‎Mathématiques‎

‎"KÄSTNER, ABRAHAM GOTTHELF.‎

‎Begyndelsesgrunde af Arithmetik, Geometrie og plane og sphæriske Trigonometrie. Oversat efter fjerde forøgede Oplag af Jacob Wolf. Mathem. Begyndelsesgr. 1 Deels 1ste Afdeling.‎

‎Kiøbenhavn, Gyldendals Forlag, 1788. 8vo. Indbundet i et samtidigt lidt slidt hellæderbind. Enkel stregforgyldning og fem ophøjede bind på ryggen. Forgyldt rygtitelfelt delvist slidt væk. Enkel blindtrykt ramme på permerne. Forgyldte initialer ""F. S. S."" på forpermen. Brugsspor ved kapitæler og false. Hjørner stødte. Enkelte spredte brunpletter og noter. (24),542,(1) pp.‎

‎"L'HOPITAL (L'HOSPITAL) LE MARQUIS DE.‎

‎Solution d'un Probléme Physico-Mathematique.‎

‎(Paris, Jean Boudot, 1703). 4to. Without wrappers. Extracted from ""Mémoires de l'Academie des Sciences. Année 1700"". Pp. 9-21 and 1 folded engraved plate.‎

‎"L'HÔPITAL (L'HOSPITAL), (GUILLAUME FRANÇOIS ANTOINE DE). - FIRST TREATISE ON THE DIFFERENTIAL CALCULUS.‎

‎Analyse des infinite Petits. Suivie d'un nouveau Commentaire pour l'intelligence des endroits les plus difficiles de cet Ouvrage. Par l'Autheur du Guide des jeunes Mathématiciens dans l'étude des Lecons de Mathematique de M. l'Abbé de la Caille.‎

‎Avignon, Veuve Girard & Francois Seguin, 1768. 8vo. Contemp. full mottled calf. Wear to top of spine. Richly gilt spine, titlelabel with gilt lettering. (2),XXXI,380 pp. and 8 folded engraved plates. On verso of title-page a stamped exlibris. On inside frontcover an engraved exlibris ""John Cookney"". Internally clean, printed on good paper.‎

‎"L'HÔSPITAL, (GUILLAUME FRANÇOIS ANTOINE) MARQUIS DE. - CARTESIAN GEOMETRY APPLIED TO THE CONIC SECTIONS.‎

‎Traité Analytique des Sections Coniques et de leur Usage pour la Resolution des Equations dans les Problêmes tant déterminez qu'indéterminez. Ouvrage Posthume.‎

‎Paris, Jean Boudot et Jean Boudet fils, 1707. 4to. Contemporary full calf. A bit of cracking to front hinges, so that cords are seen, but cover not loosening. Spine with 6 raised bands, richly gilt compartments. Wear to top of spine. Two small old paperlabels, one to upper compartment, one to frontcover. Covers slightly rubbed. (4),459,(5) pp. Large woodcut vignette on titlepage, 2 other vignettes, one engraved , one in woodcut. 32 folded engraved plates and one smaller folded plate (Fig. A). An old owners stamp on flyleaf. Internally clean and fine. A few tiny brownspots. Wide-margined and printed on good paper.‎

‎"LA CHAPELLE, (ABBÉ JEAN-BAPTISTE).‎

‎Abandlung von den Kegelschnitten von den andern krummen Linien der Alten und der Cycloide nebst ihren Anwendungen auf verschiedene Künste. Uebersetzt und mit Anmerkungen versehen von Johann Lorenz Böckmann. Mit 11. Kupfertafeln.‎

‎Carlsruhe, Michael Mackler, 1771. Contemp. hcalf. Richly gilt spine. Titlelabel with gilt lettering. A paperlabel pasted on top of spine. Stamps on title-page. (32),520,(2) pp. (Inhalt pp. 1-24 bound at end) and 11 folded engraved plates. A few brownspots.‎

‎First German edition of la Chapelle's ""Traité des sections coniques et autre courbes ancienne..."", 1750. (Poggendorff I, 1338)‎

Referenz des Buchhändlers : 51159

‎"LA GRANGE (LAGRANGE), JOSEPH LOUIS.‎

‎Sur L'Integration des Equations à differences partielle du premier ordre. - [A MASTERPIECE OF ANALYSIS]‎

‎(Berlin, C.F. Voss, 1774). 4to. Uncut with wide margins, without wrappers as issued in ""Nouveaux Memoires de L'Academie Royales des Sciences et Belles- Lettres"", Année MDCCLXXII, pp. 353-372.‎

‎First edition of a work which is a breakthrough in the theory of ""First Order Partial Differential Equations"", generalizing the method of variation of parameters for solving differential equations. "" The oldest theory of integration of partial differential equations of the first order are due to Lagrange"" it is based on the fundamental fact that the most general solution of such differential equations can be calculated with the help of differentiations and eliminations if a complete integral of the differential equationn is known"" - ""This problem (of partial differential equations) had only been lightly touched on by Clairaut, Euler, d'Alembert, and Condorcet. Lagrange wrote: ""Finally I have just read a memoir that Mr de Laplace presented recently.....This reading aweakened old ideas that I had on the same subject and resulted in the following investigations...(which constitute) a new and complete theory."" Laplace wrote on 3 February 1778 that he considered Lagrange's essay ""a masterpiece of analysis, by the importence of the subject, by the beauty of method, and by the elegant manner in which it is represented."" (DSB). - Parkinson, Breakthroughs 1774 M.‎

Referenz des Buchhändlers : 39049

‎"LA GRANGE (LAGRANGE), JOSEPH LOUIS.‎

‎Two Papers. 1. Sur une Nouvelle Espece de Calcul rélatifs à différentiation & à l'intégration des quantités variables. - 2. Sur la Forme des Racines Imaginaires des Equations. - [A NEW FOUNDATION OF THE CALCULUS]‎

‎(Berlin, Ch. Fr. Voss, 1774). 4to. Large uncut copy, broadmargins, without wrappers as issued in ""Nouvaux Memoires d l'Academie Royale des Sciences et Belles-Lettres. Année 1772."" pp. 185-221 and pp. 222-258.‎

‎First edition of these two important papers. In the first paper ""Sur une Nouvelle Espece de Calcul..."" he made the most ambitious attempt to rebuild the foundation of the calculus. The paper is in fact an outline of his ""Theorie des functions"", issued later in 1797.""This work greatly impressed Lacroix, Condorcet and Laplace. Based on the analogy between powers of biniminals and differentials, it is one of the sources of the symbolic calculuses of the nineteenth century. A typical example of Lagrange's thinking as an analyst in this sentence taken form the memoir: ""Although the principle of the analogy (between powers and diffrentials) is nor self-evident, nevertheless, since the conclusions drawn from it are not thereby less exact, I shall make use of it to discover various theorems...""""(Jean Itard in DSB). The second paper ""Sur la Forme...""When D'Alembert red the paper he gave the following respons:""Your demonstration on imaginary roots seem to me to leave nothing to be desired, and I am very much obliged to you for the justice you have rendered to mine, which, in fact, has the minor fault (pwerhaps more apparant than real) of not being direct, bu which is quite simple and easy. D'Alembert was alluding to his Cause de vents (1747).""(DSB).‎

Referenz des Buchhändlers : 38985

‎"LA GRANGE (LAGRANGE), JOSEPH LOUIS. - MAXIMA AND MINIMA.‎

‎Sur les Courbes Tautochrones. (and ) Nouvelles Réflexions sur les Tautochrones. - [THE CALCULUS OF VARIATIONS]‎

‎(Berlin, Haude et Spener, 1767 and Berlin, Ch. Fr. Voss, 1774). 4to. Without wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles Lettres"" Tome XXI, pp. 364-380 and "" Nouveau Mémoires..."", pp. 97-122.‎

‎Both first edition in the journal form. Huygens proved Geometrically in 1659 that the tautochrone was a cycloid curve. This solution was later used to attack the problem of the Brachistochrone curve. Jacob Bernoulli solved the problem by using calculus in a paper from 1690, which for the first time used the term 'integral'. Both Lagrange and Euler loked for an analytical solution to the problem. Lagrange, in the papers offered here, developed a formal calculus based on the analogy between Newton's theorem and the successive differentiations of the product of two functions. He also communicated this to Eule in a letter written in Latin slightly before the Italian publication. In a letter to D'Alembert in 1769 Lagrange confirmed that this method of maxima and minima was the first fruit of his studies - he was only 19 when he divised it - and that he regarded it as his best work.A paper by Leonhard Euler:Éclaircissement plus détailles sur La generation et Propagation du Son et sur la Formation de L'Echo"" Berlin Academy Royale 1767"" in first edition withbound.‎

Referenz des Buchhändlers : 39044

‎"LACHLAN, R.‎

‎On Systems of Circles and Spheres. Communicated by A. Cayley. Received February 23, - Read March 11, 1886.‎

‎(London, Harrison and Sons, 1887). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1886 - Vol. 177 - Part II. Pp. 481-625. Clean and fine.‎

‎First edition of an importent study on the geometry of circles, treating circles as vectors and using basic ideas from linear algebra.‎

Referenz des Buchhändlers : 44042

‎"LACROIX, (SYLVESTRE FRANCOIS).‎

‎Weitere Ausführung zu Lacroix's Geometrie oder versuch einer Geometrie über die ebnen und krummen Oberflächen, nebst Anfangsgründen der Perspektive zum besonern Gebrauch für Archotekten, und für die ausübenden Messkünstler überhaupt. Aus dem Französis...‎

‎Berlin, Heinrich Frölich, 1806. Contemp. hcalf, spine gilt. Stamp on titlepage. XXXVI,166,(2) pp. and 10 folded engraved plates. Titlepage brownspotted. Some scattered brownspots. Plates clean.‎

‎First German edition of the author's ""Essai de Geometrie sur les Plans et les Surfaces Courbes."" Lacroix's works on geometry were highly successfull, and the textbook on geometry ran through 19 editions. Lacroix received his education by CasparMonge.‎

Referenz des Buchhändlers : 40109

‎"LACROIX, S.-F.‎

‎Traité élémentaire de Calcul Différentiel et de Calcul intégral. Cinquieme Édition. Revue, corrigée et augmentée.‎

‎Paris, Bachelier, 1837. 8vo. Cont. hcalf. Richly gilt back. Back worn and loosening. Block and covers tight. XVI,734,(2) pp., 5 folded engraved plates. Some browning throughout.‎

‎Fifth edition of Lacroix's famous work, which was used in his teaching, particularly at the École Polytechnique as a popularization of his great mathematical contribution ""Traité du Calcul differentiel 1797-98.""‎

Referenz des Buchhändlers : 28569

‎"LAGRANGE, (LA GRANGE), JOSEPH LOUIS. - A FUNDAMENTAL MEMOIR IN THE THEORY OF NUMBERS‎

‎Sur La Solution des Problemes Indéterminés du Second Degré.‎

‎(Berlin, Haude et Spener, 1769). 4to. No wrappers as issued in ""Memoires de L'Academie Royale des Sciences et Belles Lettres"", tome XXIII, pp. 165-310. Clean and fine.‎

‎"LAGRANGE, (LA GRANGE), JOSEPH LOUIS. - LAGRANGE'S CONTINUED FRACTIONS.‎

‎Additions au Mémoire Sur la Résolution des Équations Numériques.‎

‎(Berlin, Haude et Spener, 1770). 4to. Clean and fine without wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", Tome XXIV, pp. 111-180. With titlepage to ""Classe de Mathematique"".‎

‎"LAGRANGE, JOSEPH LOUIS.‎

‎Nouvelle Methode pour Résoudre les Équations littérales par les moyen des Séries.‎

‎(Berlin, Haude et Spener, 1770). 4to. No wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XXIV, pp. 251-326. Clean and fine.‎

‎"LAGRANGE, JOSEPH LOUIS.‎

‎Nouvelle Méthode pour Résoudre les Problemes indéterminés en Nombre entiers.‎

‎(Berlin, Haude & Spener, 1770). 4to. No wrappers, as issued in ""Memoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XXIV, pp. 181-250. Clean and fine.‎

‎First edition. An importent paper in the Theory of Numbers. The year before Lagrange gave a complete solution to the problem of giving all integral solutions of a special general equation (Sur la Solution des Problemes Indéterminés du Second Degré). In this paper he sets up a simpler proof of the same problem. - Cajori calls Lagrange ""One of the greatest mathematicians of all times"". - Poggendorff I:1344.‎

Referenz des Buchhändlers : 35218

‎"LAGRANGE, JOSEPH LOUIS.‎

‎Sur L'Élimination des Inconnues dans les Équations.‎

‎(Berlin, Haude et Spener, 1771). 4to. No wrappers, as issued in ""Mémoires des l'Academie Royale des Sciences et Belles-Lettres"", tome XXV, pp. 303-318. Fine and clean.‎

‎"LAGRANGE, JOSEPH LOUIS.‎

‎Sur la Force des ressorts pliés. (+) Sur le Probleme de Kepler. (2 Memoirs).‎

‎(Berlin, Haude et Spener, 1771). 4to. No wrappers, as issued in ""Mémoires des l'Academie Royale des Sciences et Belles-Lettres"", tome XXV, pp. 167-203 a. pp. 204-233 a. 1 folded engraved plate. With titlepage to ""Classe de Mathematique.""‎

‎"LAGRANGE, JOSEPH LOUIS.‎

‎Théorie des fonctions analytiques, contenant les principes du calcul différentiel, dégagés de toute considération d'infiniment petits ou d'évanouissans, de limites ou de fluxions et réduits à l'analyse algébrique des quantités finies. - [FOUNDATION OF ANALYSIS]‎

‎Paris, De L'Imprimerie de la République, An V (1797). 4to. Uncut and partially unopened. Contemporary manuscript-binding. Provenance: With the exlibris of Stillman Drake - one of the most renown Galileo scholars. Some light brown spotting through out. Otherwise a very good copy. (4),VIII,276 pp.‎

‎"LAMBERT, JOHANN HEINRICH [NON-EUCLIDEAN GEOMETRY].‎

‎Observations Trigonometriques. - [FORESHADOWING NON-EUCLIDEAN GEOMETRY]‎

‎(Berlin, Haude & Spener, 1770). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles Lettres"", tome XXIV, pp. 327-354 and 1 engraved plates.‎

‎"LAMBERT, JOHANN HEINRICH.‎

‎Abhandlung Von dem Gebrauche der Mittagslinie Beym Land=und Feldmessen.‎

‎(München, 1863). 4to. Bound in recent hcloth. Issued in ""Abhandlungen der Churfürstlichen Baierischen Akademie der Wissenschaften"", Bd. I, pp. (3-)54, and 1 folded engraved plate. Fine and clean.‎

‎First edition. - Poggendorff I:1357.‎

Referenz des Buchhändlers : 38812

‎"LAMBERT, JOHANN HEINRICH.‎

‎Mémoire sur quelques Propriétés remarquable des Quantités transcendentes circulaires et logarithmiques. - [LAMBERT'S CONTINUED FRACTIONS AND IRRATIONALITY OF ""N""]‎

‎(Berlin, Haue et Spener, 1768). 4to. No wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XVII, pp. 265-322 and 1 folded engraved plate.‎

‎First edition, journal issue. ""One of Lambert's most famous results is the proof of the irrationality of ""N"" and e. It was based on the continued fractions, and two such fractions still bear his name.""(DSB).""Euler's work on continued fractions was used by Johann Heinrich Lambert.....to prove that if x is a rational number (not 0), then ex and tan x cannot be rational. He thereby proved not only that ex for positive integral x is irrational, but that all rational numbers have irrational natural (base e) logarithms.From the result of tan x, it follows tha, since tan (n/4)= 1, that neither n/4 nor n can be rational.Lambert actually proved the convergencee ofthe continued fraction expansion for tan x. (Morris Kline). - Struik, A Source Book, Chapter V, No 17).‎

Referenz des Buchhändlers : 38981

‎"LAMBERT, JOHANN HEINRICH.‎

‎Observations Analytiques.‎

‎(Berlin, C.F. Voss, 1772. 4to. Without wrappers as extracted from ""Nouveaux Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", Annee 1770, pp. 225-244 and 1 engraved plate.‎

‎First edtion. In this paper Lambert starts from a simple problem for a function of 2 variables x and y, then proceeds to expand the method to more difficult differentiations.‎

Referenz des Buchhändlers : 39084

‎"LAMBERT, JOHANN HEINRICH.‎

‎Solution générale et absolue du problème de Trois Corps, moyennant des suite infinies. - [THE THREE BODY PROBLEM]‎

‎(Berlin, Haude et Spener, 1769). 4to. Without wrappers as extracted from ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XXIII. Pp. 353-364.‎

‎First edition. In this paper Lambert shows that one can solve the classic three body problem by the use of infinite series. This allows numerical approximations, but Lambert notes that nearly nothing in the problem (excepts for the classic easier cases) allows for shortcuts in these calcualtions. More even, approximations of neighboured streches of the orbit to be calculated may even require different approximatuion series, so as to renderr even tables more or less or at least rather ineffective.‎

Referenz des Buchhändlers : 39081

‎"LAMBERT, JOHANN HEINRICH.‎

‎Sur la Méthode du Calcul Intégral.‎

‎(Berlin, Haude et Spener, 1769). 4to. Without wrappers as extracted from ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome 18, pp. 441-484.‎

‎First edition. In this paper Lambert gives a classification of integrals, with the objective that one could then list or tabulate solutions to the respective classes.‎

Referenz des Buchhändlers : 39086

‎"LAMBERT, JOHANN HEINRICH. - ESTABLISHING A MATHEMATICAL THEORY OF ORDER.‎

‎Essai de Taxéométrie ou sur la mesure de l'Ordre.‎

‎Berlin, C.F. Voss, 1772. 4to. Without wrappers as extracted from ""Nouveaux Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", Annee 1770. With titlepage to 1770 with engraved vignette. Pp. 327-342.‎

‎First appearance of this importent paper in which Lambert established a mathematical theory of order in all sorts of classifications. He treats the problem of order and its measures not only in relation to natural history or any domain of particulars, but abstractly as a problem of epistemology in general. He attempts to create a new mathematics of ordered systems and to measure by a fraction the elements to which any collection of items departed from the ordered system, and he carries his mathematical ideal even into taxonomy and systematics.‎

Referenz des Buchhändlers : 44755