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

Table of contents

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[31.] Theor. VIII. Prop. VIII.
Page: 76 (364)
[32.] Theor. IX. Prop. IX.
Page: 77 (365)
[33.] Problema I. Prop. X. Peripheriæ ad diametrum rationem invenire quamlibet veræ propinquam.
Page: 78 (366)
[34.] Problema II. Prop. XI.
Page: 83 (368)
[35.] Aliter.
Page: 84 (369)
[36.] Aliter.
Page: 84 (369)
[37.] Problbma III. Prop. XII. Dato arcui cuicunque rectam æqualem ſumere.
Page: 85 (370)
[38.] Theor. X. Prop. XIII.
Page: 86 (371)
[39.] Lemma.
Page: 87 (372)
[40.] Theor. XI. Prop. XIV.
Page: 87 (372)
[41.] Theor. XII. Prop. XV.
Page: 91 (376)
[42.] Theor. XIII. Prop. XVI.
Page: 95 (377)
[43.] Theorema XIV. Propos. XVII.
Page: 96 (378)
[44.] Theor. XV. Propos. XVIII.
Page: 98 (380)
[45.] Theor. XVI. Propos. XIX.
Page: 100 (382)
[46.] Problema IV. Propos. XX.
Page: 102 (384)
[47.] Christiani Hugenii C. F. ILLVSTRIVM QVORVNDAM PROBLEMATVM CONSTRVCTIONES. Probl. I. Datam ſphæram plano ſecare, ut portiones inter ſe rationem habeant datam.
Page: 109
[48.] LEMMA.
Page: 111 (390)
[49.] Probl. II. Cubum invenire dati cubi duplum.
Page: 112 (391)
[50.] Probl. III. Datis duabus rectis duas medias propor-tionales invenire.
Page: 114 (393)
[51.] ALITER.
Page: 115 (394)
[52.] ALITER.
Page: 116 (395)
[53.] Probl. IV.
Page: 117 (396)
[54.] Probl. V.
Page: 118 (397)
[55.] Probl. VI.
Page: 118 (397)
[56.] Probl. VII.
Page: 123 (399)
[57.] Utrumque præcedentium Aliter.
Page: 125 (401)
[58.] Probl. VIII. In Conchoide linea invenire confinia flexus contrarii.
Page: 127 (403)
[59.] FINIS.
Page: 128 (404)
[60.] DE CIRCULI ET HYPERBOLÆ QUADRATURA CONTROVERSIA.
Page: 132
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148421ET HYPERBOLÆ QUADRATURA. ter C & D, manifeſtum eſt differentiam inter A & B majo-
rem eſſe duplo differentiæ inter C & D, hoc eſt differen-
tiam inter triangulum A B P & trapezium A B F P majo-
rem eſſe duplo differentiæ inter trapezium A B I P, & po-
lygonum A B D L P, quod demonſtrare oportuit.
SCHOLIUM.
Eodem prorſus modo demonſtratur differentiam inter tra-
pezium A B I P & polygonum A B D L P majorem
eſſe duplo differentiæ inter polygonum A B E I O P & poly-
gonum A B C G K N P. denique eodem modo demonſtra-
ri poteſt hic differentiarum exceſſus in ſubdupla noſtra poly-
gonorum complicatorum deſcriptione in infinitum; differen-
tia enim priorum nempe inſcripti & circumſcripti major ſem-
per erit duplo differentiæ immediatè ſequentium nimirum in-
ſcripti quoque & circumſcripti, & proinde aufertur majus
quam dimidium a priorum differentia ut fiat differentia im-
mediatè ſequentium; & igitur continuando ſubduplam po-
lygonorum deſcriptionem, inveniri poſſunt duo polygona
complicata, quorum differentia ſit minor qualibet exhibita
quantitate, ut in præcedentis Scholio aſſumpſimus.
Sint duæ quantitates indefinitæ a minor b major, ſintque
datæ duæ rationes majoris inæqualitatis c ad d, & c ad e; de-
inde ſit ut c ad d ita b - a ad {bd - ad/c} cui addatur quantitas a ut
fiat {ca + bd - ad/c}, quæ quantitas ponatur immediate ſub a: fiatque
ut c ad e ita b - a ad {be - ae/c}, quæ quantitas ſubſtrahatur ex b &
relictum nempe {bc - be + ae/c} ponatur ſub b. continuetur de-
inde ſeries convergens cujus pri-
11
# d
c # e # a # b
## {ca + bd - ad/c} # {bc - be + ae/ c}
mi termini convergentes ſunt a, b,
& ſecundi termini convergentes
{ca + bd - ad/c}, {bc - be + ae/c}. manifeſtum eſt terminum {ca + bd - ad/c}

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