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Title : Leonhardi Euleri opera omnia. 1, Opera mathematica. Volumen VIII, Leonhardi Euleri introductio in analysin infinitorum. Tomus primus / ediderunt Adolf Krazer et Ferdinand Rudio
Author : Euler, Leonhard (1707-1783)
Publisher : B. G. Teubneri (Lipsae)
Date of publication : 1922
Contributor : Krazer, Adolf. Éditeur scientifique
Contributor : Rudio, Ferdinand. Éditeur scientifique
Subject : Mathématiques -- Ouvrages avant 1800
Type : monographie imprimée
Language : Latin
Format : 1 vol. (392 p.) ; 29 cm
Format : application/pdf
Copyright : domaine public
Identifier : ark:/12148/bpt6k69587
Source : Bibliothèque nationale de France
Relation : Notice d'ensemble : http://catalogue.bnf.fr/ark:/12148/cb37341158h
Relation : Titre d'ensemble : Leonhardi Euleri opera omnia
Relation : http://catalogue.bnf.fr/ark:/12148/cb372602892
Provenance : bnf.fr
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40 TOMI PRIMI CAPUT II § 38-39 [22-23
38. Si in functione fracta quantitas variabilis z tot vel plures habeat dimen-
siones in numeratore quam in denominatore, tum ista functio resolvi poterit in
duas partes, quârum altera est functio integra, altera fracta, in cuius numeratore
quantitas variabilis z pauciores liabeat dimensiones quam in denominatore.
Si enim exponens maximae potestatis ipsius z minor fuerit in denomina-
tore quam in numeratore, tum. numerator per denominatorem dividatur more
solito, donec in quoto ad exponentes negativos ipsius z perveniatur; hoc ergo
locô abrupta divisionis operatione quotus constabit ex parte integra atque
fractione, in cuius numeratore minor erit dimensionum numerus ipsius z quam
in denominatore; hic autem quotus functioni propositae est aequalis. Sic, si
haec proposita fuerit functio fracta
ea per divisionem ita resolvetur:
eritque
Huiusmodi functiones fractae, in quibus quantitas variabilis z tot vel plu-
res habet dimensiones in numeratore quam in denominatore, ad similitudinem
Arithmeticae vocali possunt fractiones spuriae vel functiones fractae spuriae,
quo distinguantur a functionibus fractis genuinis, in quarum numeratore quan-
titas variabilis z pauciores habet dimensiones quam in denominatore. Functio
itaque fracta spuria resolvi poterit in functionem integram et functionem
fractam genuinam haecque resolutio per vulgarem divisionis operationem ab-
solvetur.
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