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York, 1881. - 120. f. (1), pp. 275. tional scientific series, xxxi.)

2. Diffraction.

(Interna- ungen durch Reflexion. Inaug. - Diss. [1870]. 80. pp. 42. Plate.

Lommel, E. Die Fraunhofer'schen Beugungserscheinungen in elementarer Darstellung. Dresden, 1868. 8o. f. (1), pp. 47. Plates.

Rijke, P. L. Responsio ad quaestionum: "Praecipuae exponantur Naturae leges, quae in luminis diffractione observantur, earumque nexus cum aliis optices phaenomenis." [Lugduni Batavorum, 1833.] 4o. pp. 55. Plate. 3. Refraction.

Bermann, E. O. Ueber die scheinbare Veränderung des Orts und der Gestalt durch einfache Brechung. Stolp, 1863. 4°. f. (1), pp. 28. Plates

and table.

Ueber die durch einfache Brechung an einer ebenen Grenzfläche bewirkte scheinbare Aenderung des Orts und der Gestalt. Theil ii. Liegnitz, 1866. 4°. pp. 23. Plates.

Krumme, W. Die Brechung des Lichts an Kugelflächen. Duisburg, 1866. 4o. f. (1), pp. 20.

Plate.

4. Spectrum Analysis. Ängström, A. J. Recherches sur le spectre solaire spectre normal du soleil. Upsal, 1868. 4o, and Atlas of plates, obl. fo.

Kirchhoff, G. Untersuchungen über das Sonnenspectrum und die Spectren der chemischen Elemente. Th. i., ii. Berlin, 1866, '63. 2 pt. 4o.

Plates.

"Besonderer Abdruck aus den Abhandlungen der Königl.

Akademie der Wissenschaften zu Berlin, 1861-62."
Theil i., 3er Abdruck. Bd. together.

Lockyer, J. N. Studies in spectrum analysis. New York, 1878. 120. pp. xii., 258. Plates and wdcts. (International scientific series, xxiii.) Schellen, H. Die Spectralanalyse in ihrer Anwendung auf die Stoffe der Erde und die Natur der Himmelskörper. 20 Aufl. Braunschweig, 1871. 80. pp. xvi., 619. Portrs., plates and wdcts. Contents:- Die kunstlichen Quellen der höchsten Wärmeund Lichtgrade. Die einfachen und zusammengesetzten Spectra in ihrer Anwendung auf die Stoffe der Erde. Spectralanalyse in ihrer Anwendung auf die Himmelskörper. Spectrum analysis in its application to terrestrial substances and the physical constitution of the heavenly bodies; translated from the 2d German ed. by Jane and Caroline Lassell, edited by W. Huggins. London, 1872. 8°. pp. xxvi., 662. Plates

and wdcts.

Die

5. Velocity of Light. Kuckuck, A. Die Geschwindigkeit des Lichtes. Berlin, 1867. 4o. pp. 35. Lovering, J. On the velocity of light and the sun's distance. [New Haven, ] 1863. 80. pp. 12. "From the American journal of science, &c., vol. xxxvi., Sept. 1863."

Michelson, A. A. Experimental determination of the velocity of light, made at the U. S. naval acad., Annapolis. Washington, 1880. 4o. PP. 109-145. (Astron. papers Amer. Ephemeris, vol. i., pt. 3.)

6. Wave Theory.

Airy, G. B. On the undulatory theory of optics. New ed. London, etc., 1866. sm. 80. pp. viii., 159. Plates.

Briot, C. Essais sur la théorie mathématique de la lumière. Paris, 1864. 8o. pp. xxii., 132. Cauchy, L. Mémoire sur la dispersion de la lumière. Prague, 1836. 4o. pp. iv., 236. Glan, P.

Ueber die absoluten Phasenveränder

Berlin,

Honigmann, J. Analytische Betrachtung der Aethervibrationen im elementaren polarisirten Lichtstrahle. Düsseldorf, 1848. 4o. pp. 17+. Plate. Lessing, Elementare Darstellung der Gesetze der Fortpflanzung des Lichtes in einem isotropen Mittel. Prenzlau, 1863. 4o. pp. 24.

Meibauer, R. Demonstratio complurium Kummeri theorematum, quæ agunt de generalibus, et infinite tenuibus luminis fascibus, praecipue in crystallis. Diss. inaug. Berolini, 1861. 4o. pp. 20.

Theorie der geradlinigen Strahlensysteme des Lichts. Bromberg, 1864. 4o. f. (1), pp. 34. Plate.

Probabilities.

(See also Insurance.)

Airy, G. B. On the algebraical and numerical theory of errors of observations and the combination of observations. Cambridge, 1861. 8o. pp. xvi., 118.

Bernoulli, J. Ars conjectandi; opus posthumum; accedit tractatus de seriebus infinitis, et epistola Gallicè scripta de ludo pilæ reticularis. Basilea, 1713. 4°. ff. (2), pp. 35+, 306. Plates.

Chase, P. E. Remarks on the mathematical probability of accidental linguistic resemblances, and on the comparative etymology of the Yoruba language; with a mathematical. note by J. E. Oliver. [Philadelphia, 1869.] 4°. Pp. (25)-72.

"From the Transactions of the Amer. philos. society, vol.

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Condorcet, M. J. A. N. de C., marquis de. Élémens du calcul des probabilités, et son application aux jeux de hasard, à la loterie, et aux jugemens des hommes; avec un Discours sur les avantages des mathématiques sociales, et une notice sur Condorcet. Paris, An. XIII. (1805). sm. 8°. pp. (iii.)–xii.,

210.

Cournot, A. A. Exposition de la théorie des chances et des probabilités. Paris, 1843. 80. pp. viii., 448. Plate.

De Morgan, A. An essay on probabilities and on their application to life contingencies and insurance offices. London, 1838. 120. pp. xviii., 306, xl. Fries, J. F. Versuch einer Kritik der Principien der Wahrscheinlichkeitsrechnung. Braunschweig, 1842. 8o. pp. vi., f. (1), pp. 236. Traité élémentaire de calcul des Paris, 1864. 8o. pp. xi.,

Lacroix, S. F. probabilités. 4o éd. 308. Plate.

[Laplace, P. S., marquis de.] Quatrième supplément à la théorie analytique du probabilités. Paris, 1825.] 4o. f. (1), pp. 28.

Bd. with the 1808 ed. of Lagrange's "Equations numériques." [Lubbock, J. W., and J. E. D. Bethune]. On probability. London, 1830. 80. pp. 64. (Society for the diffusion of useful knowledge, Library of useful knowledge, no. 78, 79.) Michaelis, G. Mémoire sur la probabilité du jeu de rencontre. Berlin, 1846. 4°. pp. 31-36. 4o. Moivre, A. de. The doctrine of chances; or, A method of calculating the probabilities of events in play. London, 1738. 4o. ff. (2), pp. xiv., 256.

[Montmort, P. R. de.] Essay [sic] d'analyse sur les jeux de hazard. 2o éd. Paris, 1713. 4o. pp. xlii., 414, f. (1). Plates.

Quetelet, (L.) A. (J.). Letters on the theory of probabilities, as applied to the moral and political

sciences; translated by O. G. Downes. London, | of certain formulæ. [London, 1825.] 8°. PP. 1849. 8o. pp. xvi., 309.

Quetelet, (L.) A. (J.). Popular instructions on the calculation of probabilities; translated by R. Beamish. London, 1839. 120. Pp. xvi., 157. Plate.

Ruffini, P. Riflessioni critiche sopra il saggio filosofico intorno alle probabilità del Sig. conte Laplace. Modena, 1821. 8o. ff. (2), pp. 183+.

Todhunter, I. A history of the mathematical theory of probability, from the time of Pascal to that of Laplace. Cambridge, etc., 1865. 8o. pp. xvi., 624.

Venn, J. The logic of chance, an essay on the foundations and province of the theory of probability. London, etc., 1866. sm. 80. pp. xxvii.+, 370.

Same. 2d ed. London, 1876. 8°. PP.

xxvii., 488.
Whitworth, W. A. Choice and chance: two
chapters of arithmetic; with an appendix containing
the algebraical treatment of permutations and com-
binations newly set forth. Cambridge, 1867. sm.
80. pp. vi.+, 160.

a. Least Squares.

115-120.

"Philosophical magazine," lxvi., no. 328.
Lettered" Mathematical pamphlets.".

Drobisch, M. W. Observationes analyticae.
Lipsiae, 1831. 2 pt. in 1. 4o. pp. 21.
Contents:-1. Theorematis polynomialis nova demonstratio
universalis. -2. De numerorum Bernoullianorum computa-
tione.
Die algebraischen und
transcendenten Funktionen, durch die Methode der
unbestimmten Coefficienten dargestellt. Weilburg,
1858. 4o. pp. 25.

Eickemeyer,

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Gudermann, C. Allgemeiner Beweis des polyGauss, K. F. Méthode des moindres carrés : nomischen Lehrsatzes ohne die Voraussetzung bimémoires sur la combinaison des observations; trad-nomischen. Cleve, 1825. 4o. f. (1), pp. 44, f. (1). uits par J. Bertrand. Paris, 1855. 8o. ff. (4), Hindenburg, C. F., editor. Sammlung compp. 167. binatorisch-analytischer Abhandlungen. Leipzig, 1796-1800. 2 v.

Gerling, C. L. Die Ausgleichungs- Rechnungen der practischen Geometrie; oder, Die Methode der kleinsten Quadrate mit ihren Anwendungen für geodätische Aufgaben. Hamburg, etc., 1843. 80. xix.+, 409. Plates and tables.

80.

Contents:- Tetens, J. N. Formula polynomiorum. Klügel, G. S. Bemerkung über den polynomischen Lehrsatz. Kramp, C. Polynomial- und andere Aufgaben combinatorisch-analytisch bearbeitet. -Pfaff, J. F. Sätze über Potenzen und Produkte gewisser Reihen. Bemerkungen über Coefficientengleichungen.-Hindenburg, C. F. HöchstZech, J. Zur Methode der kleinsten Quadrate. wichtiger Einfluss der Combinationslehre auf die Analysis. Tübingen, 1857. 4°. ff. (2), pp. 43.

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235. Plates.

Salmon, G. Lessons introductory to the modern higher algebra. 2d ed. Dublin, 1866. 80. pp. xv., 296.

Series.

ii. Hindenburg, C. F. Entwickelung gebrochener Func-
tionen in lokal- und combinatorischen Zeichen. - Trembley,
J. Verfahren das allgemeine Glied der wiederkehrenden
Reihen zu finden. - Hindenburg, C. F. Vergleichung ver-
schiedener, combinatorischer und anderer Verfahren. - Klügel,
G. S. Erläuterungen seines Beweises des polynomischen Lehr-
Localformeln für höhere Differentiale.
satzes. -Pfaff, J. F.
Auflösung einiger verwickeltern Coefficientengleich-
ungen.— Über Lagrange's neuen Beweis seiner Rever-
sionsformel. Hauber, K. F. Auflösung des Elevations-
problems für Gleichungen.
Von Wegschaffung der Ir-
rationalitäten aus Gleichungen. - Rothe, H. A. Über Per-
mutationen und ihre Anwendnung auf das Eliminationsprob-
würdiger Reihen. - Kramp, C. Verschiedene combinatorisch-
analytisch bearbeitete Aufgaben.
Über die Summen
der Potenzen der natürlichen Zahlenreihe, vermittelst der Com-

lem.

Lokalausdrücke von Potenzen besonders merk

binationenlehre.

Jacobi, A. Kurze Bemerkungen über einige Puncte der Analysis. Naumburg, 1848. 4o. f. (1), PP. 47. Treating of negatives, imaginaries, series and differential equations. Jürgensen, C. De certo quodam serierum sumHauniæ, [1832]. 4o. f. (1), (See also Algebra, Calculus, and Finite Dif- mabilium genere. pp. 23, f. (1). Landen, J. Observations on converging series, occasioned by Mr. Clarke's translation of Mr. Lorgna's treatise on the same subject. 1781. 4o. f. (1), pp. 28, f. (1), pp. 27, 32. Lorgna, A. M. De casu irreductibili tertii gra dus et seriebus infinitis exercitatio analytica. Vero næ, 1776. 4o. pp. 116.

ferences.) Die arithmetischen Reihen höherer Ordnungen und die figurirten Zahlen. Oels,

Anton,

1850. 4o. pp. 30.

Barfuss, F. W. Die Entwickelungsmethoden der gemeinen mathematischen Analisis. 20 Ausg. Berlin, 1869. 80. pp. xiv., 229. (In his Lehrbuch der mathematischen Analysis, 1er Theil.)

London,

Specimen de seriebus convergentibus. Veronæ, 1775. 4o. pp. viii., 110.

A dissertation on the summation of infinite converging series with algebraic divisors; translated, with notes and an appendix, by H. Clarke. London, 1779. 4o. pp. xiv., 221+. Plates.

Björling, E. G. Doctrinæ serierum infinitarum exercitationes. Pars i., ii. Upsaliae, 1846. 2 pt. 4o. "Ex Actis reg. societ. scient. Upsal." Two copies. Chrzescinski, Ueber höhere arithmetische Reihen, logarithmische und Kreis-Functionen. Rastenburg, 1832. sm. 4o. f. (1), pp. 17. Supplement to [his] Summation of series, Davies, T. S. Thoughts on the demonstration [and] Remarks on Mr. Landen's observations on

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Der polynomische Lehrsatz für beliebigen Exponenten. Lissa, [1845]. 4o. f. (1), pp. xxiii., f. (1). Scheibert,

Herleitung der Allgemein

Diophantus Alexandrinus. Arithmeticorvm libri sex, et de nvmeris mvltangvlis liber vnvs; cvm commentariis C. G. Bacheti & obseruationibus D. P. de Fermat; accessit Doctrinæ analyticæ inuentum nouum, collectum ex varijs eiusdem D. de Fermat epistolis Tolosa, 1670. fo. ff. (7), pp. 64, 341, 48.

Greek text, with Latin translation and notes. Zahlentheorie. Frankfurt a. O., 1850. 4o. f. (1), Emsmann, A. G. Über eine Aufgabe aus der PP. 36. Erler, De periodis, quæ compositione formarum quadraticarum ejusdem determinantis fiunt. Züllichau, 1847. 4o. f. (1), pp. 16.

Eine zahlentheoretische Abhandlung. Zül

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gültigkeit der Binomialformel, sowie der logarith-lichau, 1847. 4o. f. (1), pp. 19. mischen Fundamentalreihe durch die Hauptsätze aus der Methode der unbestimmten Koeffizienten. bing, 1862. 4o. pp. 20.

El

Schlömilch, O. Die Reihenentwickelungen der Differential- und Integralrechnung. Dresden, 1851. 4o. f. (1), pp. 39. Plate.

Schmidt, J. P. Von der Convergenz und Divergenz der unendlichen Reihen. Köln, 1867. 4°. f. (1), pp. 21.

Schnürlein, L. C. Erweiterung und Verallgemeinerung der bisher zwischen den trigonomet

rischen und anderen Functionen und zwischen den Koefficienten der niedrigsten Glieder in den Summen der Potenzen ganzer Zahlen bekannt gewesenen Relationen. Hof, [1833]. 4°. pp. 16.

Schwarz, A. Die Lehre von den einfachen Reihen. Siegen, 1863. 4o. pp. 17.

Taylor, T. The elements of a new arithmetical notation and of a new arithmetic of infinities, with appendix. London, 1823. 8°. pp. vii.+, 151.

Theory of Numbers

(including Indeterminate and Diophantine Analysis). (See also Algebra.)

Arendt, G. Éléments de la théorie des nombres complexes de la forme a+bv-1, d'après un cours de M. Dirichlet. Berlin, [1863]. 4o. f. (1), pp. 43.

Barlow, P. Demonstration of a curious numerical proposition: [The equation xyzn is always impossible, either in integers or fractions, for every value of n greater than 2.] [London], 1810. 80. pp. 13.

From Nicholson's "Journal of natural philosophy, chemistry and the arts," xxvii., Nov. 1810. Lettered " Mathematical pamphlets."

Fülle, Zur Zahlen-Theorie. 1867. 4°. f. (1), pp. 20.

Ratibor,

Gauss, C. F. Theorematis fundamentalis in doctrina de residuis quadraticis demonstrationes et ampliationes novae. Gottingae, 1818. 4o. pp. 20. Genochi, A. Intorno ad alcune somme di cubi nota. Roma, 1866. 4o. pp. 10. "Estratta dagli Atti dell' Accademia pontificia de nuovi lincei

(tomo xix., anno xix., sessione ii., del 7 Gennaio 1866)."

Gill, C. Application of the angular analysis to the solution of indeterminate problems of the second degree. New York, etc., 1848. 120. pp. 90, f. (1).

Gorgas, R. Ueber Lösung diophantischer Gleichungen zweiten Grades in ganzen Zahlen. Magdeburg, 1867. 4o. f. (1), pp. 32. Götting, Untersuchungen über die biquadratischen Reste und Nichtreste der Primzahlen von der Form 4n+1. Halle, 1861. 40. f. (1), PP. 23.

Kummer, E. E. De residuis cubicis disquisitiones nonnullae analyticae. Vratislaviae, [1842]. 4o. f. (1), pp. 18, f. (1).

Lejeune-Dirichlet, P. G. Vorlesungen über Zahlentheorie; herausgegeben und mit zusätzen versehen von R. Dedekind. 20 Aufl. i. Braunschweig, 1871. 8o. pp. 288. Meyer, C. F. Potsdam, 1867. 4o.

Ein diophantisches Problem. f. (1), pp. 14.

Poinsot, L. Réflexions sur les principes fondamentaux de la théorie des nombres. Paris, 1845. 40. ff. (2), pp. 101.

From the "Journal de mathématiques pures et appliquées," tome x., Jan. 1845. Poselger, F. J. Ueber einige merkwürdige Eigenschaften periodischer Divisionsreihen. Berlin, 1830. 4o. f. (1), pp. 16.

meinen Theorie der höhern Congruenzen, deren Schönemann, (T.). Grundzüge einer allgeModul eine reelle Primzahl ist. Brandenburg, 1844.

Elemente der Zahlen-Theorie. Halle, 1855. 8o. pp. vi., 467.

An elementary investigation of the theory of numbers, with its application to the indeterminate and diophantine analysis, the analytical and geometrical division of the circle, and several other prob-4°. f. (1), pp. 50. lems. London, 1811. 80. pp. xxiv., f. (1), pp. Schwarz, H. 507. Bertram, F. H. T. Einige Sätze aus der Zahlenlehre. Berlin, 1849. 4o. f. (1), pp. 17. Boncompagni, B. Intorno alla risoluzione delle equazioni simultanee x2+h=y2, x2—h=z2. Roma, 1855. 80. f. (1), pp. 22.

"Estratta dagli Annali di scienze matematiche e fisiche, Aprile, 1855."

Cantor, G. De aequationibus secundi gradus indeterminatis.-Diss. inaug. Berolini, [1867]. 4°. f. (1), pp. 25+.

De transformatione formarum ternariarum quadraticarum. Halis Saxonum, [1869]. 4o. f. (1), pp. 12, f. (1).

Tenner, G. W. Einige Bemerkungen über die Gleichung ax2+1=y2. Merseburg, [1841]. 4o. PP. 12.

Weirauch, K. Untersuchungen über eine Gleichung des ersten Grades mit mehreren Unbekannten. Dorpat, 1869. 4o. pp. 43+, f. (1).

Trigonometry.

(See also Crystallography, Logarithms, and Triangles.)

Bourdon, P. L. M. Trigonométrie rectiligne et sphérique. Paris, 1854. 8o. pp. 159.

Bourdon, P. L. M. Same. Nouv. éd., revue par C. Brisse. Paris, 1877. 8o. ff. (2), pp. 127. Briot, C., et C. Bouquet. Leçons nouvelles de trigonométrie. 3e éd. Paris, 1858. 8o. ff. (2), pp. 224.

and tables.

Cagnoli, A. Trigonometria piana e sferica. Ed. 2. Bologna, 1804. 4o. pp. xx., 533. Plates Trigonométrie rectiligne et sphérique; traduite par N. M. Chompré. 2e éd. Paris, 1808. 4o. f. (1), pp. xvi., 508, ff. (2). Plates and tables. Caswell, J. A brief (but full) account of the doctrine of trigonometry, both plain and spherical. London, 1685. fo. f. (1), pp. 17.

Bd. with Wallis's "Algebra.'

Cavalieri, B. Trigonometria plana, et sphærica, linearis, & logarithmica; hoc est tam per sinuum, tangentium & secantium multiplicationem ac diuisionem iuxta veteres, quam per logarithmorum simplicem ferè additionem iuxta recentiores. Bononiæ, 1643. 4°. pp. 16, 71, ff. (52). Frontisp. & plate. Chauvenet, W. A treatise on plane and spherical trigonometry. 7th ed. Philadelphia, 1869. 8°. pp. 256.

Chrześciński, Auflösungen einiger trigonometrischen Aufgaben. Lyck, 1849. 4o. pp. 19. Copernicus (Polish Koppernigk), N. Die Trigonometrie; übersetzt von Menzzer. Halberstadt, [1857]. 4o. f. (1), pp. 21. Plate.

De Morgan, A. Trigonometry and double algebra. London, 1849. 120. pp. xi., 167. Plate. Emerson, W. The elements of trigonometry, containing the properties, relations, and calculations of sines, tangents, secants, &c., the doctrine of the sphere, and the principles of plain and spherical trigonometry. 2d ed., with tables. London, 1764. 80. pp. viii., 240, ff. (141). Plates.

Greenleaf, B. Elements of plane and spherical trigonometry; with practical applications. Improved electrotype ed. Boston, 1867. 120. ff. (2), PP. 108, 62.

Gützlaff, K. Ueber das Auflösen trigonometrischer Aufgaben. Marienwerder, 1866. 4o. f. (1), pp. 19. Plate.

Hassler, F. R.

Elements of analytic trigonom-
etry, plane and spherical. New York, 1826.
Plate.
Pp. 192.

120.

Another copy bd. with his "Geometry."
Heydenreich, F. F. Transformationen der
Formeln aus der ebenen und sphärischen Trigonom-
etrie. Tilsit, 1826. 4o. f. (1), pp. 13.

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Le Cointe, I. L. A. Leçons sur la théorie des fonctions circulaires et la trigonométrie. Paris, 1858. 8°. pp. xii., 387.

Lefébure de Fourcy, L. E. (L.). Élémens de trigonométrie; contenant la trigonométrie rectiligne, la trigonométrie sphérique, et quelques applications à l'algèbre. 2e éd. Paris, 1831. 80. ff. (2), pp. 119+. Plate.

Elements of trigonometry, plane and spherical; translated from the last French ed. by F. H. Smith; with tables. Baltimore, 1870. 8°. pp. vi., 138, xvi., 150.

Loomis, E. Elements of plane and spherical trigonometry, with their applications to mensuration, surveying and navigation. 14th ed. York, 1859. 80. pp. 193.

New

Same. 25th ed. New York, 1867. 80.

pp. 193.
Contains "Tables of logarithms, and of sines and tangents"
bd. at end.

Oliver, J. E., L. A. Wait and G. W. Jones. A treatise on trigonometry. Ithaca, [N. Y.], 1881. 80. pp. vi., f. (1), pp. 102.

Olney, E. Elements of trigonometry, plane and spherical. New York, 1872. 8o. f. (1), pp. 113,

88.

Oughtred, W. Trigonometria, hoc est modus computandi triangulorum latera & angulos, ex canone mathematico traditus & demonstratus; unâ cum tabulis sinuum, tangent. & secant, &c. Londini, 1657. 4°. ff. (7), pp. 36, 234, ff. (5).

[Peacock, G.] A syllabus of a course of lectures upon trigonometry and the application of algego. ff. (3), pp. 120. bra to geometry. 2d ed. Cambridge, etc., 1836.

Plates.

Peirce, B. An elementary treatise on plane & spherical trigonometry, with their applications to navigation, surveying, heights and distances, and spherical astronomy. 3d ed. Boston, 1845. 8°. pp. iv., f. (1), pp. 449. This copy lacks Pp. 1-10. Same. Revised ed. 1. 8o. pp. vi., f. (1), pp. 359. Serret, J. A. Traité de trigonométrie. 4o éd. Paris, 1868. 8o. pp. xi., 336.

Boston, etc., 1861.
Plates.

Simpson, T. Trigonometry, plane and spherical; with the construction and application of logLon-arithms; with an appendix on spherical projections. Philadelphia, 1810. 80. pp. 125. Plates.

Hopkins, W. Elements of trigonometry. don, 1833. 80. pp. 68. (In Society for the diffusion of useful knowledge. Library of useful knowledge.)

Lettered "Mathematics. vol. ii."

Snowball, J. C. The elements of plane and spherical trigonometry; with the construction and use of tables of logarithms both of numbers and for angles. 10th ed. Cambridge, etc., 1863. 8°. pp.

Hymers, J. A treatise on plane and spherical trigonometry, and on trigonometrical tables and log-x., 240. arithms, with a selection of problems and their solutions. 3d ed. Cambridge, 1847. 8o. pp. viii., 216.

Plates.

Kayer, E. Ein Beitrag zur Trigonometrie. Erfurt, 1863. 4o. ff. (2), pp. 21.

Sperling, J. Analytische Miscellen. Gumbinnen, 1863. 4o. f. (1), pp. 15.

Treating of trigonometry, compound interest, Diophantine analysis, and cubic equations. Stade, 1. Einige trigonometrische EleKribben, J. J. Versuch einer neuen Begründ-mentaraufgaben für Schüler. Zeitz, 1862. 4o. ung des Positiven und Negativen in der Trigonom- PP. 10. etrie. Elberfeld, 1832. 4o. f. (1), pp. 15. Plate. Todhunter, I. Trigonometry for beginners; Lacroix, S. F. Traité élémentaire de trigono- with examples. London, etc., 1866. 120. metrie rectiligne et sphérique, et d'application de 192. l'algèbre à la géométrie. Se éd. Paris, 1827. 80. pp. xii., 311. Plates.

Same. 11 éd. Paris, 1863. 8o. pp. xvi.,

299. Plates.

pp. viii., Wilson, R. A system of plane and spherical trigonometry; to which is added a treatise on logarithms. Cambridge, 1831. 8°. pp. xv., 330, f. (1).

Young, J. R. Elements of plane and spherical

trigonometry; with their applications to the principles of navigation and nautical astronomy. 2d ed. London, 1841. 120. pp. xii., 250.

a. Goniometry.

Bredow, F. (C. F.). De potestatibus sinuum et cosinuum, quae secundum sinus aut cosinus multiplicium arcuum procedunt, explicate. Olsnae, 1829. 4o. ff. (2), pp. 40.

Brinkmann, Beiträge zur analytischen Trigonometrie. Halle, 1859. 4o. f. (1), pp. 22. Förstemann, W. A. Inquisitio in plurimorum angulorum functiones goniometricas. Halae, 1820. 4o. f. (1), pp. 25+.

Grebe, E. W. Ein Schema zur Erleichterung des Elementarunterrichtes in der Trigonometrie. Cassel, 1840. 4o. pp. 8.

Koppe, C: F. A.

De theoremate trigonometrico sin (A+B)=sin A. cos B+cos A. sin B cos (A+B)= cos A. cos B-sin A. sin B. Mariaeinsulae, [1828]. 4o. pp. 16.

Roehr,

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