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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xml:space
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">Eſto Circuli portio, ſemicirculo minor, cui maximum ſit in-
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">TAB. XXXVIII.
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Fig. 3.</
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ſcriptum triangulum A B C. </
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angulum majorem rationem habere quam quatuor ad tria. </
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ſcribantur enim & </
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<
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">reliquis portionibus duabus maxima triangu-
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la A D B, B E C. </
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<
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xml:space
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">Itaque minus eſt triangulum A B C quam illo
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rum ſimul quadruplum : </
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<
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xml:space
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">ac proinde ſpatium aliquod
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">per. 1. huj.</
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poteſt triangulo A B C, quod una cum ipſo minus etiam ſit
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quam quadruplum dictorum ſimul triangulorum A D B, B E C.
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</
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<
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">Eſto itaque eâ ratione adjectum triangulum A F C, ut to-
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tum ſpatium A B C F minus ſit quam quadruplum triangu-
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lorum A D B, B E C. </
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<
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xml:space
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">Et porro in reſiduis portionibus ma-
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xima triangula inſcribi intelligantur; </
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<
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">itemque in reſiduis ſem-
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per, donec portiones quibus poſtremùm inſcribentur ſimul
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minores ſint triangulo A C F, hoc enim fieri poteſt. </
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<
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que & </
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<
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">triangula poſtremùm inſcripta ſimul triangulo A C F
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minora erunt. </
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">Quia autem ſpatii A B C F quarta parte ma-
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jora ſunt duo ſimul triangula A D B, B E C. </
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<
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quarta horum parte majora triangula quatuor, quæ portio-
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nibus reliquis inſcribuntur. </
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<
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xml:space
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">Et horum quartâ majora ſimili-
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ter, quæ deinceps: </
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ſcripta. </
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<
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">Erit propterea ſpatium ex quadrilatero A B C F & </
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cæteris inſcriptis triangulis, & </
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inſcripta erunt, compoſitum, majus quam ſeſquitertium i-
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pſius quadrilateri A B C F. </
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<
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ſtratum eſt, quod ſi fuerint ſpatia quotcunque in ratione qua-
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drupla, ea omnia ſimul cum triente minimi ad maximum ra-
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tionem habebunt ſeſquitertiam. </
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<
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xml:space
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">Dividendo itaque, triangula
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omnia intra portiones A D B, B E C deſcripta cum trien-
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te poſtremo diſcriptorum majora erunt tertia parte ſpatii
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A B C F. </
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<
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xml:space
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Igitur dempto illinc triente poſtremò inſcriptorum; </
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autem A B C F ablato triangulo A F C, erunt triangula
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omnia intra portiones A D B, B E C deſcripta, majora
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triente trianguli A B C . </
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<
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rectilinea portioni A B C inſcripta major quam ſeſquitertia
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trianguli A B C, multoque magis portio ipſa. </
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demonſtrandum.</
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