Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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VARIA CIRCA
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<
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<
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plano fuerint, ſive non: </
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<
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">ſi à puncto quod eorum commune eſt
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gravitatis centrum, ad unum quodque datorum fila extendan-
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tur, eaque ſingula trahantur à potentiis quæ ſint inter ſe ut
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filorum longitudines, fiet æquilibrium manente nodo commu-
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ni in dicto gravitatis centro.</
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<
s
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">Sint data puncta A, B, C, D, E, quæ vel in eodem
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Fig. 2.</
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plano vel aliter utcunque collocata intelligantur: </
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<
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autem ſingulis æquali gravitate, conſtat commune eorum
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gravitatis centrum inveniri hoc modo.</
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<
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<
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">Jungantur nempe duo quælibet datorum punctorum rectâ
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A B, quâ bifariam ſectâ in F, erit hoc centrum gravitatis
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punctorum A, B. </
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<
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cta F C quæ ſecetur in G, ut ſit C G dupla G F; </
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">& </
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<
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G centrum gravitatis punctorum trium A, B, C. </
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<
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ducatur ad aliud punctum recta G D, ſeceturque in H, ut
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ſit D H tripla H G, & </
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<
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quatuor A, B, C, D.</
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<
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">Similiterque ductâ H E ad punctum quintum E, ſectâque
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in K, ut K E ſit quadrupla K H, erit K centrum gravi-
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tatis punctorum quinque A, B, C, D, E. </
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<
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quotcunque punctorum centrum gravitatis invenire licebit.</
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<
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">Porro extentis filis à puncto K ad A, B, C, D, E,
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quæ trahantur ſingula à potentiis quæ ſint inter ſe ut ipſæ
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longitudines K A, K B, K C, K D, K E: </
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<
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quilibrium manente nodo communi in K. </
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<
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centris gravitatis inventis F, G, H, ad centrum gravitatis
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omnium punctorum K, rectæ F K, G K, H K. </
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ſtat filis A K, B K, punctum K trahentibus cum potentiis quæ
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ſint ut longitudines eorum filorum, æquipollere filum F K,
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tractum à potentia quæ ſit ut dupla longitudo F K. </
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verò duobus his, filo F K trahenti cum potentia quæ ſit ut
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dupla F K, & </
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<
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">filo C K trahenti cum potentia quæ ſit ut
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ſimplex longitudo C K, æquipollet filum G K tractum à
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potentia quæ ſit ut tripla K G per præcedentem: </
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<
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filum G K ita tractum æquipollet filis tribus K A, K </
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