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Titre : Oeuvres complètes de Christiaan Huygens. Correspondance [de Christiaan Huygens], 1666-1669 / publ. par la Société hollandaise des sciences
Auteur : Huygens, Christiaan (1629-1695). Auteur du texte
Éditeur : M. Nijhoff (La Haye)
Date d'édition : 1888-1950
Contributeur : Koninklijke Hollandsche maatschappij der wetenschappen. Éditeur scientifique
Sujet : Huygens, Christiaan (1629-1695) -- Contribution aux mathématiques
Sujet : Huygens, Christiaan (1629-1695)
Notice d'ensemble : http://catalogue.bnf.fr/ark:/12148/cb38949978f
Type : monographie imprimée
Langue : latin
Langue : français
Langue : néerlandais
Format : 23 vol. : ill. ; 29 cm
Description : Correspondance
Description : Autobiographie
Droits : Consultable en ligne
Droits : Public domain
Identifiant : ark:/12148/bpt6k778547
Source : Bibliothèque nationale de France, département Philosophie, histoire, sciences de l'homme, 4-R-788 (6)
Conservation numérique : Bibliothèque nationale de France
Date de mise en ligne : 15/10/2007
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trinGck quantity) ofye two ndt, & ofye two fecond, converging terms; by help ofthis quantity, that Series may be Analytically terminated That is, the termination thereof may by Analytical operations be compounded of the two nrft converging Terms. This is proved by Propofition 10. (as it is now reformed & explained in his Reply *?) to Monfieur Huygens;) But not ye converfe of it; becaufë ye converfe of that propofition is not proved. Which is ye exception of Monfieur Huygens '~).
6. And, confequently, if the two firft converging-terms be Analytical each to other; the Termination will be Analyticall to both of them. Which may be proved from Petition t.
y. If therefore any quantity can be found analytically compofed of a, b (the two firft terms of ye converging feries propofed,) and, in ye very fame manner, of (the two next terrns)~ (without ye intermi(!ton of any other
a + k-ab'
quantity in either of ye compofitions) then may this feries be analytically terminated. This (but not ye converfe ofit) follows from § 5.
8. And confequently (when as a, b, be analyticall each to other, viz. § 3) the Termination thereof, (yt is, ye ~or M~?/y/~ taken,) will be analytical with both ofthem. which follows from $ 6. y.
9. And confequently, every fuch ~~o~with its retpedive Triangle & Trapezium. For fuch Sedor indefinitely taken, is any fuch Se6tor whatfoever. 10. Now of fome Sectors ye chord is analytical with ye radius as, for inftance, ofye Quadrantal Sedor, and confequently ye Triangle & Trapezium are Analyticall with ye (quare ofye Radius, or ofye Diameter. As is eafyly proved. t i. And therefore their Se~ors will then be(b; & therefore may be analytically fquared That is, their proportion to ye Square of ye Radius or ye Diameter, may be defigned by Analyticall operations, or by commenfurable quantities & furd Roots. Which may be proved from Definitions 6, 7, and Petition ï. tt. Now to fome at ieftofthofeSe~ors, thé Circle is Analytical!, and particularly to ye Quadrantall; As being ye quadruple thereof.
13. And will therefore be Analyticall to their Triangles, Trapezia, and Squares of ye Radius and diameter; (and fo may be analytically fquared.) Which may be proved from Definitions 6– and Petition i.
i But, on the contrary, if in fuch a converging feries no fuch quantity can be found, (as is mentioned § 5) which can, in ye fame manner, be analytically compounded of the two firft, & of the two fecond converging terms then cannot this feries be by that procefs analytically terminated. For that procefs fuppofeth fuch à quantity; at $ 5 &c.
ï S. And if~o~ by /A~of~, then not at ail. Which is yct to be proved.
'7) Consultez la Lettre ?. 1653.
'~) Consuttez la Lettre ?. id~.