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

Table of contents

< >
[81.] PROP. XIII. THEOREMA.
[82.] PROP. XIV. THEOREMA.
[83.] PROP. XV. THEOREMA.
[84.] PROP. XVI. THEOREMA.
[85.] PROP. XVII. THEOREMA.
[86.] PROP. XVIII. THEOREMA.
[87.] PROP. XIX. THEOREMA.
[88.] CONSECTARIUM.
[89.] PROP. XX. THEOREMA.
[90.] PROP. XXI. THEOREMA.
[91.] PROP. XXII. THEOREMA.
[92.] SCHOLIUM.
[93.] PROP. XXIII. THEOREMA.
[94.] PROP. XXIV. THEOREMA.
[95.] PROP. XXV. THEOREMA.
[96.] PROP. XXVI. THEOREMA.
[97.] PROP. XXVII. THEOREMA.
[98.] PROP. XXVIII. THEOREMA.
[99.] PROP. XXIX. PROBLEMA. Dato circulo æquale invenire quadratum.
[100.] PROP. XXX. PROBLEMA. Ex dato ſinu invenire arcum.
[101.] PROP. XXXI. PROBLEMA. Ex dato arcu invenire ſinum.
[102.] PROP. XXXII. PROBLEMA. Invenire quadratum æquale ſpatio hyperbolico con-tento à curva hyperbolica, uno aſymptoto & dua-bus rectis alteri aſymptoto parallelis; quod ſpatium æquale eſt ſectori hyperbolico cujus baſis eſt eadem curva.
[103.] PROP. XXXIII. PROBLEMA. Propoſiti cujuscunque numeri logorithmum invenire.
[104.] SCHOLIUM.
[105.] PROP. XXXIV. PROBLEMA. Ex dato logorithmo invenire ejus numerum.
[106.] Tom. II. Mmm
[107.] PROP. XXXV. PROBLEMA. Rectâ per datum punctum in diametro ductâ, ſemicirculum in ratione data dividere.
[108.] SCHOLIUM.
[109.] FINIS.
[110.] II. HUGENII OBSERVATIONES IN LIBRUM JACOBI GREGORII, DE VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
< >
page |< < (442) of 568 > >|
169442VERA CIRCULI C, G; & ideo terminatio ſeriei A, C, E, nempe Z, major
erit terminatione ſeriei A, C, G, nempè X;
at ex Archime-
dis quadratura parabolæ conſtat X æqualem eſſe ipſi C dem-
pto triente exceſſus A ſupra C, &
proinde Z eadem major
eſt, quod demonſtrare oportuit.
PROP. XXIV. THEOREMA.
IIsdem poſitis; dico Z ſeu ſe-
11
A B # A B
C D # G H
E F # M N
K L # O P
Z # X
ctorem hyperbolæ minorem eſ-
ſe quam minor duarum mediarum
arithmeticè continuè proportio-
nalium inter A &
B. Inter A &
B ſit media arithmetica G, &
in-
ter G &
B ſit media Arithmetica
H, Item inter G &
H ſit media Arithmetica M, & inter M
&
H ſit media Arithmetica N: continueturque hæc ſeries con-
vergens A B, G H, M N, O P, in infinitum, ut fiat ejus termi-
natio X.
ſatis patet ex prædictis G majorem eſſe quam C;
atque H media arithmetica inter G & B major eſt media har-
monica inter easdem G &
B; media autem harmonica inter
G &
B; major eſt media harmonica inter C & B, nempe D, quo-
niam G major eſt quam C;
& ideo media Arithmetica inter G
&
B nempe H major eſt quam D media harmonica inter C & B
eodem modo M media Arithmetica inter G &
H major eſt me-
dia geometrica inter eaſdem G &
H; & quoniam G eſt ma-
jor quam C &
H quam D, media geometrica inter G & H
major eſt quam E media geometrica inter C &
D; & proin-
de M major eſt quam E.
Deinde N media Arithmetica in-
ter M &
H major eſt media harmonica inter easdem; & quo-
niam H major eſt quam D &
M quam E, media harmonica
inter M &
H major eſt quam F media harmonica inter E &
D;
& ideo N eadem F major eſt. eodem modo utramque
ſeriem in infinitum continuando, ſemper demonſtratur ter-
minum quemlibet ſeriei A B, C D, minorem eſſe quam idem
numero terminum ſeriei A B, G H;
& igitur terminatio ſe-
riei A B, C D, nempe Z, minor erit terminatione ſeriei A

Text layer

  • Dictionary

Text normalization

  • Original

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index