and the mercantile rules are exemplified and diverfified with great variety of curious examples. In Exchange are exhibited Sir Ifaac Newton's tables of the affay and real and standard-weight, and value, of moft of the gold and filver coins in Europe; together with thofe of the conformity of weights and measures, by the Sieur John Larue, merchant, at Lyons; alfo the method of folving questions in the arbitration of exchange by a numerical equation. Contains the lefs ufeful, though most pleasant and delightful parts of arithmetic; viz. Alligation, medial, partial, and total; the Specific Gravity of Metals; the Rule of False, or Pofition; Progreffion both arithmetical and geometrical; alfo Variations, Combinations, and the method of filling Magic Squares: thefe, though they are done and accounted for better by Algebra, &e. yet may serve to open the mind, and excite the curiofity of youth to proceed to the most fublime and abftrufe fciences. To these are added Compound Intereft, with the method of calculating the value of freehold eftates at any rate of intereft; alfo annuities in reverfion, according to that late ingenious mathematician Mr. Thomas Sympfon, F. R. S. from a fet of tables calculated by him for that purpofe. •Alfo a collection of questions in Mensuration, with fuch directions as may enable any perfon to perform the measurement of moft forts of fuperficies and folids; and alfo fome curious mifcellaneous questions. This treatise concludes with an Appendix, by Mr. Thomas Allen, teacher of the mathematics at Spalding, containing rules and examples for finding the fum of any given number of terms in certain progreffions. A collection of problems concerning the maxima and minima of quantities, with the theorems annexed. And the investigation of the fums of certain infinite series. This work contains feveral hundred questions rationally folved; among which are all thofe in Clare's Introduction to Trade, &c. feveral from the Palladiums, Ladies Diaries, and other periodical books, as well as the most valuable and entertaining that could be found in other authors. N. B. We were favoured with the Cribbage Question by Major Watson. The algebraic demonftration of the rules here laid down are omitted for these three reafons; first, as arithmetical computations often carry their rationale along with them, the offering to prove a self evident truth renders it more obfcure, Secondly, the mathematicians are already acquainted with them. And thirdly, the young ftudent is as little benefited by them as a pure English scholar would be by an expofition of the Bible in Greek. What overfights may have escaped the authors, either in the prefs (from whence their refidence is more than 100 miles) or otherwife, hope their worthy fubfcribers will generously excufe; they having in the whole endeavoured to remove the difficulties, and render the paffage eafy and pleafant through this useful and delightful science. The following algebraic figns or characters are very neceffary to be underflood, as being a much fhorter, better, and more fignificant way of expreffion, than by words at length. 1 is } into or by S Divided by Equal to Is to So is Significations The fign of addition; as 9 +5 The fign of Subftraction; 83, The 2 fign of Divifion; 82, is 8 divided by 2: also thus or 2) 8 (4, which fignifies the famé thing. The fign of Equality; 99, or 9+6=15, or 9-6 3, that is 9 is equal to 9, or 9 more 6, is equal to 15, and 9 lefs 6, is equal to 3. The Signs of Proportion, or Rule of Three; thus, 2:8:: 6:24 are to be read, as 2 is to 8, fo is 6 to 24. Continued Proportionals in Geometric Progreffion. Thus 273 or 273, fignifies that 27 is to be involved to the third power. Thus 42, fignifies that the fquare root of 4 equals 2, or √243 = 3; viz. the furfolid or root, or the 5th power of SUB SUBSCRIBERS NAME S. M' A R. Thomas Allen, teacher of the mathematics at Mr. Daniel Arnold, merchant, in ditto Mr. William Adkin, of Leak, chief constable, Lincolnshire Mr. Samuel Aiftrup, of Whapload, ditto. Mr. Robert Allen, of Gofberton, ditto Mr. Samuel Ayre, of Frampton, ditto Mr. Richard Allen, of Ketton in Rutlandshire, quarry-man. B The right-honourable the Lord Brownlowe Bertie, member of parliament for Lincolnshire The Rev. Mr.Everard Buckworth, rector of Washingbrough The Rev. Mr Bryant, of Norwich Mr. Stephen Bee, fteward and land-furveyor, of Aswarby Theophilus Buckworth, of Spalding, gent. Mr. John Berridge, of London, watchmaker Mr. William Benton, of Thorney, Cambridgfhire Mr. Thomas Broderick, watchmaker, of Kirton, Lincoln'fhire Mr. Amos Burr, of Donnington, Lincolnshire Mr. Charles Boyles, fon of collector Boyles, of Wells, Norfolk. Thomas Baley, of Dunton, Norfolk, efq. Mr. Jofeph Blackith, of Frampton Mr. Jofeph Barker, of Lincoln, writing-master Mr. Brampton, attorney at law, at Oundle, Northampton shire Mr. Black Mr. Henry Bruce, of Holbeach, Lincolnshire Mr. John Burton, of Partney, ditto Mr. George Bland, fchool mafter, of Bafton Mr. Henry Bennet, of Spalding. Mr. Thomas Butler, of Donington, grocer Mr. Abfalom Bates, of Donnington Mr. Thomas Black, of Melton-Mowbray, Leicestershire Mr. Sutton Banks, of Sleaford, Lincolnshire Mr. Mr. John Bell, of Gofberton, felmonger Mr. Christopher Berry, ftationer, of Norwich, 6 copies Mr. William Butterworth, of Ecclesfield, ditto. Mr. Daniel Bullivant, of Sproxton, Leicestershire, 2 copies C The Rev. Mr. John Calthrop, vicar of Bofton' Mr. Thomas Cole, of Donington Mr. William Cole, of Donington, mercer Mr. Richard Clay, of Swinefhead, Lincolnshire Mr. George Chapman, of Surfleet, Lincolnshire Mr. Maxamillion Clifton, of Donington Mr. Thomas Cheshire, of Spalding, furveyor of the roads Mr. Edward Crane, of Quadring, school-mafter Mr. Charlton, of North Charlton Mr. Clifton, of Swarby, malfter of Surfleet Mr. John Chapman, of Boston, chief conftable William Crowe, of Norwich, efq. Mr. Joshua Chown, riding officer in the cuftoms Mr. Thomas Coleman, ironmonger, ditto Mr. Samuel Louis Chriftin, of Bern, en Suiffe Mr. Thomas Morley Clyatt, of Norwich, 2 copies Mr. Benjamin Cole, haberdafher, of ditto Mr. John Carman, comptroller at Yarmouth Meffrs. Chambers and company, merchants in Newcastle, 6 copies Mr. Thomas Cole, of Norwich Mr. Hugh Clark, of Spalding, maltster D Mr. John Daverfon, efq; of Yarmouth, Norfolk Mr. Dodds, fchoolmafter, of Elton Mr. William Dennis, fchoolmafter, of Bitchfield Mr. |