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Title: De Latino sine Flexione; Principio de Permanentia
Author: Giuseppe Peano
Release Date: April 9, 2011 [EBook #35803]
Language: Latin
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DE LATINO SINE FLEXIONE
LINGUA AUXILIARE INTERNATIONALE
Lingua latina fuit internationalis in omni scientia, ab imperio Romano,
usque ad finem saeculi XVIII. Hodie multi reputant illam nimis
difficilem esse, iam in scientia, magis in commercio.
Sed non tota lingua latina est necessaria; parva pars sufficit ad
exprimendam quamlibet ideam.
§ 1.--Casus.
«Nominum casus semper eliminari possunt substitutis in eorum locum
particulis quibusdam».
LEIBNIZ. Ed. Couturat a. 1901, p. 67.
Lingua latina exprimit nominum casus cum praepositionibus «_de_, _ad_,
_ab_, _ex_, ...» et cum postpositionibus vel desinentiis. Prima methodus
sufficit; ipsa sola invenitur in latino populare, a quo derivant linguae
neolatinae, ut italica, franca, hispanica, etc.
Sumimus nomen inflexibile sub forma simpliciore, quae est ablativus, vel
nominativus, vel alia.
Indicamus genitivo cum _de_, dativo cum _ad_, ablativo cum _ab_,
_ex_, ... Accusativo indicatur cum constructione, ut in linguis
neolatinis, scilicet cum serie: nominativo--verbo--accusativo, vel cum
serie: _qui_-accusativo--nominativo--verbo.
Vocabulario latino commune continet nominativo et genitivo de nomen.
Regula commoda haec est:
«Sumimus nomen inflexibile
a) aut identico ad nominativo,
b) aut nominativo, mutata desinentia _-us_, _-um_, _-u_, _-es_
in _-o_, _-o_, _-o_, _-e_,
c) aut genitivo, mutata desinentia _-i_ in _-o_, _-is_ in _-e_.
d) ad nominativo _ego_, _tu_, _aliquis_,
responde (ablativo) _me_, _te_, _aliquo_.»
Regula a) producit nulla ambiguitate, quae iam non sit in latino.
Regulae b) c) d) brevi exprimunt formatione de ablativo, cum reductione
de 4-a declinatione ad 2-a, et cum reductione ad forma unica de 3-a
declinatione.
§ 2.--Genere masculino, feminino et neutro.
«Discrimen generis nihil pertinet ad grammaticam rationalem».
LEIBNIZ.
Nomen isolato non habet genere. Quum volumus indicare ille, scribemus
explicite "mas, femina".
Ita "mater est _bona_" fit "mater est femina bono"; sed idea de femina
iam continetur in mater; igitur post simplificatione(1): "mater est
bono".
(1) Juxta _Formulaire de Mathématiques_ a. 1902, p. 7, Prop. 3·1 et
5·3.
Indicatione de genere evanescit saepe in lingua scientifica.
In lingua familiare sufficit conservare genere in uno pronomen "is, ea,
id", vel in antiquo "hi, hae, ho".
§ 3.--Numero singulare et plurale.
«Videtur pluralis inutilis in lingua rationali».
LEIBNIZ.
Nomen isolato non habet numero. Ad indicando ille scribemus explicite
"uno, plure".
Ex. "unum os habemus et duas aures"
fit "habemus uno uno ore, et duo plure aure",
et post simplificatione logico "uno uno" = "uno", et "duo plure" =
"duo", nam "duo" continet idea de "plure", propositio
fit: "habemus uno ore et duo aure".
Ex. "Omne homo est mortale, aliquo homo est nigro, multo homo est
pauper, pauco homo est divite, plure homo est sapiens".
Propositione: "Romani eligebant duo consules"
fit "Populo Romano eligebat duo consule".
§ 4.--Conjugatione de verbo.
«Personae verborum possunt esse invariabiles, sufficit variari
_ego_, _tu_, _ille_, etc.».
LEIBNIZ.
Lingua latino habet discurso directo, ut:
"Amicitia inter malos esse non potest"
et discurso indirecto:
"(Verum est) amicitiam inter malos esse non posse".
Si nos utimur semper de discurso indirecto, in verbo evanescit
desinentia de persona, de modo, et saepe de tempore.
Sumimus ergo nomen inflexibile, per persona modo et tempore, sub forma
magis simplice, qui es imperativo, activo et passivo. Regula es:
«a) Ad forma inflexibile "es, pote, vol, fi"
responde infinito "esse, posse, velle, fieri".
b) Ad forma inflexibile de alio verbo adde _-re_, et te habe
infinito, ut es in vocabulario latino.
c) Ad verbo activo adde _-re_, et te habe passivo.
d) Nos transforma verbo deponente in activo».
(Verbo "vol, dice, duce, face", et regula d) non es exacto latino
classico).
Nos indica persona cum "me, te, nos ...", modo cum "si, ut, quod, ...",
tempore cum "heri, jam, in passato, nunc, cras, in futuro, vol,
debe, ...".
Ex. "Me scribe.--Vos lege.--Cras me i ad Roma.--Cras me, postquam veni
ad Roma, scribe ad te.--Heri me lege dum te scribe et antequam Petro
veni.--Si te narra, nos audi.--Ut te vale."
§ 5.--Altero reductione de desinentia de verbo.
Exsta aequalitate logico:
lauda-nte = qui lauda
lauda-ndo = dum lauda
lauda-to = qui aliquo lauda
(hoc es: "quem aliquis laudat", juxta regula de § 1)
lauda-turo = qui lauda in futuro
Petro lauda-re ab Paulo = Paulo lauda Petro.
Si in loco de primo membro de uno ex hic aequalitate nos scribe secundo,
omne desinentia evanesce.
Sed aliquo desinentia, et non necessario, pote es utile, ut "-nte, -to",
desinentia "-vi, -bi" de passato et de futuro, et forma neolatino: "habe
ama-to, es ama-to, ...".
§ 6.--Vocabulario.
Vocabulario latino commune suffice ut nos traduce hic lingua. Sed si
plure auctore adopta "latino sine flexione", tunc es utile publicatione
de proprio vocabulario, qui:
1) Contine nomen et verbo, solo sub forma inflexibile.
2) Contine vocabulo internationale, ut "metro, dyne, ...".
3) Elige suo voce ex toto latinitate, etiam ex latino populare. Igitur
nos posse sume regula:
«Omne voce qui pertine ad duo lingua neolatino, p. ex. italo et franco,
es latino».
4) Simplifica derivatione et compositione de vocabulo.
De ultimo subiecto me hic breviter dice.
a) Substantivo diminutivo: "hortulo = parvo horto", etc.
b) Substantivo abstracto ex adiectivo vale adiectivo. Ex. "bonitas =
bono", "altitudo = alto".
c) Adiectivo qui deriva ab sustantivo vale genitivo: "aureo = de auro",
"vitulino = de vitulo", "Romano = de Roma", "chartaceo = ex charta",
"animoso = cum animo".
d) Substantivo abstracto ex verbo vale verbo.
"Laudatio" = italico "il lodare" = anglo "to laud", vel simpliciter
"laud".
"Vita est cogitatio" fi "vivere est cogitare", in discurso indirecto (§
4) "vivere esse cogitare", post reductione ad radice: "vive es cogita".
Ita "amor = ama", "gaudio = gaude", ...
e) "Lauda-tore = qui lauda", vel "qui sole lauda".
f) Adiectivo verbale: "erra-bundo = qui saepe erra", "tim-ido = qui sole
time", "mord-ace = qui sole morde", "ama-bile = qui aliquo pote ama".
g) Adverbio extracto ex adiectivo vale adiectivo. Ita in latino classico
"brevi, raro, ..." es adiectivo et adverbio.
h) In modo simile ad "ne-sci, ne-fasto, n-ullo" nos forma: "ne-facile =
difficile" "ne-digno = indigno" "ne-normale = abnormale" "ne-es = de-es"
"ne-multo = pauco", etc.
i) Alio praefixo, p. ex. "ab", indica oppositione.
j) In modo simile ad "agricola = agro-colente" "homicidio = homo-caede",
lice scribe: "auro-corona = corona de auro", "me-patre = meo patre",
etc.
Lingua sinense habe omne hic simplificatione, et alio.
§ 7.--Pronuntia de latino.
Pronuntia de latino non es uniforme in diverso populo. Forma meliore es
antiquo:
_ce_, _ci_ ut italo _che_, _chi_, franco _que_, _qui_, germano _ke_,
_ki_.
_ge_, _gi_ » _ghe_, _ghi_, » _gue_, _gui_, » _ge_,
_gi_.
_ti_ » _ti_, non _zi_.
_y_ ut franco _u_, germano _ü_.
_ae_ ut _e_ aperto, franco _è_, germano _ä_.
_oe_ ut franco _eu_, germano _ö_ (hoc es conventione).
_th_ ut anglo _th_, graeco moderno [theta].
_ph_, sono producto quando nos suffla flamma. (Deriva ex graeco antiquo
[phi]; graeco moderno pronuntia _f_).
_ch_, ut germano _ch_, etrusco _c_.
_h_, aspirato, ut germano.
_rh_, ut franco _r_.
_qu_ sona ut _cu_ in neolatino; hic duo syllaba es differente et in
positione, et in pronuntiatione antiquo(5).
(2) Vide A. ~Meillet~, _Introduction à l'étude comparative des langues
indo-européennes_, Paris a. 1903 pag. 56.
Omne alio litera ut in italo.
HISTORIA
Quum plure populo es in reciproco contacto, per ratione de politica,
scientia et commercio, semper se manifesta necessitate de inter-lingua.
Diverso populo, sub imperio Romano, adopta latino populare, qui es
latino cum simplificatione de caso (§ 1).
Populo Saxone, in contacto cum Anglo, forma lingua anglo moderno, qui
contine simplificatione de caso (§ 1), de genere (§ 2), et in parte
simplificatione de persona et de modo (§ 4). Lingua anglo tende ad
perdita de omne flexione et ad monosyllabismo.
Ita, in tempore historico, ori "Lingua franca" in porto de Mediterraneo,
"Pidgin" in Sina, "Urdu" in India, etc.
Hodie omne homo de Europa et de America, qui habe plure relatione cum
extero, clama lingua internationale. Nam suffice lingua nationale ad qui
habe solo relatione nationale. Conoscentia de tres aut quatuor lingua
principale suffice ut nos lege, in originale aut in versione omne libro
jam celebre. Sed hodie Russo, Polacco, Rumeno, Japonico, ... publica in
suo lingua libro originale, et non solo libro scholastico.
Adoptio, ut inter-lingua, de lingua vive-nte, non es possibile, per
causa de politica.
Plure homo propone latino classico. Vide:
Prof. A. VALDARNINI de universitate de Bologna, _Necessità d'una lingua
internazionale e lo studio del latino_, in "Primo congresso
internazionale latino", Roma a. 1903.
Hic congresso exopta:
«ut sermo latinus inter gentes universas communis habeatur, et
adhibeatur ad humanitatis commercium fovendum, augendum, tenendum».
Ibi congressista loque neolatino, ut italico, franco, provenzale, rumeno
et castellano, raro latino classico.
Et periodico "Phenix" in London, "Praeco latinus" in Philadelphia, "Vox
urbis" in Roma sustine idem idea; sed primo mori in anno 1892, et
secundo in 1902. Ergo adoptio de latino fi semper minus probabile.
Multo auctore, in vario tempo, propone lingua plus vel minus
artificiale.
Vir doctissimo, L. COUTURAT professore in Universitate de Toulouse, in
libro _La Logique de Leibniz_, Paris a. 1901 p. 608, expone:
_Ars magna_ de R. LULLE a. 1234-1315,
_Ars magna sciendi_ de KIRCHER a. 1669,
_Ars signorum_ de DALGARNO a. 1661,
_Philosophical language_ de WILKINS a. 1668.
Postea Leibniz diffuse et profunde stude hic subjecto; sed nihil
publica. Suo studio mane sepulto in bibliotheca de Hannover, usque ad
nostro die; primo Dr Vacca in RdM., postea Couturat in libro citato
detege et publica parte de hic manuscripto. Suo importantia magis pate,
et denique L. COUTURAT publica «Opuscules et fragments inédits de
Leibniz», Paris a. 1903, p. XVI-682, qui contine studio de Leibniz,
summe praetioso per constructione de Vocabulario philosophico.
Libro, nunc edito, L. COUTURAT et L. LEAU _Histoire de la langue
universelle_, Paris a. 1903 p. XXI+571, expone 56 projecto de lingua
artificiale.
Me hic breve loque de magis noto.
* * * * *
SCHLEYER, parrocho, in anno 1881 publica «Volapük», qui es
transformatione de lingua anglo, ut ipse dice.
Hic lingua regularisa declinatione de nomen, et conjugatione de verbo;
sed introduce nullo simplificatione rationale, qui Leibniz propone. Ille
contine immenso numero de conventione. Volapük sume in principio multo
diffusione. In anno 1888 habe 283 club, et 25 periodico, in omne parte
de terra. Plure conventione produce discordia inter sectatore, et post
congresso de Paris, in anno 1889, hic lingua decade et mori.
* * * * *
ZAMENOF, doctore in medicina, in anno 1887, publica «Esperanto», qui
contine simplificatione de genere (§ 2), de persona (§ 4). Sed non
contine simplificatione de caso (§ 1), de numero (§ 3) et de modo (§ 5).
Esperanto reduce toto grammatica ad 16 regula, de qui nullo es
necessario.
Et Esperanto contine magno numero de conventione, etsi minus quam
Volapük, et in grammatica, et in vocabulario.
Esperanto habe hodie 9 periodico; jam plure sectatore propone
simplificatione; ille seque via de Volapük.
* * * * *
Et notato-digno es «Langue bleue» de L. BOLLACK. Ibi, ex numero de
littera, nos vide si voce es vacuo, vel pleno, ut in sinense.
* * * * *
Nunc me loque de projecto cum pauco novo conventione.
* * * * *
«Lingua» de HENDERSON, a. 1888, es vocabulario latino, cum grammatica de
typo Anglo.
* * * * *
Dr Daniel ROSA simplifica idea de Henderson, et publica «Le
nov-latin»(2). Ille dice:
(3) _Bollettino dei Musei di Zoologia e Anatomia comparata della Regia
Università di Torino_, a. 1890.
«Le nov-latin non requirer pro le sui adoption aliq congress. Omnes
poter, cum les praecedént regulas, scriber statim ist lingua. ... Sic
faciént ils vol valide cooperar ad le universal adoption de ist
international lingua et simul ils vol poter star legé ab un mult major
numer de doctes quam si ils haber scribé in quilibet alter vivént
lingua».
Ex hoc resulta quod Novlatin conserva pauco flexione (plurale in _-s_, 2
participio, ...), et es quam proximo ad "lingua rationale" de Leibniz et
ad "latino sine flexione".
Domino George J. HENDERSON, in periodico, «The lingua franca of the
future», qui ille dirige, a. 1901, perfectiona suo projecto, et dice:
«Quare debe-nos non facere ex i Latine Lingue i Internationale Lingue?
«I Latine Lingue esse nimis difficile. Post decem annes de studere,
pauce discipules pote, legere facile, vel scribere accurate, vel loquere
aliquantulum i Latine Lingue.»
(_I_ articulo, plurale in _-s_, desinentia _-e_, ...)
* * * * *
Societate, qui habe nomen "Akademi internasional de lingu universal"
adopta vocabulo magis internationale, et post multo studio et
discussione, in a. 1902, publica "Idiom neutral".
«Idiom neutral es usabl no sole pro scribasion, ma et pro parlation.»
Ergo, principio de maximo internationalitate duce ad vocabulo latino.
* * * * *
"The American Philosophical Society" in an. 1887, pro formatione de
inter-lingua, propone abolitione de articulo (ut in latino et in russo),
de flexione de adjectivo, de caso de nomen, de persona et modo de verbo,
et, in modo dubitativo, abolitione de plurale de nomen, et tempo de
verbo.
* * * * *
Quaestio de inter-lingua nihil habe hodie commune cum ideographia, qui
nos adopta in «Formulario mathematico».
Ideographia es synthese; cum auxilio de pauco idea primitivo, circa
decem, ille compone idea complexo; ita _hodie_ cum ideographia nos pote
scribe toto mathematica, sed mathematica solo.
Lingua artificiale es analyse. Ille decompone idea de lingua commune in
alio idea plus simplice.
Si in futuro analyse et synthese invicem conveni, ut duo exercito de
minatore, qui labora tunnel ex duo extremitate, tunc «Lingua rationale»
et «Characteristica universale» de Leibniz fore idem.
* * * * *
Vide quoque:
H. DIELS, _Ueber LEIBNIZ und das Problem der Universalsprache_, Berlin
Sitzungsberichte d. Akademie, a. 1899 p. 579.
Prof. G. BELLAVITIS, _Pensieri sopra una lingua universale e su alcuni
argomenti analoghi_, Mem. dell'Ist. Veneto; vol. XI a. 1862, pag. 33-74.
* * * * *
_Délégation pour l'adoption d'une langue auxiliaire internationale_, qui
porta firma de numeroso scientiato de plure universitate, academia,
repraesentante de societate philosophico, de commercio et de sport. Ipse
delegatione declara:
«Lingua auxiliaria internationale
«1. posse servi ad relatione de vita sociale, de commercio, et de
scientia et philosophia.
«2. Omne homo, qui habe instructione elementare medio, facile disce hic
lingua.
«3. Hic lingua es proprio ad nullo natione.»
Prof. L. COUTURAT explica hic idea in opusculo: «_Pour la langue
internationale_» a. 1901. Periodico _Revue des questions scientifiques_,
Bruxelles a. 1902, t. 1, p. 547-586 reproduce scripto de Couturat, cum
observatione de P. P. PEETERS. Couturat responde in t. 2, pag. 213-230.
Nullo objectione de PEETERS vale per "Latino sine flexione".
CONCLUSIONE
Articulo, qui praecede, proba quod flexione de nomen et de verbo non es
necessario.
«Se, invece di dizionario latino, noi cercare ogni parola in dizionario
italiano, noi scrivere in italiano senza flessione.»
Articulo, qui seque, contine versione litterale de plure propositione
Germano et Anglo. Ille proba, quod suppressio de omne flexio non redde
discurso magis longo.
G. PEANO.
PRINCIPIO DE PERMANENTIA
Exercitio de Latino recto
[Omne vocabulo es inflexibile.
Vocabulario latino commune, qui contine nominativo et genitivo de nomen,
infinito de verbo, contine omne vocabulo de hic Nota, aut identico, aut
cum abbreviatione:
a) Si termina in _-a_, muta _-a_ in _-are_, vel in _-ari_, et es
infinito de verbo.
b) Si termina in _-e_, muta _-e_ in _-ere_, vel _-i_, et es infinito de
verbo;
vel muta _-e_ in _-is_ et es genitivo de nomen,
» » » _-es_ et es nominativo de nomen.
In loco de _me_, _te_, _aliquo_, quaere _ego_, _tu_, _aliquis_.
c) Si termina in _-i_, muta _-i_ in _-ire_, vel _-iri_, et es infinito
de verbo.
d) Si termina in _-o_, muta _-o_ in _-us_ _-um_ _-u_, et est nominativo
de nomen, vel muta _-o_ in _-i_ et es genitivo de nomen.
e) _es_ quaere _sum_, _esse_.]
Aliquo auctore introduce numero negativo, fracto et imaginario, ut
applicatione de regula, qui ille dice "principio de permanentia". Hic
principio varia aliquanto prope diverso auctore.
Prof. SCHUBERT, in _Encyclopädie der Mathematischen Wissenschaften_,
t. 1, p. 11, expone hic principio sub forma claro sed erroneo. Ille
dice:
«_Princip der Permanenz_ in viererlei besteht:
«erstens darin, jeder Zeichen-Verknüpfung, die keine der bis dahin
definierten Zahlen darstellt, einen solchen Sinn zu erteilen, dass die
Verknüpfung nach denselben Regeln behandelt werden darf, als stellte sie
eine der bis dahin definierten Zahlen dar;
«zweitens darin, eine solche Verknüpfung als Zahl im erweiterten Sinne
des Wortes zu definieren und dadurch den Begriff der Zahl zu erweitern;
«drittens darin, zu beweisen, dass für die Zahlen im erweiterten Sinne
dieselben Sätze gelten, wie für die Zahlen im noch nicht erweiterten
Sinne;
«viertens darin, zu definieren, was im erweiterten Zahlengebiet gleich,
grösser und kleiner heisst».
Versione:
«Principio de permanentia ex quatuor articulo consta:
«1. ad omne signo-reunione(3) qui non repraesenta numero qui nos ante
defini, nos tribue tale senso, ut nos posse tracta reunione juxta idem
regula, velut si hic reunione repraesenta numero, qui nos ante defini;
«2. nos defini hic reunione ut numero, in lato senso de vocabulo, et ita
nos extende idea de numero;
«3. nos demonstra quod per numero in lato senso omne theorema vale, ut
per numero in non lato senso;
«4. nos defini, quod in campo de numero lato nos voca aequale, maiore et
minore».
(4) Vide «Latino sine flexione» § 6 j).
Si omne regula et omne theorema super numero in senso non lato subsiste
super numero in senso lato, necesse es ut numero in senso lato es
identico ad numero in senso non lato. Nam duo ente es inter se aequale,
si omne proprietate de uno es quoque proprietate de alio. Hoc es ipse
definitione de aequalitate:
«Eadem sunt quorum unum in alterius locum substitui potest, salva
veritate» (Leibniz, vide Formulario § 2, P4·3) quod me traduce: «Plure
ente es idem, si nos posse substitue uno de ille in loco de altero, et
veritate (de propositione) es salvo».
Quum nos trans-i ab uno specie de numero ad specie magis lato, semper
debe omitte aliquo proprietate.
Relatione a + b > a es vero per numero absoluto, falso per numero cum
signo.
Si nos trans-i ab numero imaginario simplice ad quaternione, nos omitte
proprietate commutativo de producto.
Ergo definitione, qui nostro auctore da de 0, de numero negativo, de
fracto, etc. basa super principio absurdo. Hic definitione non es
legitimo.
* * * * *
Nos repete idem critica ad _Elementare Arithmetik und Algebra_ de ipse
Prof. SCHUBERT (Leipzig a. 1899, pag. 33) qui enuntia ipse principio cum
primo et secundo articulo.
* * * * *
HANKEL, _Theorie der Complexen Zahlensysteme_, Leipzig, a. 1867, quum
nancisce «principio de permanentia de lege formale», dice in pagina 5:
«Wenn b > c ist, ... die Subtraction ist ... unmöglich. Nichts hindert
uns jedoch, dass wir in diesem Falle die Differenz (c - b) als ein
Zeichen ansehen, welches die Aufgabe [(c - b) + b = c] löst und mit
welchem genau so zu operiren ist, als wenn es eine numerische Zahl aus
der Reihe 1, 2, 3 ... wäre».
Versione: «Si b > c es, subtractione es ne-possibile. Nihil obsta tamen,
quod nos in hic caso considera differentia (c - b) ut signo, qui resolve
quaestio, et cum qui exacte nos debe opera, ut si ille numero ex serie
1, 2, 3, ... es».
Contra hic modo de ratiocinio Gauss antea dice:
«Quodsi quis dicat, triangulum rectilineum aequilaterum rectangulum
impossibile esse, nemo erit qui neget. At si tale triangulum impossibile
tanquam novum triangulorum genus contemplari, aliasque triangulorum
proprietates ad illud applicare voluerit, ecquis risum teneat? Hoc esset
verbis ludere seu potius abuti». (Formul. pag. 219). Versione:
«Si aliquo dice quod triangulo rectilineo aequilatero rectangulo
impossibile es, nemo tunc es qui nega. Sed si aliquo velle contempla
tale triangulo impossibile tanquam novo genere de triangulo, et applica
ad illo omne alio proprietate de triangulo, an qui tene riso? Hoc es
lude cum verbo, vel potius abute».
* * * * *
Prof. CHRISTAL, _Algebra_, Edinburgh a. 1889, p. 6, re-dice idea de
Hankel:
«Assuming that the quantity +a - b always exists, we may show that the
laws of commutation and association hold».
Versione:
«Si nos assume quod quantitas +a - b semper existe, posse monstra quod
lege de commutatio et associatio mane».(4)
(5) Nota analogia grammaticale de «show» cum «monstra».
Hoc es, si nos assume absurdo, non solo nos posse deduce lege de
commutatione, sed omne lege qui nos velle, nam ex absurdo omne
consequentia deriva.
Non sub forma de principio absoluto, sed sub forma de consilio, lice
quod nos dice:
«Quum nos introduce novo calculo, es multo utile quod nos sume
nomenclatura et notatione ita ut novo calculo fie quam maxime simile ad
calculo antiquo».
Me dice «quam maxime simile»; «identico» es absurdo.
Ita Algebra, qui indica cum idem signo +, ×, = ... operatione non solo
inter numero integro, sed etiam inter fracto, es magno progresso super
longo methodo de antiquo graeco; Algebra reduce toto libro X de Euclide,
noto per magnitudine et difficultate, ad uno pagina, qui professore sole
doce in uno lectione in Instituto tecnico (Vide Formul. p. 111).
In saeculo ultimo plure auctore indica cum idem signo +, sive summa de
algebra, sive resultante de vectore, et ita construe Calculo geometrico,
qui in respecto ad Geometria, es idem progresso quam Algebra in respecto
de Arithmetica graeco.
Tunc principio de permanentia idem es ac principio generale de
oeconomia, qui subsiste in linguistica, didactica et politica, ut
demonstra E. MACH, in capitulo de «natura oeconomico de progresso
physico» de _Populär-wissenschaftliche Vorlesungen_, Leipzig a. 1903.
G. PEANO.
[ Transcriber's Note:
The following is a list of corrections made to the original.
The first line is the original line, the second the corrected one.
c) Ad verbo activo adde _re_, et te habe passivo.
c) Ad verbo activo adde _-re_, et te habe passivo.
_ge_, _gi_ » _ghe_, _ghi_, » _gue_, _gui_ » _ge_,
_ge_, _gi_ » _ghe_, _ghi_, » _gue_, _gui_, » _ge_,
internationale latino", Roma a. 1903.
internazionale latino", Roma a. 1903.
contine simplicatione de genere (§ 2), de persona (§ 4). Sed non
contine simplificatione de genere (§ 2), de persona (§ 4). Sed non
Et notato-digno es «Langue bleu» de L. BOLLACK. Ibi, ex numero de
Et notato-digno es «Langue bleue» de L. BOLLACK. Ibi, ex numero de
Prof. L. COUTURAT explica hic idea in opusculo: Pour la langue
Prof. L. COUTURAT explica hic idea in opusculo: «_Pour la langue
Articulo, qui praecede, proba quod flexio de nomen et de verbo non es
Articulo, qui praecede, proba quod flexione de nomen et de verbo non es
cum abreviatione:
cum abbreviatione:
«erstens darin, jeder Zeichnen-Verknüpfung, die keine der bis dahin
«erstens darin, jeder Zeichen-Verknüpfung, die keine der bis dahin
definierten Zahlen darstellt, einem solchen Sinn zu erteilen, dass die
definierten Zahlen darstellt, einen solchen Sinn zu erteilen, dass die
Verknüpfung nach denselben Regeln behaldelt werden darf, als stellte sie
Verknüpfung nach denselben Regeln behandelt werden darf, als stellte sie
eine des bis dahin definierten Zahlen dar;
eine der bis dahin definierten Zahlen dar;
«drittens darin, zu beweisen dass für die Zahlen im erweiterten Sinne
«drittens darin, zu beweisen, dass für die Zahlen im erweiterten Sinne
grösser und minor heisst».
grösser und kleiner heisst».
«Wenn b > c ist, ... die Substraction ist ... unmöglich. Nichts hindert
«Wenn b > c ist, ... die Subtraction ist ... unmöglich. Nichts hindert
Versione: «Si b > c es, subtractione es ne-possible. Nihil obsta tamen,
Versione: «Si b > c es, subtractione es ne-possibile. Nihil obsta tamen,
physico» de _Populär Vorlesungen_, Leipzig a. 1903.
physico» de _Populär-wissenschaftliche Vorlesungen_, Leipzig a. 1903.
]
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