſum deorſumque
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moveri poſſit.</
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<
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">Ut hoc expediamus, primo penduli ipſius, ex virga gra-
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Fig. 3.</
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vitate prædita, & </
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">appenſo parte ima pondere, compoſiti,
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centrum oſcillationis inveniendum eſt.</
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<
s
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">Sit virga, cum appenſo pondere, A C, cujus longitudo
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dicatur a. </
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<
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">Intelligantur autem, tum virga ipſa, tum pondus
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appenſum C, in particulas minimas æquales diviſa, earum-
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que particularum virga habeat numerum b, pondus vero C
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numerum c, ponendo nempe b ad c, ſicut gravitas virgæ ad
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gravitatem appenſi ponderis. </
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<
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">Longitudo igitur penduli ſim-
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plicis, dato iſochroni, habebitur, ſi ſumma quadratorum à
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diſtantiis particularum omnium à puncto ſuſpenſionis A, di-
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xml:space
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">Prop. 6.
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huj. in fine.</
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vidatur per ſummam earundem diſtantiarum . </
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">Quia
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ergo M eſt centrum gravitatis lineæ A C, & </
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trica cunei ſuper ipſa abſciſſi plano per A D, perpendicu-
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larem ad A C; </
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">qui cuneus hîc revera triangulum eſt; </
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ma quadratorum, à diſtantiis particularum virgæ à puncto
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A, æqualis rectangulo A M T, una cum quadrato A M;
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</
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<
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">hoc eſt, rectangulo T A M, multiplici ſecundum numerum
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particularum b; </
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">hoc eſt, {1/3} a a b; </
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{2/3} a, ac proinde rectangulum T A M = {1/3} a a. </
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quadratorum, à diſtantiis particularum ponderis C ab eo-
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dem puncto A, æquabitur quadrato A C, multiplici ſecun-
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dum numerum particularum ipſius ponderis; </
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Adeoque ſumma quadratorum omnium, tam à diſtantiis par-
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ticularum virgæ, quam ponderis C, erit {1/3} a a b + a a c.</
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<
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">Porro, diſtantiæ omnes particularum virgæ A C à pun-
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cto A, æquantur {1/2} b a; </
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