Al'.LK. 



mge nd date namely, ' The Compleat Art of Uy ailing .... by 

 T. Wells of Deptfort, Ea,\.,' London, 1887. 



This table contains logarithms of numbers (1) 10,000, i 

 decimal*, and a complete canon inf logarithms only, and 

 qnadrantal form) to every iiiinuto and to seven decimals. But the 

 u-rim coiue, cotangent, cosecant, are n< -iced. 



iirl John Maire 



. ntiom-d by Murl imd sines of 



rami' imals, in Napierian logarithms; with ditlerencw to 



tan si' 



. John Kepler. ' Tabulte Rudolphinic,' f u^ the tables 



in tlii- I work are the following : First, :i variation of the 



-arithins, opposite to which an- the 

 angles of which thevare the .Vu;wm logarithms of sines, ami adapted 



to the two . < 5", 10', 60', and '2'", I" 1 , 



. . . .4*, and to the reciprocal, or harmonic series, 720, SCO, "210 1. 



This table, from its number of terms, he calls a hc/.taamat of 

 logarithms : we thall Bee that Batsc'ii extended the first term ; ami 

 we note that Kepler here introduced the other. Secondly, ;i reprint of 

 Napier's own table of sines and (now culled) cosines, t > two tig':i 

 than in Napier. Kepler calls the logarithms of cosii "it/im*, 



and abandons his right to the word at the same time. For in 

 Mtniquadrantal form, the cosines do stand urer a- nhift the situ-s : but 

 in Kepler's quadrantal form they do not. Napier does not use any 

 distinctive word. Thirdly, Napier's diftrintiie, called by Kepler 

 metulwiarttkins (being in Napier in the middle), ore reprinted 

 separately to every minute of the first ten degrees, fur the sak. 

 latitudes of the planets. Fourthly, more accurate cosines (10) 1 40', 

 are given. 



1628. Adrian Vlacq, ' Arithmetics Logarithmica,' Oouda. The 

 whole hundred chiliads of numbers, from to 100,000, to ten deci- 

 mals. Sines, Ac., to every minute. This work very much displeased* 

 Briggs's friends in England. Ou the one hand the work is called a 

 tecoi'tl edil'tjn of Brings; and, being all in numerals and in Latin, it 

 needed no translation. The pretexts were, first, that copi< 

 scarce in Belgium, which was bad : and that Briggs had omitted the 

 logarithms from 20,000 to 90,000, which was good. On the other 

 hand, it may be held that the supplying of this defect made a new 

 work of the whole ; and that the description of it as a second edition 

 of Briggs was too large a concession. A middle course ought to have 

 been taken : Briggs ought to have been consulted. Had this been 

 done, an arrangement would probably have been made which would 

 have satisfied all parties. The error, if any, was purely commercial : 

 there is nothing the least resembling literary plagiarism, but rather the 

 opposite fault, over ascription. 



(It80). Bartschius. The tables which Bartschius published inde- 

 jiendently of his father-in-law ( Kepler) had fallen into oblivion, when 

 hiaidt found a copy and republished them with Kepler's last 

 tables, and with interscript differences, under the title of 'Joh. Kepleri 

 et Jacobi Bartschii TabultB mainulcs logarithmicse,' Strasburg, 1700, 

 liino. What the titles and dates of the original Works were, we can 

 find only from Lipenius, who gives them as follows : 



Jac. Bartschii ' Tabulaq NOVJB Logarithmieo logistics;,' Leipzig, 

 folio, 1635; and ' Trichil. Hexacosias Logarithm!.' Sagan, 

 8ro, 1630. 



Whether the first was an original edition we do not know : if HO, it 



MIOUS. The reprint by Eisenschmidt contains (from 



Da table of logarithmic eines to six figures, 0"(10) 



')48(20"i ;(1')0; a table of logarithmic tangents 

 ()' OO'li'ii . call" 1 'ihrng; a more accurate table of loga- 

 rithmic co.ines o '-'! i" 7'; an astronomical table which it is not in 

 our plan to describe ; and a table called Tridttl-Jl 'ijanlh- 



iii, being a table of what are still called logistic loga- 

 rithms with 1" and 24 11 for first terms. 



(1680). J. Faulhaber, ' Ingeniours-schul., Erster Theyl;' Frankfort. 

 Tliia work contains logarithms, according to Seheibel, who & 

 give * description. 



. Korwood, 'Tri ' Logarithms to se.vcu places; 



numbers to 10,000, sines, &c. to every minute. We do not know the 

 date of the first edition of Norwood's ' Epitomio ' : there is one of 

 (1(145) (Wilson) and we have one of 1659. The tables are of five 

 decimal places, 0(l')4 5 and 0(1)1000; with a separate title 'A 

 Triangular Canon Lo^irithmical.' 



- Cavalieri, Directorium Generate Uranometrictim,' Bologna 

 'igure logarithms, the ten tin-t thousand numbers in columns of 



twenty : the sines, Ac. to various divisions in different parts of the 

 quadrant. It is very convenient to have a short mode of denoting 

 change of intervals; the following could hardly be misuml. 

 Cavalieri's tables are, 0(l")5 (6")_ I0'(10")2ll'(20")30' (30") 1" 30' 

 (]') 45". The table of logarithmic versed sines id said to be the first 

 given. Cavalieri gave logarithms again in his trigonometry (see loK'O ; 



Norwood, In bin Trigonometry (preface dated November 1, 1631), remind* 

 hU reidcr thatwi.cn he quoU-H the ' Arltliraetica Logarithmica ' he im:ni- 

 Brigg' book of 1 624, not th.it put forth a month since in English (see ante, 

 I6M, BiifrB"), "being nothing like hi, nor wort 1 ,, e." II i- blames 



Vlacq for his "second edition " of Briggs's work, against Briggs's "mind and 

 liking," which he ay fruitiatcd the second edition of the original, lesides 

 sonic things of special moment 



TABLE, 

 and also in his ' Tabula Trigonometrica,' of which we do not know thu 



. Gellibrand, Trigonottetria IJritannica.'Gouda. Briggs's work, 



which he did not live quite to complete. Sines, tali' t cants, 



with logarithms of the sines and tangents: sines to fifteen decimals, 



tan_'c nt.s and secants to ten, logarithms of sines to fourteen decimals, 



.ins of tangents to ten decimals. It is to hundredth* of 



. not to mill 



168^. rtificiaiis,' (.'" Mi. Logarithms of 



vconds, and to ten places of 

 Is. Twenty thousand of Briggs's logarithms of uumln 



1883. Nathaniel Hoc. ' Tabula,' Logarithmica),' London. 



to Inmdredths of 



degrees. The lir.st table in which attempt at compn 

 the numbers are in columns of tii'ties, the first figures of the logarithm-; 

 the top. A good model for a small and clear type. The 

 explanations are called \Vingatc 's, whose name is by the aunouin 

 made so conspicuous in the title-page, that the whole book must have 

 often been attributed to him. 



1633. J. B. Morin, ' Trigonometric Canonical Libri Tres,' Paris. 



li'ciuial Logarithms; of Numbers 0(1)1000, with iuterscript 

 differences; of Sines and Tangents (!') 45. The decimal point is not 

 used. 



(1634). Cruger. Kastner gives Dautssig as the place. The loga- 

 rithms are Naperian, according to him. 



1684. Herigone, ' Cursus Mathematicus,' vol. iii., Paris. Said to be 

 the first digested course of mathematics; contains logarithms, appa- 

 rently from Wingate's French of 1626. 



(1634). Frobenius, ' Clavis Univ. Trigoii.' The (by that time 

 Briggs's logarithms to seven places. 



(1634). Cruger, 'Praxis Trig. Logarith. cum Logar. Tab. 

 i < lain. 



>). Cruger, ' Doctrina Astronomioj,' Dantzig. Contains loga- 

 rithmic tables. 



lt!35. Anonymous, ' Logarithmeticall Table,' London. ['Atti, 

 to Wingate. Dodson is followed by Huttou in sayiilg il. 

 published an English edition of his French logarithms. But Hutton 

 aw any prior to this of 1635, and we can tind no mention of 

 anything of Wiugate's translated from French, except (in an old 

 catalogue which gives no dates) ' The Construction and Use of the 

 Logarithmeticall Tables,' not tables themselves. The logarithms of 

 the table now before us are of six figures, and for tli units' 



figures are at the head of the columns, and the tens down the margin. 

 There arc tables of 1632, attributed to Wingate.] 



W allow the preceding paragraph in [ ] to stand as in the I 

 Cyclopaedia,' in illustration of the difference between the i 

 can be got from second-hand sources, and the results of a look at the 

 original. We have found a copy of the following work : ' Aoyapie- 

 HoTexvlai, or the Construction and Use of the Logarithmeticall Tables, 

 .... first published in the French Tongue by Edmund Winy 

 and, after translated into English by the same author. The third 

 Edition, diligently corrected and enlarged by the Author hini.-eh'.' 

 London, 164S, 12mo. The work is the letter-press of Wingate oi 

 and li;2'i, already noticed, translated into English. The tables haw 

 a French title of 1635, ' Une table logarithuiique . . . Imprime a 

 Londres." But our separate copy of the tables, being that which heads 

 this article, has an English title, though both tables are fro: 

 type. No doubt the first edition was of 1033, and the supply of 

 tables, lasted several editions of the supply of text. Wi.i 

 wealthy man, and probably found his disposition to alter and . 

 his descriptions outrun the sale of the work. But the tables . 

 reprints of the French tables of 1625. They are to six i 

 seven; the numbers are 0(1) 10,000 ranged by double entry, 

 digits and one : and the trigonometrical tables are arranged in a 

 manner more like that now in use. 



1635. Henry Gellibrand, ' An Institution Trigonometrical!,' London. 

 Saved decimals; logarithms of numbers 0(1)10,000; sines, tan 

 and secants, with logarithms of sines and tangents, dividing tin 

 into two parts, one of three columns, the other of two. The form not 

 wmiquadraiihil, but quadrantal, with the coniplemeutal degree (in- 

 verted) on the opposite page. No differences ; some subsidiary tables 

 toi astronomy and navigation; the name of Briggs prefixed to the 

 logarithms of numbers only. This is the form of a series of tables 

 which i.m lliion,'h many continental editions; but they all br; 

 name of Vlacq. It is stated , i lirst edition of them air 



in (1686) : and Dechales (i. *2'2) describes a work of Vlacq of precisely 

 the above contents, as of Gouda (1638). Karh null works 



are often lost to history. Now we have Seen that Vlacq was a rapid 

 appropriator of English ideas : in less than four years he rupro.lmvd 

 Uriggs, with the 70,000 missing logarithms, and a table t) 



that he seized upon Gellibi , and imme- 



diately reprinted it. We havi !'i) that Vlacq's previous idea 



of a small table had been very different. 



The originator, then, of the long ..f small table* isCclli- 



brainl. All the tables of this (i,l!,i,r-n,:i ,.i<nl,l an- kn..wn at a glance 

 by containing, on one page, sines, tangent;-, iv.-mts, with logarithms of 

 jtnes and tatigents, and some white between the sines, &c., and tin: 



