TRACT 20.

LOGARITHMS.

331

which VJacq hath published, and that which hath hithertoborne his name in English, as in the form, so likewise in thematter of it; for in the two last-mentioned editions, there issomething left out in the second chapter of plain triangles,the third chapter wholly omitted, and a part of the third inthe spherical; but in this edition nothing: something we haveadded to both, by way of explanation and demonstration.”

In 1670, John Caramuel published his “ Mathesis Nova,”in which are contained 1000 logarithms both of Napier’s andBriggs’s form, as also 1000 of what he calls the Perfect Loga-rithms, namely, the same as those which Briggs first thoughtof, which differ from the last only in this, that the one in-creases while the other decreases, the radix or logarithm ofthe ratio of 10 to 1 being the same in both.

The books of logarithms have since become very numer-ous, but the logarithms are mostly of that sort invented byBriggs, and which are now in common use. Of these, themost noted for their accuracy or usefulness, besides the worksabove mentioned, are Vlacq’s small volume of tables, parti-cularly that edition printed at Lyons, in 1670; also tablesprinted at the same place in 1760 ; but most especially thetables of Slier win and Gardiner, particularly my own im-proved editions of them. Of these, Sherwin’s “ MathematicalTables,” in 8vo, formed, till lately, the most complete col-lection of any, containing, besides the logarithms of all num-bers to 101000, the sines, tangents, secants, and versed sines,both natural and logarithmic, to every minute of the quadrant,though not conveniently arranged. The first edition was in1706; but the third edition, in 1742, which was revised byGardiner, is esteemed the most correct of any, though con-taining many thousands of errors in the final figures, as wellas all the former editions: as to the last or fifth edition, in1771, it is so erroneously printed that no dependance can beplaced in it, being the most inaccurate book of tables I everknew; I have a list of several thousand errors which I havecorrected in it, as well as in Gardiner’s octavo edition, and inSherwin’s edition.

VOL. I.

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