S.7 



TABLE. 



TABLE. 





logarithms. Under the name of Vlacq, lib idea prevailed till 17t!0, when 

 Lalande first commenced a new series. Lalande himself originated a 

 third series in 1805 ; and the next series begins, for England, with the 

 reprint of Lalande by the Useful Knowledge Society in 1S3!). Schulze 

 speaks of some small tables by Wolf, as being as common hi Germany 

 as those of Vlacq : of these we do not remember to have met with 

 a copy. 



1643. F. B. Cavalieri, ' Trigonometria plana et sphserica," Bologna. 

 Seven-decimal Briggs's logarithms 0(1)1000, with interscript differ- 

 ences; also sines, tangents, secants, and their logarithms, 0(10") 30' 

 (30") 1 (!') 45. But the decimal point is not used. The logarithms 

 of sine, tangent, secant, are styled logarithm, mesologarithm, tonio- 

 logarithm. 



1651. Vincent Wing, ' Harmonicon Coeleste,' London. The logar- 

 ithms have separate title-pages, and might, if torn out, pass for separate 

 They have the decimal point and are to six decimal places. 

 Sines and tangents II (!') 45' ; numbers, in decads, (1) 1010, without 

 ics. Wing was a much more learned man than his reputa- 

 tion (which is that of an almanac maker) wuuld imply. 



1 >j~i 1. John Newton, ' Institutio Mathematical London, 2 vols. 12 mo. 

 Contains tables. 



, . Uughtred's ' Trigonometric,' London, published both in Eng- 



li*h and Latin in the same year. The logarithms however are from 



ae type, with the Latin title in both : they are complete six- 



.rhms; the numbers, which go to 10,oiio, having seven 



uometrical part contains sines, tangents, and secants, 



he logarithms of tines and tangents. The table is quadrantal, 



etital degree being in the opposite page inverted. It 



100 parts, though each part is called a / < 

 bn Xewtoii, ' Help to Calculation,' &c., for converting 

 sexagenary tables into decimal by logarithms. 



. Ni-wton, ' Trigonometria Britannica,' London. The loga- 



of sines, &c, are Oi" |U; also 



< 15 and logarithms of sines to 14 decimals, 45 (15') aO. The 



logarithms of numbers are thrown into the form which they have ever 



since preserved in seven-ligiire tables. But, instead of ilitt'erences to the 



I numbers, ti'.v decimal logarithms of ilitt'erences are given. 



. .lohn Newtn, ' The Scale of Interest, or the use of Decimal 



Fractions.' Here is a table of logarithms to six decimals (1 i 1 QOQO 



arranged in linen of decads, with a separate table of proportional parts. 



it the first attempt at a school-book and a woikman's book. 



udiz of application to carpentry and gauging. 



. ' A Mathematical Manual." Six-figure logarithms, 

 :i and trigonometrical without secants or cosecants, 0(1) IIMMMJ, 



' A table containing ten Miliada ' and ' A triangular Canon 



Logr . ,'ii-'leeinial tables, numbers 0(1) 10,000, 



:nl secants Od'i l.V. These tables belong to 



. hirh our eopy is cut out: signatnr. .< from Aaa to 



. V|;icq, ' Tabtilx' Simmm,ie., Amsterdam : also ll>S3. Vlacq, 



:', Vlarij, Tain lieu der 

 - im-tioii. one 



-in, the other in Fr.-neh, the third in Herman, have sines, 

 its, secants, and logarithms of sines and : minute 



. imals. A! "i 1 to 



h'-adfd ' H. I'.rL'gii Tabi o. The lit 



Dl Mis:;, v>Ir tor the 



moat correr- beautifully legible bold type, 



large I -i book. Ti ' tn use 



>.-.! above, at the y ml. 



; is Moore, ' New Systemc of the ilathcmaticks,' L 

 In the KI- , as part of 



lables of logarithms of numi 



[pro] ' b a . pal I ' ' . i l:;^n; 



ii 1 secants, and their logarithms Ot I '' Uso, fof 



;e miuute-t.ible of natural an 



rith: 



..oiii. ' Tables des Sinus,' kc.., Tans. This is really 



. though his name is not mentioned. 



1 fiawoi. nometry. JIany a writer 



in his own trigonometry, 



ng, &c., and that the table was an accessory of whi.'li no 



ken. And BO, in our own day, many persons , 



quite above plagarisni of text think it no sin to borrow plates or 

 thout acknowledgment. 



, rsus sen Mundus Mathematicus. The first 



volume has seven-decimal tables; logarithms of numbers to (1) lOOuO ; 

 of nines and tangents (!') 45", and the sines and tangents also. 



\Vm. Ley-bourn, ' Curaus Mathematicus.' This book has in- 



1 evidence of having been writt-m before 1660. Seven-decimal 



.thms of numbers 0(1)10000; six-figure logistic logarithms 0(1") 



\-i'; xign*, tangents, and secants, &c., 0(1')4.' ; UK; 



names conine and secant not used. 



naiii, ' Tables des Sinus,' &c., Paris. This is a. reprint (see 



it trigonometry, and Vlacq is acknowledged. The printing 



.11 of th" Hague, 1665, which ranks amongst the most 



correct- the correction from that of Arosterdaui, 1683, which passes 



for the more correct. Two years afterwards, in 10S9, the tables only 

 were reprinted (Paris), the name of Vlacq was restored to the title- 

 page, and the ' Au Lecteur,' written by Ozanam in 1697, was added at 

 the end. 



1699. John Wing (nephew of Vincent), ' A compleat Body of Sur- 

 veying, formerly publish'd by Vincent Wing/ London. Five-decimal 

 logarithms of sines and tangents, (10') 45 ; of numbers, 0(1) 1000. 



(17U4). J. H[arris], ' Table of Logarithms,' quarto, mentioned in 

 Button's sale catalogue. 



1705. (Second edition.) Anonymous, ' A Table of Logarithms for 

 Numbers increasing in their natural order, &c.,' London. Six-decimal 

 logarithms of numbers (1) 10000. The trigonometrical part has a 

 separate title, 1704, 'A Triangular Canon Logarithmical.' London. 

 Six-decimal logarithms of sines, tangents, and secants o(l')45. So 

 far as appears, this table was got up by J. Seller and C. Price, mathe- 

 matical-instrument makers, who seem to have desired to sell their own 

 table of logarithms as well as their own quadrants. This table appears 

 to be a second edition, so called, of a table precisely resembling it, 

 except only in having seven decimals, attached to the ' Practical Navi- 

 gation ' of the same John Seller, who appears as the, <( -- 



(1706). Sherwin, 'Mathematical Tables,' London. The first work, 

 we believe, in which the proportional parts are in the same p.-ige with 

 the logarithms ; and thp common differences in the trigonometrical 

 logarithms made lawman. Second edition, 1717; third, revked by 

 Gardiner, and the best, 1742 ; fifth and last, 1 ,71, very erroneous the 

 inaccurate table Hutton ever met with. 



1710. John Harris, ' Lexicon Technicum,' vol. ii. This volume eon- 

 tains seven-decimal tables of logarithms 0(1)10,000, and a complete 

 canon (including versed sines), 0(1')45, both natural and logarithmic. 

 There is also a table of proportional parts for every integer from 44 to 

 4320. These tables, except the last, seem to be taken from Sherwin. 



1717. Abraham Sharp, ' Geometrj Improved,' London. A large 

 table of areas of the segments of circles : but it contains logarithms of 

 all numbers to 101', and all primes under 1100, true to sixty decimals; 

 63 decimals of logarithms 999990(1)1000000 with differences to the 

 tenth; and 63 decimals of the logarithms 1000001(1)1000010. Also 

 an immense mass of results on the regular solids. 



(1721). 'Magnus Canon Logarithmorum .... Typis Sinensibus in 

 Aula Pekinensi jussu 1 mpu-atoris excusus.' In this year was printed 

 at Pekiu, by command of the emperor Kang-Hi, in Chinese type and in 

 three folio volumes, Vlacq's logarithmic tables of sines, Sic., to ten 

 seconds, and of numbers to 100,000. (Vega, who had seen a copy at 

 Vienna.) The Royal Society possesses some Chinese logarithms, and, 

 id, there were in 1827 some who believed that the Chinese had 

 possessed logarithms from all eternity. Jlr. Babbage (' Astron. Soc. 

 Notices,' vol. i. p. !'), examined these tobies, and found that six slight 

 errors which run through most European tables were committed in 

 them. Only Vega and the last impressions of Callet were free from 

 rror.s. Jt appeal's that the Chinese, according to their usual 

 practice, had taken from the European work repubhshed at Pekm, 

 without any allusion to the source. 



1711. 1 'epateieux, ' Nouveaux Traites tie Trigonome'trie Rectiligne et 

 Sphdriquc,' I'.nis. iirparcieux is so much better known by his tabLa 

 of annuities, that his other writings * are neglected. The tables arc all 

 to seven decimals \thongh the decimal point is not used). There are 

 Jogaritb iiiibers 0(1)20000; sines, tangents, and recants, &c., 

 (!"') 5 (!') 45, .ami logarithms of sines and tangents. This is the 



earliest . iiM-nib. r '<> have seen in which the argument of 



, and seconds accompanies the logarithms of numbers. 

 Tl:.. 1... 'istingiiished by its gnomnuical tables, and by the 



excellence of its solid diagrams. 



iM_'. i)odsn, ' AnUlogarithmic Canon,' London. This work was 



iini'im; of its kind until 154U : it contains the number, to eleven figures, 



."Hiding to every logarithm from '00001 to I'OOOOO : the author t 



'A lu'ii a pcr.-on is distinguished by one particular work, his other, and. 

 purti.'Uliirly his previous, writings, even on the same suljjeei, &:o out of notice. 

 HOA many persons, for instance, know that J.npUee publUheii (separately i'roiu 

 ii.c .M. moirs of the Acadfinj ) a small work on the elliptic motion an.i on the 

 figprcs ul tiie planets in 1784 T (See Lalande, LJibl. A*tron. ann. jiSi.) And 

 li.;\v many biographical ace. urns (it Laplace n.cntioii it? 



t In tuc rnil. Mag. for 1853 arc extracts from the diary of Reuben Burrow, 

 uho stales that Robertson (the author of the Navigation) told him ihat William 

 J ::i s [beticr kno\\n than his son among tlic mathematicians) wrote Doits, .II'H 

 preface, because Dodson wrote such a cimmsed style that it had neither head 

 nnr :ail. This was not the cjse, a.s uny one may see : unless inde d Doilson 

 (,'ot a friend to write all he published. Hut there is also sometaintf like a 

 charge of plagiarism on a ditfi rent matter ; and there are imputations ag.unst 

 other persons. We do not object to the production of old diaries ; but when 

 they contain imputations, it is of importance that their authors should be truly 

 painted. Burrow's biography, estlacts. from which accompany those fruin the 

 dwiy, d ies no more than allude to "eccentricities in private tile icli-c.'ifreqtu'nrly 

 dtii'iul yrniu.i," ami " habits 1\ rmed by casualty and the necessities ot tiie moment, 

 rather than by design and the prudent liand of a master." Tiic trutti is tnat 

 licrrow, a very able mathematician, was envious and foul-mouthed to an extent 

 which it would be an insult to thousands of self-elevated men to palliate by the 

 plea of want of early education. Of this we slmll give an instance. Green and 

 \Valce, two very worthy as well as able men, were successively the astronomers 

 who accompanied Captain Cook in his voyages : probably Burrow had been a 

 competitor for the post. In his copy of any book published by either of them, 

 Burro r .Y usually wrote some scurrilous aspersion, of which we have seen several 



