[1] Dr Thomas Smith thus describes the ardour with which Briggs
studied the _Descriptio_: "Hunc in deliciis habuit, in sinu, in
manibus, in pectore gestavit, oculisque avidissimis, et mente
attentissima, iterum iterumque perlegit,..." _Vitae quorundam
eruditissimorum et illustrium virorum_ (London, 1707).
[2] William Lilly's account of the meeting of Napier and Briggs at
Merchiston is quoted in the article NAPIER.
[3] It was certainly published after Napier's death, as Briggs
mentions his "librum posthumum." This _liber posthumus_ was the
_Constructio_ referred to later in this article.
[4] Frisch's _Kepleri opera omnia_, ii. 834. Frisch thinks Bramer
possibly relied on Kepler's statement quoted in the text ("Quibus
forte confisus Kepleri verbis Benj. Bramer...."). See also vol. vii.
p. 298.
The claims of Byrgius are discussed in Kästner's _Geschichte der
Mathematik_, ii. 375, and iii. 14; Montucla's _Histoire des
mathématiques_, ii. 10; Delambre's _Histoire de l'astronomie
moderne_, i. 560; de Morgan's article on "Tables" in the _English
Cyclopaedia_; Mark Napier's _Memoirs of John Napier of Merchiston_
(1834), p. 392, and Cantor's _Geschichte der Mathematik_, ii. (1892),
662. See also Gieswald, _Justus Byrg als Mathematiker und dessen
Einleitung in seine Logarithmen_ (Danzig, 1856).
[5] See Mark Napier's _Memoirs of John Napier of Merchiston_ (1834),
p. 362.
[6] In the _Rabdologia_ (1617) he speaks of the canon of logarithms
as "a me longo tempore elaboratum."
[7] A careful examination of the history of the method is given by
Scheibel in his _Einleitung zur mathematischen Bücherkenntniss_,
Stück vii. (Breslau, 1775), pp. 13-20; and there is also an account
in Kästner's _Geschichte der Mathematik_, i. 566-569 (1796); in
Montucla's _Histoire des mathématiques_, i. 583-585 and 617-619; and
in Klügel's _Wörterbuch_ (1808), article "Prosthaphaeresis."
[8] Besides his connexion with logarithms and improvements in the
method of prosthaphaeresis, Byrgius has a share in the invention of
decimal fractions. See Cantor, _Geschichte_, ii. 567. Cantor
attributes to him (in the use of his prosthaphaeresis) the first
introduction of a subsidiary angle into trigonometry (vol. ii. 590).
[9] The title of this work is--_Benjaminis Ursini_ ... _cursus
mathematici practici volumen primum continens illustr. & generosi Dn.
Dn. Johannis Neperi Baronis Merchistonij &c. Scoti trigonometriam
logarithmicam usibus discentium accommodatam_ ... _Coloniae_ ...
_CI[~C] I[~C]C XIX_. At the end, Napier's table is reprinted, but to
two figures less. This work forms the earliest publication of
logarithms on the continent.
[10] The title is _Logarithmorum canonis descriptio, seu
arithmeticarum supputationum mirabilis abbreviatio_. _Ejusque usus in
utraque trigonometria ut etiam in omni logistica mathematica,
amplissimi, facillimi & expeditissimi explicatio. Authore ac
inventore Ioanne Nepero, Barone Merchistonii, &c. Scoto. Lugduni_....
It will be seen that this title is different from that of Napier's
work of 1614; many writers have, however, erroneously given it as the
title of the latter.
[11] In describing the contents of the works referred to, the
language and notation of the present day have been adopted, so that
for example a table to radius 10,000,000 is described as a table to 7
places, and so on. Also, although logarithms have been spoken of as
to the base e, &c., it is to be noticed that neither Napier nor
Briggs, nor any of their successors till long afterwards, had any
idea of connecting logarithms with exponents.
[12] The smallest number of entries which are necessary in a table of
logarithms in order that the intermediate logarithms may be
calculable by proportional parts has been investigated by J. E. A.
Steggall in the _Proc. Edin. Math. Soc._, 1892, 10, p. 35. This
number is 1700 in the case of a seven-figure table extending to
100,000.
[13] Accounts of Sang's calculations are given in the _Trans. Roy.
Soc. Edin._, 1872, 26, p. 521, and in subsequent papers in the
_Proceedings_ of the same society.
[14] In vol. xv. (1875) of the _Verhandelingen_ of the Amsterdam
Academy of Sciences, Bierens de Haan has given a list of 553 tables
of logarithms. A previous paper of the same kind, containing notices
of some of the tables, was published by him in the _Verslagen en
Mededeelingen_ of the same academy (Afd. Natuurkunde) deel. iv.
(1862), p. 15.
LOGAU, FRIEDRICH, FREIHERR VON (1604-1655), German epigrammatist, was
born at Brockut, near Nimptsch, in Silesia, in June 1604. He was
educated at the gymnasium of Brieg and subsequently studied law. He then
entered the service of the duke of Brieg. In 1644 he was made "ducal
councillor." He died at Liegnitz on the 24th of July 1655. Logau's
epigrams, which appeared in two collections under the pseudonym "Salomon
von Golaw" (an anagram of his real name) in 1638 (_Erstes Hundert
Teutscher Reimensprüche_) and 1654 (_Deutscher Sinngedichte drei
Tausend_), show a marvellous range and variety of expression. He had
suffered bitterly under the adverse conditions of the time; but his
satire is not merely the outcome of personal feeling. In the turbulent
age of the Thirty Years' War he was one of the few men who preserved
intact his intellectual integrity and judged his contemporaries fairly.
He satirized with unsparing hand the court life, the useless bloodshed
of the war, the lack of national pride in the German people, and their
slavish imitation of the French in customs, dress and speech. He
belonged to the _Fruchtbringende Gesellschaft_ under the name _Der
Verkleinernde_, and regarded himself as a follower of Martin Opitz; but
he did not allow such ties to influence his independence or originality.
Logau's _Sinngedichte_ were edited in 1759 by G. E. Lessing and K. W.
Ramler, who first drew attention to their merits; a second edition
appeared in 1791. A critical edition was published by G. Eitner in
1872, who also edited a selection of Logau's epigrams for the
_Deutsche Dichter des XVII. Jahrhunderts_ (vol. iii., 1870); there is
also a selection by H. Oesterley in Kürschner's _Deutsche
Nationalliteratur_, vol. xxviii. (1885). See H. Denker, _Beiträge zur
literarischen Würdigung Logaus_ (1889); W. Heuschkel, _Untersuchungen
über Ränders und Lessings Bearbeitung Logauscher Sinngedichte_ (1901).
LOGIA, a title used to describe a collection of the sayings of Jesus
Christ ([Greek: logia Iêsou]) and therefore generally applied to the
"Sayings of Jesus" discovered in Egypt by B. P. Grenfell and A. S. Hunt.
There is some question as to whether the term is rightly used for this
purpose. It does not occur in the Papyri in this sense. Each "saying" is
introduced by the phrase "Jesus says" ([Greek: legei]) and the
collection is described in the introductory words of the 1903 series as
[Greek: logoi] not as [Greek: logia]. Some justification for the
employment of the term is found in early Christian literature. Several
writers speak of the [Greek: logia tou kuriou] or [Greek: ta kuriaka
logia], i.e. oracles of (or concerning) the Lord. Polycarp, for
instance, speaks of "those who pervert the oracles of the Lord."
(Philipp. 7), and Papias, as Eusebius tells us, wrote a work with the
title "Expositions of the Oracles of the Lord." The expression has been
variously interpreted. It need mean no more (Lightfoot, _Essays on
Supernatural Religion_, 172 seq.) than narratives of (or concerning) the
Lord; on the other hand, the phrase is capable of a much more definite
meaning, and there are many scholars who hold that it refers to a
document which contained a collection of the sayings of Jesus. Some such
document, we know, must lie at the base of our Synoptic Gospels, and it
is quite possible that it may have been known to and used by Papias. It
is only on this assumption that the use of the term Logia in the sense
described above can be justified.
"The Sayings," to which the term Logia is generally applied, consist of
(a) a papyrus leaf containing seven or eight sayings of Jesus discovered
in 1897, (b) a second leaf containing five more sayings discovered in
1903, (c) two fragments of unknown Gospels, the former published in
1903, the latter in 1907. All these were found amongst the great mass of
papyri acquired by the Egyptian Exploration Fund from the ruins of
Oxyrhynchus, one of the chief early Christian centres in Egypt, situated
some 120 m. S. of Cairo.