Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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HUGENII OBSERVATIONES
"/>
eodem modo analytice componi e terminis a
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+ aab, abb
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+ b
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quo componitur e terminis aab + bba, 2 bba. </
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<
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xml:space
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hilominus invenitur per eandem methodum quam indi-
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cat in 7. </
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<
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xml:space
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xml:space
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mo quærenda eſt quantitas perquam ſi multiplices a
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+ aab,
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& </
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<
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xml:space
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">producto addas productum abb + b
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multiplicati per da-
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tam quantitatem m, ſumma æqualis ſit ſummæ duorum alio-
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rum productorum, unius aab + bba multiplicati per eandem
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quantitatem quæſitam, alterius 2 bba multiplicati per datam
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quantitatem m. </
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xml:space
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">Ponamus igitur quantitatem illam æqualem
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z, erit a
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z + aabz + abbm + b
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m = aabz + bbaz + 2 bbam;
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</
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<
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xml:space
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<
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xml:space
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">z = {bbm/aa + ab}: </
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<
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xml:space
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">Et certum eſt, ſive multiplicetur {bbm/aa + ab} per a
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+ aab
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& </
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<
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xml:space
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">addatur abb + b
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multiplicatum per m, ſive eadem illa
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quantitas multiplicetur per aab + bba & </
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ſemper prodire eandem quantitatem 2 abbm + b
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m, & </
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<
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xml:space
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quenter ultimam hanc quantitatem componi eodem modo e
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primis & </
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poſitæ, quod Autor fieri poſſe negavit.</
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utamur ad quærendam terminationem progreſſionis propo-
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ſitæ, juxta methodum ab auctore indicatam in 7 propoſi-
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tione, & </
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xml:space
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">in 10, reperietur = {3 aab3 + ab4 + 2 a3 bb/bb + ab + aa}; </
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<
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xml:space
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& </
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<
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xml:space
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">b = 2, illa terminatio, quæ deſignat in eo caſu ſectorem
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circuli continentem {1/3} totius circuli, erit = {48/7}; </
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xml:space
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<
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">primus ter-
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minus progreſſionis a
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+ aab, qui deſignat {1/3} trianguli æquila-
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teri inſcripti in eodem Circulo, erit æqualis 3; </
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<
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tio circuli ad triangulum æquilaterum inſcriptum ſit ut {48/7} ad
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3@ id eſt 16 ad 7. </
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">a vero nihilominus omnes has proportiones ab-
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errare facile patet.</
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<
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ra per methodum Autoris, ut in 7 Propoſitione, interdum
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verò non; </
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