LOGARITHMS. 



Tiiefe formuljE might have been extended to a much 

 greater length, bat thofe that are given will be found to em- 

 brace the generality of cafes, and will be found ufeful on va- 

 rious occaiions. 



The publications on the fubjeft of logarithms have been fo 

 numerous, that we can only find room to mention a fmall 

 portion of them, but as it is ufeful to know which are re- 

 puted the teft, and particulai'ly the beil editions of the 

 fame authors, we (liall fubjoin the following enumeration, 

 which may be confidered as contaming the moft refpeclable 

 and accurate works of tlus kind. 



I. The firlt canon of logarithms for natural numbers from 

 I to 2o,coo, and from 90,000 to 100,000, was conftrucled 

 and publifhcd in 1624, by Briggs, with the approbation of 

 the inventor lord Napier. 



I. Briggs's logarithms, with their difference to 10 places 

 of figures ; as alfo the logarithmic fines, tangents, &c. by 

 George Miller, London 1 63 1. 



3. " Trigonometria," by Richard Norwood 163 1, con- 

 taining a table of logarithms from 1 to io,coo, befides fines, 

 tangents, &c. 



4. " DireSorium Generale Uranometricum," by Francis 

 Bonaveniura Cavalerius, Bologna 1633. This work, befide 

 the ufual table of logarithms, contains feveral new and ufe- 

 ful tables of fines, verfed fines, &c. and fome other original 

 matter. * 



5'. In 1643 appeared the " Trigonometria" of the fame 

 author, which may alfo be confidered an interefting work. 



6. " Tabulae Logarithmic*" by Nathaniel Rowe, Lon- 

 don 1633. In this work the logarithms are given to eight 

 places of figures, for every nu.mber from I to ioc,ooo, and 

 logarithmic fines, tangents, &c. to every hundredth part of 

 degrees to ten places. 



7. " Trigonometria Britannica" by John Newton, Lon- 

 don, 16^8. Here the logarithmic tables are put in the mott 

 convenient form, being nearly the fame as is now adopted 

 by authors of the prefent period. 



5. Adrian Viacq alfo pubhfhed different editions of loga- 

 rithmic tables, which have been fince republiftied ; thefe are 

 generally confidered very accurate and ufeful tables, parti- 

 cularly the edition of 1631. , 



g. Sherwins's mathematical tables, publifhed in 8vo. Lon- 

 den 1706, form the moll complete colleftion of any we have 

 yet noticed ; containing, befides the logarithms of all numbers 

 from 1 to 100,000, the fines, tangents, fecants, and verfed 

 •fines, both natural and logarithmic, to every minute of the 

 quadrant. The firfl edition was printed in 1706, but the 

 third, publifhed in 1742, as reviled by Gardiner, is coi.fi- 

 dered as fuperior to any other. The fifth, and lall, edition 

 publifhed in 1 7 17, is fo incorreft, that no dependence can 

 be placed upon it. 



The third edition abovc-menti&ned, which is called Gar- 

 diner's tables, was republifked at AvignoB, ia France, in 



177c, but this is not confidered fo accurate as the original 

 one by Gardiner himfelf. 



10. An " Antilogarithmic Canon," for readily finding 

 the number corrcfponding to any logarithm, was begun by 

 the algcbraift Harriot, and completed by Warner, the editor 

 of the former's works, but it was never publifned for want 

 of proper encowragcment. But a complete canon of this 

 kind was publifhed by James Dodfon 1742, in which the 

 numbers anfwering to each logarithm from i to 100,000, are 

 computed to 1 1 places of figures. 



1 1 . In T 7S3 tvas publifjied, by M. Callet, at Pari?, a very 

 neat and ufeful colkaion of logarithmic tables ; and in 1795 

 an enlarged edition of the fame work, under the title of 

 " Tables Portative de Logarithms." This ii an elegant 

 work, beautifully printed and fiercotyped, at the celebrated 

 Didot's prefs ; it is more correft than the former edition, 

 though it contains a few eiTors not noticed in the fill of errata. 



12. Dr. Hutton's " Mathematical Tables," containing 

 the common hyperbohc and logiftic logarithms, alfo fines, 

 tangents, fecants, and verfed fines, both natural and loga- 

 rithmic, together with feveral other tables ufeful in mathe- 

 matical calcularions. To which is prefixed a hiflory of the 

 d-.fcoveries and writings of the mofl celebrated author's on this 

 fubjea. This work was firfi; publifhed in 1785, fince 

 which time it has pafled through feveral editions, which £re 

 all very correct. 



13. Taylor's tables of logarithmic fines and tangents to 

 every fecond of the quadrant, to wluch is prefixed a table of 

 logarithms from i to 100,000. This is a very valuable 

 work, and has a ufeful introduction compofed by the late 

 afironomer royal Dr. Mafkelyjie. 



14. Vega's tables, publifhed in Latin and German, is alio 

 a very excellent performance, particularly the fecond edition 

 of 1797. 



15. Another very accurate and extenfrve colledion of 

 tables, computed for the decimal divifisn of the circle by 

 Borda, and revived and augmented by Delambre, was pub- 

 lifhed in Paris. This work is held in great erteem by the 

 French ; but it is of little ufe to Englifh mathematicians on 

 account of the particular divifion ot the circle. It is, how- 

 ever, preceded by a very perfpicuous and fcientific invelliga- 

 tion of the moft ufeful logarithmic feries, and trigonometrical 

 formuli ; and may therefore be read with interell by the o-e- 

 neral mathematician. Befides the authors above-mentioned, 

 many others have treated on the fubjed of logarithms, among 

 the principal of whom are Halley, Leibnitz, Mercator, 

 Cotes, Brook Taylor, Euler, MacLaurin, Wolfius, Keill, 

 and Simpfon. 



As we have frequent occafion to refer to tables of loga- 

 rithms in the courfe of this work ; we have fubjoined a table 

 of logarithms of all numbers from 1 to io,coo, which will, 

 be found ufeful ia various cafes wlfien other tables may not 

 be at biuid. 



