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Title: De Latino sine Flexione; Principio de Permanentia Author: Giuseppe Peano Release date: April 9, 2011 [eBook #35803] Language: Latin Credits: Produced by David Starner, Jana Srna and the Online Distributed Proofreading Team at http://www.pgdp.net (This book was produced from scanned images of public domain material from the Google Print project.) *** START OF THE PROJECT GUTENBERG EBOOK DE LATINO SINE FLEXIONE; PRINCIPIO DE PERMANENTIA *** Produced by David Starner, Jana Srna and the Online Distributed Proofreading Team at http://www.pgdp.net (This book was produced from scanned images of public domain material from the Google Print project.) [ Transcriber's Notes: Every effort has been made to replicate this text as faithfully as possible, including inconsistencies in spelling and hyphenation; changes (corrections of spelling and punctuation) made to the original text are listed at the end of this file. Italic text has been marked with _underscores_. Letter-spaced text has been marked with ~tildes~. Greek letters theta and phi have been reproduced as [theta] and [phi]. ] 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. ] *** END OF THE PROJECT GUTENBERG EBOOK DE LATINO SINE FLEXIONE; PRINCIPIO DE PERMANENTIA *** Updated editions will replace the previous one—the old editions will be renamed. Creating the works from print editions not protected by U.S. copyright law means that no one owns a United States copyright in these works, so the Foundation (and you!) can copy and distribute it in the United States without permission and without paying copyright royalties. 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