Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Table of figures

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[61] Fig. 5.G L B H D O A E C K
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[62] Fig. 7.K F A C D B E H G
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[63] Pag. 404.TAB. XLII.Fig. 1.K F M A C D B L E N G
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[64] Fig. 3.G R D B H F E N A X C M P Q K
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[65] Fig. 2.K A F c S C L E B T G D R d
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[66] Fig. 4.K e G P E m B D f R F S H M C A N L Q n
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[67] Fig. 5.B C R E G A F M Q D O
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[68] Fig. 6.B C H G E A M Q P K D
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[69] Fig. 7.B C E G A M P Q K H D
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[Figure 70]
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[71] Pag. 450.TAB.XLIII.Fig. 4.B A F R P C D E G H I K S L M N O
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[72] Fig. 1.F G I K D L E S T O C N H M V R B Q P A
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[73] Fig. 2.F G I K D L E S T O C N V R B Q P A
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[74] Fig. 5.A C B D E
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[75] Fig. 3.A F G I K D L S T E O C N H M V R B Q P
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[Figure 76]
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[Figure 77]
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[Figure 78]
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[Figure 79]
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[Figure 80]
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[Figure 81]
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[Figure 82]
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[83] TAB. XLIV.Fig. 2.D H A B E F G
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[84] Fig. 1.E G N L O I Q P D K M H F A
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[85] Fig. 3.B E F A D G C
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[86] I. CasusFig. 4.Y Q R C A B M L I K V C O S X
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[87] II. CasusFig. 5.R C Y Q A B I L M K V O X S C
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[88] III. CasusFig. 6.Q C D Y K L I N M S V B X C A G O
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[89] Fig. 7.IV. CasusQ D C A B S L N X M I V Y K C G O
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[Figure 90]
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194464HUGENII OBSERVATIONES eodem modo analytice componi e terminis a3 + aab, abb
+ b3 quo componitur e terminis aab + bba, 2 bba. Hæc ni-
hilominus invenitur per eandem methodum quam indi-
cat in 7. Propoſitione. Methodus autem hæc eſt. Pri-
mo quærenda eſt quantitas perquam ſi multiplices a3 + aab,
& producto addas productum abb + b3 multiplicati per da-
tam quantitatem m, ſumma æqualis ſit ſummæ duorum alio-
rum productorum, unius aab + bba multiplicati per eandem
quantitatem quæſitam, alterius 2 bba multiplicati per datam
quantitatem m. Ponamus igitur quantitatem illam æqualem
z, erit a3z + aabz + abbm + b3m = aabz + bbaz + 2 bbam;
& z = {bbm/aa + ab}: Et certum eſt, ſive multiplicetur {bbm/aa + ab} per a3 + aab
& addatur abb + b3 multiplicatum per m, ſive eadem illa
quantitas multiplicetur per aab + bba & addatur 2 bbam,
ſemper prodire eandem quantitatem 2 abbm + b3m, & conſe-
quenter ultimam hanc quantitatem componi eodem modo e
primis & ſecundis terminis progreſſionis convergentis pro-
poſitæ, quod Autor fieri poſſe negavit.
III°. Datâ autem hac quantitate 2 abbm + bbbm, ſi hac
utamur ad quærendam terminationem progreſſionis propo-
ſitæ, juxta methodum ab auctore indicatam in 7 propoſi-
tione, & in 10, reperietur = {3 aab3 + ab4 + 2 a3 bb/bb + ab + aa}; & poſito a = 1
& b = 2, illa terminatio, quæ deſignat in eo caſu ſectorem
circuli continentem {1/3} totius circuli, erit = {48/7}; & primus ter-
minus progreſſionis a3 + aab, qui deſignat {1/3} trianguli æquila-
teri inſcripti in eodem Circulo, erit æqualis 3; ita ut propor-
tio circuli ad triangulum æquilaterum inſcriptum ſit ut {48/7} ad
3@ id eſt 16 ad 7. a vero nihilominus omnes has proportiones ab-
errare facile patet.
IV°. Si examinemus, cur terminatio aliquando occurrat ve-
ra per methodum Autoris, ut in 7 Propoſitione, interdum
verò non; reperiemus id ex eo oriri quod problema 10mæ

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