Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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DE CIRCULI MAGNIT. INVENTA.
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ptum. </
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<
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">Et circulus minor eſt polygono iſtis ſimili cu-
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jus ambitus majori mediarum æquetur.</
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<
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<
s
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xml:space
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">Eſto circulus B D, cujus centrum A. </
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<
s
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xml:space
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">Et inſcribatur ei po-
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">TAB. XXXIX.
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Fig. 6.</
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lygonum æquilaterum B C D L, ſimileque circumſcri-
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batur lateribus parallelis H K M N. </
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<
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xml:space
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">Sitque perimetro po-
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lygoni H K M N æqualis recta T, perimetro autem B C D L
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æqualis Z. </
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<
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">Et inter Z & </
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<
s
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echoid-s1579
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xml:space
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">T duæ ſint mediæ proportionales
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X & </
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<
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">V, quarum X minor. </
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<
s
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xml:space
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">Dico circumferentiam circuli
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B D minorem eſſe rectâ X. </
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<
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xml:space
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">Et ſi fiat polygonum in quo Y,
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cujus perimeter æquetur rectæ V, ſimile autem ſit polygono
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B C D L aut H K M N; </
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<
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xml:space
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">Dico circulum B N minorem
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haberi polygono Y. </
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<
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">Ducatur enim diameter circuli P E,
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quæ dividat bifariam latera parallela B C, H K, inſcripti
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circumſcriptique polygoni in R & </
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<
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">E; </
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<
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contactus lateris H K, & </
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<
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">B C ſecabitur in R ad angulos
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rectos. </
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<
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xml:space
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">Ducatur etiam ex centro recta A C K, quæ utriuſ-
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que polygoni angulos C & </
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<
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">K bifariam ſecet, nam hoc ab
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eadem recta fieri conſtat; </
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">& </
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<
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">jungatur C E. </
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">Ipſi autem C E
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ponatur æqualis C F; </
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<
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">ſitque duabus his C R, C F tertia
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proportionalis C G. </
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">Ergo qualis polygoni inſcripti latus eſt
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C E ſive C F, talis circumſcripti latus erit C G . </
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">per 13. huj.</
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duæ tertiæ C F cum triente C G ſimul majores erunt arcu
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E C . </
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<
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xml:space
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lis recta S. </
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<
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<
s
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">Et quoniam ſe habet C R ad C F, ut C F ad C G;
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</
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<
s
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">erit quoque dupla C R una cum C F ad triplam C R,
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hoc eſt, utraque ſimul B C, C F ad utramque B C, C R,
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ut dupla C F una cum C G ad triplam C F: </
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<
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">vel ſumptis
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horum trientibus, ut {2/3} C F una cum {1/3} C G ad C F, hoc
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eſt, ut S ad C F. </
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<
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">Quare etiam triplicata ratio ejus quam ha-
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bet utraque ſimul B C, C F ad utramque B C, C R ea-
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dem erit triplicatæ rationi S ad C F. </
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<
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R B ad B F quam triplicata ejus, quam habet utraque ſi-
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mul B C, C F ad utramque B C, C R . </
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<
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præ.</
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dem ratio R B ad B F quam triplicata ejus quam habet S </
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