Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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ET HYPERBOLÆ QUADRATURA.
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libet data C ad D: </
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quantitatem, ut ratio ejus ad A ſit multipli-
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cata rationis B ad A in ratione C ad D.</
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EDC # AFBG
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ſurabilis, ſitque inter C & </
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munis menſura E; </
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ratio F ad A ſubmultiplicata rationis B ad A; </
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continetur in C toties ſit ratio G ad A multiplicata rationis
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F ad A: </
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<
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">dico G eſſe quantitatem illam quæſitam. </
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A eſt multiplicata rationis F ad A in ratione C ad E, & </
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tio F ad A eſt multiplicata rationis B ad A in ratione E ad D; </
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igitur ex æqualitate, ratio G ad A eſt multiplicata rationis
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B ad A in ratione C ad D, quod demonſtrare oportuit.</
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<
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">Quod ſi ratio C ad D ſit incommenſurabilis, geometricam
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hujus problematis praxim eſſe impoſſibilem mihi perſuadeo;
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">approximatione tamen fieri poteſt, aſſumendo rationem com-
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menſurabilem ejus loco, quæ quàm proximè ad illam acce-
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dat.</
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## G # H # A # B
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# N # I # K # C # D
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M ## R # S # E # F
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# O # T # V # X # Y
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### L ## Z
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termini convergentes ſint A, B, ſe-
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cundi C, D, tertii E, F; </
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ſecundi termini ita facti à primis, ut
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ratio B majoris ad A minorem ſit
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multiplicata rationis C ad A in ra-
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tione data mojoris inæqualitatis M ad N, & </
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A ſit multiplicata rationis D ad A in ratione data majoris
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inæqualitatis M ad O: </
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facti ex ſecundis quo ſecundi facti ſunt ex primis; </
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continuetur ſeries.</
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