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Alexander Macfarlane.

Bibliography of quaternions and allied systems of mathematics online

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INTERN Al ION AL ASSOCIAl^ION



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PROMOTING THE STUDY OF QUATERNIONS AND ALLIED
SYSTEMS OF MATHEMATICS. :Mc:^~i^}J[



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BIBLIOGRAPHY



OF



QUATERNIONS AND ALLIED SYSTEMS OF
MATHEMAlTCS;Ai v:;:t



HY



ALEXANDER MAGFARLANE,

D.Sc, LL.D., F.R.S.K., •. :

GENKHAL SliCRF.TAliy OF THE ASSOCIATION.



DUBLIN:

PHI N TED AT THE UNIYEIISITY PRESS,
BY rONSONBY AND GIBBS. ,.

1904.



(L^



INTERNATIONAL ASSOCIATION

PKOMOTING THE STUDY OF QUATKMIONS AND ALLIED
SYSTEMS OF MATHEMATICS.



BIBLIOGRAPHY



OF



QUATERNIONS AND ALLIED SYSTEMS OF
MATHEMATICS.



BY

ALEXANDER MACFARLANE,

D.Sc, LL.D,, F.R.S.E.,

GENERAL SECRETARY OF THE ASSOCIATION.



OF THE

UNIVERSITY

OF



DUBLIN:

PRINTED AT THE UNIVERSITY PRESS,

BY PONSONBT AND GIBBS.

1904.




SEfiEttA^



K



Printed by Ponsonby & Gibbs, Dublin University Press'.



PREFACE.



The International Catalogue of Scientific Literature places
Quaternions as one division (83), and Ausdehnungslehre and
Vector Analysis as another division (84) of Universal Algebra
(8). The proximate divisions on either side are General Theory
■of Complex Numbers (82) and Matrices (85). These are the
main and allied branches of Mathematics comprised in this
Eibliography. I have also included publications in which
vector ideas and methods are applied.

The contributions of each writer are arranged chronologically,
the date taken being that of the volume in which the contribu-
tion appears. The mark f is printed before the first posthumous
publication.

In the use of contractions for the names of serial publications,
I have followed the system of the Jahrbuch fiber die Fortschritte
der Mathematik; and I have likewise followed it in avoiding the
use of Koman numerals. Where the number of the pages of a
book is indicated by the sum of two numbers, the former
number refers to the preface, and the latter to the text.

The following contractions are used : M.P. for Collected
Mathematical Papers ; S.P. for Collected Scientific Papers ;
G-.W. for Gesammelte Werke ; Pr. for Programmabhandlung.



7G36?



( 4 )

For facilities in the preparation of this Bibliography, I
wish to thank the Librarian of the University of Michigan,
and, for special assistance, the following members of the
Association : Combebiac, Dickstein, van Elfrinkhof, Grassmann,
Joly, and Schlegel. Almost every living writer has responded
to the request to make the list of his own contributions
complete.

ALEXANDER MACEAELANE.

17th November, 1903



BIBLIOGRAPHY



QUATERNIONS AND ALLIED MATHEMATICS.



Max Abraham.

1899 Ueber einige bei Schwingungsproblemen auftretende Diffe-

rentialgleicbungen. Math. Ann. 52, 81-112.

1901 Geometriscbe Grundbegriffe. Encykl. d. math. Wiss., ^2,

3-47.

Robert Edgar Allardice.

1889 Note on a formula in quaternions. Edinb. M. S. Proc, 7,
8-12.

MoRiz All6.

1892 Ueber die Ableitung der Gleichungen der drehenden Bewe-
gung eines starren Korpers nach der Grassmann'schen
Analyse. Prag Math. Ges., 64-69.

Alexandre All^gret.

1862 Essai sur le calcul des quaternions de M. W. Hamilton. Paris :

Gauthier-Villars. 7+72. 4°.

1868 The above reviewed by M. Prouhet. Nouv. Ann., (2), 2,

333-334.

Edwyn Anthony.

1881 Notes on quaternions. Messenger (2), 10, 66-72.

Jean-Robert Argand,
1806 Essai sur une maniere de representer les quantites imagi-
naires dans les constructions geometriques. (Anonymous.)
Paris : 78. Small 8°.



( 6 )

1814 Essai sur unc maniere de representer les quantites imagi-

naires dans les constructions geometriques. Ann. de
Math, de Gergonne, i, 133-147.

1815 Reflexions sur la nouvelle theorie des imaginaires, suivies

d'uiie application a la demonstration d'un theorems
d'analyse. Ann. de Math, de Gergonne, 5, 197-209.

tl874 Essai sur une maniere, etc. 2° edition, precedee d'une
preface par M. J. Hoiiel et suivie d'un appendice con-
tenant des extraits des Annales de Gergonne relatifs a
la question des imaginaires. Paris : Gauthier-Villars.
19+126. 8°.

1881 Imaginary Quantities. The second edition of the above

translated into English by A. S. Hardy. New York : Van

Nostrand.

Badokff.

1877 Beitrag zur Geometrie des Kreises und der Kugel Pr.

Baden,

Alfked Baker.

1901 The principles at the base of quaternion analysis. Trans.
E. S. C, Section III, (2), 7, 17-20.

Valentin Balbin.
1888 Elementos de calculo de los cuaterniones y sus aplicaciones
principales a la geometria al analysis y a la mecanica.
Buenos Aires. 19 + 359. 8°.

Sir PiOBERT Stawell Ball.
1876 The theory of screws : a study in the dynamics of a rigid

body. Dublin : Hodges, Foster, & Co. 24 + 194. 8°.
1893 The discussion on quaternions. Nature, 58, 391.
1900 A treatise on the theory of screws. Cambridge University

Press. 19 + 544. Royal 8°.

L. Ballauff.

1844 Beitriige zur syetematischen Darstellung der allgemeinen

Arithmetik. Grunert Arch., 5, 269 — .

1845 Ueber die Potenzen mit imaginaren Exponenten. Grunert

Arch., 6, 409—



( 7 )

KiCHAED BaLTZER,

1883 Ueber die Einfiihrung der complexen Zahlen. J, fiir
Math., 95, 87-92.

Napol^on-Eenest Bakisien.
1901 Application de la methode de Grassmann k une demonstration
de deux theoremes de geometric differentielle. Nouv.
Ann., (4), 1.

William Beebe.

1890 The orbit of Swift's comet 1880 V determined by Gibbs's
vector method. By W. Beebe and A. W. Phillips.
Astronomical Journal, 9, 113-117 and 121-124.

R. Bebz.

1875 Ueber conforme Abbildung von Mannigfaltigkeiten hoherer

Ordnung. Schlomilch Z., 20, 258-270.
1896 Zur Theorie der Vectoren und Quaternionen. Schlomilch Z.,

51, 85-57 and 65-84.

GiusTO Bella viTis.

1832 Sulla geometria derivata. Ann. Lomb. Veneto, 2, 250-253.

1833 Sopra alcune applicazioni di un nuovo metodo di geometria

analitica. Poligrafo di Verona, 13, 63-61.

1835 Saggio di applicazioni di un nuovo metodo di geometria

analitica (Calcolo delle equipollenze). Ann. Lomb.
Veneto, 5, 244-259.

1836 Teoria delle figure inverse e loro uso nella geometria

elementare. Ann. Lomb. Veneto, 6, 136-141.
1837-8 Memoria sul metodo delle equipollenze. Ann. Lomb.

Veneto, 7, 243-261 ; 8, 17-37 and 85-121.
1843 Soluzioni grafiche di alcuni problemi geometriei del primo

e del secondo grado trovato col metodo delle equipollenze.

Ven. 1st. Mem., 1, 225-267.
1847 Dimostrazione col metodo delle equipollenze di alcuni

teoremi in parte eonsiderati dai sig. Bellati e Ridolii.

Ven. 1st. Atti, (1), 6, 53-59.
1852 Saggio suU' algebra degli immaginarie. Ven. 1st. Mem., 5,

243-344.



( 8 )

1854 Sposizione del metodo delle equipollenze. Mem. Soc.

Ital., 25, 225-309. Published separately at Modena, 1854.

Translated by C. A. Laisant, Paris. 1874.
1858 Calcolo del quaternioni di W. R. Hamilton e sua relazione

col metodo delle equipollenze. Ven. 1st. Atti, (2), 1,

334-342. Also Mem. Soc. Ital. (1862), 1, 126-186.
1860. Sposizione dei nuovi metodi di geometria analitica. Ven

1st. Mem. 159 pages.
1871 Sul calcolo dei quaternioni. Undecima Eivista di Giornali.

Ven. 1st. Atti, (2), 204.
1873 Sul calcolo dei quaternioni ossia teoria dei rapporti

geometrici nello spazio. Duodecima Rivista di Giornali.

Ven. 1st. Atti, (2), 69.
1873-4 Exposition de la methode des Equipollences de Giusto

Bellavitis : traduction par C. A. Laisant. Nouv. Ann. (2),

12 and 13.
1876 Sulle origini del metodo delle equipollenze. Ven. 1st.

Mem., 19, 449-491.
1878 Sur la these de M. Laisant relative au calcul des quaternions.

Quattuor dicesima Rivista di Giornali. Ven. 1st. Atti.

(2), 116.

WoosTER Woodruff Beman.

1881 A brief account of the essential features of Grassmann's
extensive algebra. Translation of Grassmann's " Kurze
Uebersicht " in Grunert's Archiv. Analyst, 8, 96-97,
and 114-124.

1897 A chapter in the history of mathematics. Amer. Assoc. Proc,

46, 33-50.

B. Berloty.

1886 Theorie des quantites complexes a n unites principales.
These. Paris : Gauthier-Villars. 12 pp. 4°.

V. Bjerknes.

1898 Zur Theorie gewisser Vectorgrossen. Christiania. 27 pp.

8°.
1900 Vorlesungen iiber hydrodynamische Fernkriifte. Bd. I.
Leipzig.



( 9 )

Carl F. E. Bjorling.
1876 Ueber eine vollstandige geometrische Darstellung einer
Gleichung zwischen zwei veranderlichen Grossen.
Stockholm Akad. Handl., 13, No. 4.

Frank Hagar Bigelow.

1902. Eclipse meteorology and allied problems. Chap. V., Funda-
mental physical relations, p. 135-166. Bulletin of the
United States Weather Bureau.

1902 Studies on the statics and kinematics of the atmosphere
in the United States. Bulletin of the United States
Weather Bureau.

Maxime Bocher.

1893 The geometric representation of imaginaries. Annals of
Math., 7, 70-72.

Otto Boklen.

1882 Die Kechnung mit Vectoren. Correspondenzbl. f. Gel. u.
Realschule.

A. J. BOGUSLAWSKY.

1891-2 Algebra of the plane and of space, or calculus of position.

(Russian.) Mosk. Math. Samml. 15-16.
1893 Calculus of position. (Russian.) Charkow Ges., (2), i,

86-96.

George Boole.

1848 Notes on Quaternions. Phil. Mag., (3), 33, 278-280.

1856 Application of the method of Quaternions to the solution of

the partial differential equation VHi = 0. Dublin Proc,

6, 375-385.

A. Breuer.

1893 Die Gauss'sche Darstellung complexer Zahlen in geometri-
scher Beleuchtung. Hoppe Arch., (2), 12, 337-344.

R. Bricard.

1901 Sur la similitude directe dans le plan. Application de la
methode des equipollences. Nouv. Ann., (4), 1, 112-120.



( 10 )

John Bkill.

1886 On the application of the theory of complex quantities to plane

geometry. Mesenger, (2), 16, 8-20.

1887 A new method for the graphical representation of complex

quantities. Messenger, (2), 17, 80-93.
1889 A new geometrical representation of the quaternion analysis.

Cambr. Proc, 6, 156-169.
1892 Note on the application of quaternions to the discussion of

Laplace's equation. Cambr. Proc, 7, 120-125 and 151-

166.

1895 Note on the application of analysis to geometry. Messenger,

(2), 25, 49-59.

1896 On the generalization of certain properties of the tetrahedron.

Cambr. Proc, 9, 98-108.

Andke Bkoca.

1900 Champs de vecteur et champs de force. Action recipvoque des

masses scalaires et vectorielles. C.R. 130, 109-112.

1900 Sur les masses vectorielles de discontinuite. C. R. 130,

317-319.

Henei Brocard.

1877 Applications mecaniques du calcul des quaternions, par C. A.
Laisant. Compte rendu bibliographique. Nouv. Corresp.
Math. 5, 115-116.

1882 Introduction a la methode des quaternions, par C. A. Laisant.

Compte rendu bibliographique. Nouv. Ann., (3), 1,
332-335, and Mathesis, 2, 32-34.
1887 Theorie et applications des EquipoUences, par C. A. Laisant.
Compte rendu bibliographique. Mathesis, 7, 184-185.

A. H. BUCHERER.

1903 Elemente der Vectoranalysis. Leipzig: Teubner, 6+91

pp. 8vo.

Arthur Buchheim.

1883 On the application of quaternions to the theory of the lii'ear

complex and the linear congruence. Messenger, (2), 12^
129-130.



( 11 )

1883 On the quaternion treatment of the linear complex. Mes-

senger, (2) iS, 120-124. _ T ^ M S

1884 7 On the theory of screws in elliptic space. Lond. M b.
'' Proc, 15, 88-^8 ; IS', 15-27 ; 17, 240-254 ; 18 88 96.

1885 On the theory of matrices. Lond. M. S-^- 16, 63-82.

1885 A memoir on biquaternions. ^^^^^^^/^ I' ^fT? 80 106


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Online LibraryAlexander MacfarlaneBibliography of quaternions and allied systems of mathematics → online text (page 1 of 6)