TRACT 33.
history of algebra.
301
In 1690 was also published, in 4 vols 4to, Dechale’sCursns seu miindus matkematicus ; in which is a piece of al-gebra, of a very old-fashioned sort, considering the timewhen it was written.
About 1692, and at different times afterwards, De Lagnypublished many pieces on the resolution of equations in num-bers, with many theorems and rules for that purpose.
In 1693 was published, in a neat little volume, Sy>iopsisAlgebraica, opus posthumum Johannis Alexandri.
In 1694, Dr. Halley gave, in the Philos. Trans, an inge-nious tract on the numeral extraction of all roots, -withoutany previous reduction. And this tract is also added tosome editions of Newton’s Universal Arithmetic.
In 1695 Mr. John Ward, of Chester, published, in 8vo,A Compendium of Algebra , containing plain, easy, and con-cise rules, with examples in an easy and clear way. And in1706 he published the first edition of his Young Mathema-tician's Guide, or a plain and easy introduction to the ma-thematics : a book which is still in great request, especiallywith beginners, and tvhich has been ever since the ordinaryintroduction of the greatest part of the mathematicians ofthis country.
In 1696 the Marquis de I’Hopital published his Analysedes infiniment petits. And gave several papers to the LeipsicActs and the Memoirs of the Academy of Sciences. Heleft behind him also an ingenious treatise, which was pub-lished in 1707, intitled Traite analytique des Sections Coniques ,et de la construction des lieux geometriques.
In 1697, and several other years, Mr. Ab. Demoivre gavevarious papers in the Philos. Trans, containing improvementsin Algebra : viz, in 1697, a method of raising an infinitemultinomial to any'power, or extracting any root of thesame. In 1698, The extraction of the root of an infiniteequation. In 1707, Analytical solution of certain equationsof the 3d, 5th, 7th, See degree. In 1722, Of algebraicfractions and recurring series. In 1738, The reduction ofradicals into more simple forms. Also in 1730, he published