An Account of Books

VI. An Account of BOOKS. 1. The Mathematical Works of Dr. John Wallis, Savilian Professor of Geometry in the University of Oxford, and Fellow of the Royal Society, in Two large Volumes in Folio. è Theatro Oxon. In the former of them are contained, 1. His Inaugural Oration, when he entered upon that Employment, Octob. 31. 1649. 2. His Mathesis Universalis, or Opus Arithmeticum; containing not only Numerall Arithmetick, but the Specious and Algebrick, or the Calculus Geometricus (Philologically and Mathematically handled;) with many Discourses or smaller Tracts intermixed, thereunto relating. 3. A Treatise concerning Proportions; distinguishing the Proporatio Dupla, Tripla, &c. from the Duplicata, Triplicata, &c. (occasioned by a Treatise of Meibomius, entituled, De Proportionibus Dialogus;) With a Preface concerning Cubical Equations. 4. A Treatise of Conick Sections, in a New and Easie Method; considered as plain Figures, exempted out of the Cone. Whereby the Doctrine of Conicks is made much more Intelligible than formerly, when it was esteemed so perplex and intricate, as to deter many from meddling with it. 5. His Arithmetick of Infinites, being a New Method of Investigation or Enquiry into the Quadrature of the Circle and other Curve-lined Figures; and many other Mysteries in Mathematicks, which were before held as deplorate. 6. An Observation of a Solar Eclipse at Oxford, Aug. 2. 1654. Stil. Vet. 7. A Treatise of the Cycloide, with the Bodies and Surfaces thence derived; occasioned by a Publick lick Challenge Ad omnes Europae Mathematicos. 8. A Treatise of the Cissoid; and the Rectification and Com- planation of Curve Lines and Surfaces, in a Method de- rived from the Arithmetick of Infinites. 9. His Mecha- nica, or a large Treatise of Motion. Wherein are hand- led; not only the Machines or Engines, commonly cal- led the Mathematical or Mechanical Powers, but the whole Doctrine of Motion; derived and demonstrated from its Genuine and first Principles; with great va- riety (especially in the Second Part, which is De Cen- tro Gravitatis ejusque Calculo,) of intricate and perplexed Enquiries into the most abstruse Mysteries in Mathema- tics, many of them not formerly handled by any; the Doctrine of Percussions, Repercussions, Springs, and Reflexions; the Doctrine of Hydrostaticks, from the Counterpoise of the Air; and many other things newly discovered. In the latter Volume is contained, 1. A large Trea- tise of Algebra, Historical and Practical: Shewing the Original and Progress of that Art, from time to time, and the steps whereby it hath attained to that height whereat now it is, amongst the Greeks, the Arabs, and the later Europeans: With the several and successive Me- thods of Operations thereunto appertaining; and the great Improvements thereof in the present Age: Toge- ther with many occasional Discourses intermixed. 2. A Treatise of Combinations, Alternations, and Aliquote Parts; and divers Problems relating thereunto. 3. A Treatise of Angular Sections, with other things thereunto apper- taining; as the Canon of Sines, Tangents, and Secants, &c. 4. A Treatise of the Angle of Contact, (as it is commonly called;) shewing it to be of No-Magnitude, and not any part of a Right-lined Angle. 5. A Defence of that Treatise, against the Objections of Leotand and others: Together with several Discourses concerning Composition of Magnitudes, Inceptives of Magnitudes, and Compositions of Motion; which give Light to the clearing of many Difficulties formerly apprehended, as relating thereunto. 6. A Discourse concerning Euclid's Fifth Postulate, and his Fifth Definition of his Sixth Book; in Vindication of Euclid from the unjust Exceptions of divers, occasioned by their mis-apprehensions of Euclid's Design therein. 7. A Treatise of the Cono-Cuneus, or a Body representing partly a Cone, and partly a Wedge, with the Sections thereof made by a Plane; considered in like manner as what are called the Conick Sections. 8. A Geometrical Disquisition of Gravity and Gravitation; wherein the Doctrine of the Counter-poise of the Air is defended against that of the Ancients Fuga Vacui. 9. A New Hypothesis concerning Tides, or the Seas Ebbing and Flowing; derived from the Common-Center of Gravity of the Earth and Moon, considered as Conjunct Bodies. 10. Commercium Epistolicum; being a Collection of Letters which passed between Messieurs Fermat and Frenicle on the one Part, and the Lord Viscount Brounker and Dr. Wallis on the other Part, by the Intervention of Sir Kenelm Digby; concerning divers Questions Mathematical. 11. A Treatise of Trigonometry, Plain and Spherical, of Mr. John Caswell. 2. Traité 2. Tractatus de Salis Cathartici amari in aquis Ebeshamensibus & hujusmodi aliis contenti Naturâ &c. usw. Aut. Nehemia Grew, M.D. Utriusque Reg. Soc. Soc. Lond. Impensis S. Smith & B. Walford. In 12°. The Learned Author of this Treatise, having found by his own Experience, and that of many other Eminent Physicians in London, the manifold Use of the Purging Waters near Epsom, and others of the same kind; as also of the Bitter Purging Salt contained in these Waters; concluded the giving a Publick Account hereof, would be a Work not unacceptable to Physicians remote from London, whether in England or elsewhere; to most of whom this Medicine hath hitherto been a Stranger. The Book itself is divided into Two Parts. The former, of the Nature of the Purging Waters, and of the Purging Salt therein contained. The latter, of their Use. The former hath Six Chapters. The First shews how these Waters came to be commonly known and used. The Second shews the Nature of the Waters. The Third, the Nature of the Purging Salt of these Waters. Where, among many other Experiments, it is observed, That the Crystals hereof, when permitted to shoot at a due distance, are most of them Rectangular Prismes with four Parallelogram Planes. By which, and divers other Properties, it is distinguished from all other Salts. The Fourth shews the difference between this Salt and Allom; and that the Waters are falsely supposed by many to be Aluminous. As also between this and Common Salt; although some quantity of Common Common Salt be contained in all the Purging Waters. The Fifth demonstrates the difference of this Salt, both from Nitre, and from the Salt of Lime; notwithstanding it hath been taken for a Calcarious Nitre. The Sixth containeth some further Observations of this Bitter Purging Salt, grounded chiefly upon the foregoing Experiments. The Latter Part hath Seven Chapters. The First sheweth the Use of the Waters, and of their Purging Salt in general. Wherein, those Objections, as may seem to lye against the Salubrity hereof, are fully answered. The Second sheweth the ways of using the Salt; whereof one of the best is to take it dissolved in its own Purging Water, raw, or first a little boyled: Whereby the said Water will work, both in a far less quantity, and more kindly and effectually. The Third sheweth in what Diseases this Medicine is to be used; particularly of the Stomach, as in want of Appetite, Vomitings, Pains like those of the Colick, Hypochondriacal Melancholy with Heat, and that Disease called the Heart-burning. The Fourth, in what Diseases of the Guts, and adjacent Parts; as the Colick, Worms, Nephritick Pains, commonly called, the Stone-Colick, Hot Urine, Suppression of Urine, Diabetes, and the Jaundies. The Fifth, in what Diseases of the Head; as Madness, Head-ach, and the Megrim. The Sixth, in what other Diseases more Universal; as Mother-Fits, the Wandring Gout, commonly called a Rheumatism, and the Scorbutick Itch. The last mentioneth the Diseases wherein it is improper and hurtful. To all which, the Doctor premiseth this necessary Caution, That this Medicine, in any more than ordinary Case, be never used alone, but in conjunction with other convenient Remedies; some whereof he hath thought fit to mention. Yet so, as no where to set down an entire Method of Cure; in regard the Treatise is intended for the Use, not of Young Beginners, but Experienced Physicians. The chief Experiments of the Nature of this Salt (whereupon its Vertue depends) were shewed at a Meeting of the Royal Society (some Learned Physicians being present) to their great Satisfaction. LONDON: Printed for Sam. Smith, and Benj. Walford, Printers to the Royal Society, at the Prince's Arms in St. Paul's Church-yard. 1695.