Leibnizens Mathematische Schriften, Herausgegeben Von C.I. Gerhardt ...

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H.W. Schmidt, 1855 - 180 Seiten
. 1860 edition.: ...pro ipso aequipollens (ut volunt) pondus C ut 1 celeritate ut 2, quod ascendat usque ad C seu ad altitudinem 4 pedum. Itaque solo descensu ponderis A duarum librarum ex altitudine unius pedis 2AH, substitutoque aequipollente, effecimus ascensum librae unius ad pedes quatuor, quod est duplum prioris. Ergo tantundem virium lucrati sumus, seu motum mechanicum perpetuum effecimus, quod utique absurdum est. Nec refert, an per motuum leges actu efficere possimus hanc substitutionem; nam inter aequipollentia etiam mente tuto fieri substitutio potest. Quamquam etiam varias rationes excogitaverimus, quibus actu tam propo quam velis efficeretur, ut vis tota corporis A transferretur in corpus C, antea quiescens, sed quod nunc (ipso A ad quietem redacto) sit solum in motu positum. Unde fieret, ut pro pondere bilibri celeritatis ut 1 successura esset libra una celeritatis ut 2, si haec aequipollerent; unde absurdum oriri ostendimus. Neque ista sane inania sunt, aut in logomachiis consistunt, sed in machinis et motibus comparandis maxiinum usum habent. Nam si quis vim habeat ab aqua vel animalibns vel alia causa, per quam corpus grave centum librarum in motu constanti conservetur, quo intra minuti temporis quartam partem absolvere possit circulum horizontalem diametri triginta pedum; alius vero ejus loco eodem tempore duplum pondus nonnisi dimidium circulum constanter absoivere praestet, minore impensa, idque tibi velut in lucrum imputet; deceptum te ac dimidia virium parte frustratum scito. Sed nunc fugatis erroribus, veras et saue admirandas Naturae leges paulo distinctius in Schediasmatis hujus parte secunda proponemus. XVI, SPECIMEN DYNAMICUM PRO ADMIRANDIS NATURAE LEGIBUS CIRCA CORPORUM VIRES ET MUTUAS ACTIONES DETEGENDIS ET AD SUAS CAUSAS REVOCANDIS. Pars II. Natura corporis, imo substantiae in universum non satis cognita effecerat (quod jam attigimus) ut insignes quidem philosophi nostri temporis, cum corporis notionem in sola extensione...
 

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Seite 60 - Caetera qui vitae servaret munia recto More, bonus sane vicinus, amabilis hospes, Comis in uxorem, posset qui ignoscere servis Et signo laeso non insanire lagenae, Posset qui rupem et puteum vitare patentem.
Seite 132 - Tom. 4. Man weiss nicht, wer die Herausgabe besorgt hat. Sie ist sehr lückenhaft und unvollständig; nur die wenigsten Briefe sind ohne Auslassungen abgedruckt, besonders aber fehlen viele Briefe Joh. Bernoulli's vom Jahre 1699 an. Die Lücken in den Briefen Joh. Bernoulli's sind...
Seite 129 - ... erläutert; von ihm genöthigt giebt denn auch Job. Bernoulli zu Anfang des Jahres 1707 nach seiner Methode eine Construction der transformirten Curve, wobei er zugleich noch zeigt, dass sich Kreise angeben lassen, zwischen denen als Gränzen die transformirte Curve liegt. Durch die Abhandlung Job. Bernoulli's über den Motus reptorius war Leibniz bewegen worden, Idee.n über die Erzeugung der Curven mittelst Bewegung , die vielleicht schon seit langer Zeit in seinen Manuscripten niedergelegt...
Seite 299 - Briefe. problème, mihi scribit, me paroist des plus curieux et des plus jolis que l'on ait encore proposé, et je serois bien aise de m'y appliquer; mais pour cela il seroit nécessaire que vous me l'envoyassiez réduit à la Mathématique pure, car la Physique m'embarasse etc.). Intérim idem Tibi accidit, quod illis qui detegunt thesaurum, cujus tarnen pretium nondum aestimare possunt, quod etiamnum inclusus est cistis et capsis, quibus vero reseratis, eum longe pretiosiorem deprehendunt quam...
Seite 386 - PROBLEMA NOVUM, ad cujus Solutionem Mathematici invitantur. " Datis in piano verticali duobus punctis A et B, " assignare mobili M viam AMB, per quam gravitate " sua descendons, et moveri incipiens a puncto A, bre" vissimo tempore perveniat ad alterum punctum B...
Seite 99 - Pensionarii Wittii scriptum nondum satis quaerere licuit inter chartas; non dubito tamen, quin sim tandem reperturus, ubi vacaverit. Sed vix aliquid in eo novum Tibi occurret, cum fundamentis iisdem ubique insistat, quibus cum alii viri docti jam erant usi, turn Paschalius in Triangulo Arithmetico, et Hugenius in diss. de Alea, nempe ut medium Arithmeticum inter aeque incerta sumatur; quo fundamento etiam rustici utuntur, cum praediorum pretia aestimant, et rerum fiscalium curatores, cum reditus...
Seite 5 - ... assez pour nous , pour en approfondir en peu de jours tout le secret, témoin quantité de pièces que nous publiâmes ensuite sur le sujet des infiniment petits.
Seite 21 - Hue accessit etiam maeror ex Tui paulo post offensione conceptus, qui me a scribendo aliquanto diutius retraxit: quo vehementius enim illam semper abhorrui nequitiam, quo quis ultro laedit eum cui gratias deberet, hoc acerbius dolebam, me in ejus apud Te suspicionem incidiese.
Seite 128 - Jahres 1704 in eine schwere Krankheit verfiel und zugleich mit der Rückkehr in sein Vaterland umging, so geschah es , dass erst , nachdem er die durch den Tod seines Bruders erledigte Professur der Mathematik an der Universität zu Basel angetreten hatte, seine Methode zur Lösung des ia Rede stehenden Problems in der Act.
Seite 364 - Hugenianis: nude ego quoque dissinuilavi talia mihi ex Te esse nota, quae ipse attingere noluerat, praesertim cum sese novam Newtoniani Operis editionem moliri scripserit: quam tarnen dissuasi, quod de ea cogitare Newtonum ipsum intellexissem. Et suspicor Hugeniana ibi adjicere voluisse. Quod si iterum scribat, videbo an commode efficere possim, ut haec nobis communicet; praesertim si editionis cogitationem deposuerit.

Autoren-Profil (1855)

Gottfried Wilhelm Leibniz, one of the last real polymaths, was born in Leipzig. Educated there and at the Universities at Jena and Altdorf, he then served as a diplomat for the Elector of Mainz and was sent to Paris, where he lived for a few years and came into contact with leading scientists, philosophers, and theologians. During a trip to England, he was elected to the Royal Society; he made a visit to Holland to meet Spinoza. Back in Germany he became librarian to the Duke of Brunswick, whose library was the largest in Europe outside the Vatican. From there he became involved in government affairs in Hanover and later settled in Berlin at the court of Queen Sophie Charlotte of Prussia. Leibniz was involved in the diplomatic negotiations that led to the Hanoverian succession to the English throne. From his university days he showed an interest in mathematics, logic, physics, law, linguistics, and history, as well as theology and practical political affairs. He discovered calculus independently of Newton and had a protracted squabble about which of them should be given credit for the achievement. The developer of much of what is now modern logic, he discovered some important physical laws and offered a physical theory that is close to some twentieth-century conceptions. Leibniz was interested in developing a universal language and tried to master the elements of all languages. Leibniz corresponded widely with scholars all over Europe and with some Jesuit missionaries in China. His philosophy was largely worked out in answer to those of other thinkers, such as Locke, Malebranche, Bayle, and Arnauld. Although he published comparatively little during his lifetime, Leibniz left an enormous mass of unpublished papers, drafts of works, and notes on topics of interest. His library, which has been preserved, contains annotations, analyses, and often refutations of works he read. The project of publishing all of his writings, undertaken in the 1920s by the Prussian Academy, was delayed by World War II but was resumed thereafter. It is not likely that the project will be completed in the twentieth century.

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