An Account of Some Books

An Account of some Books. I. MECHANICA, sive De MOTU Tractatus Geometricus; PARS SECUNDA; in qua, De CENTRO GRAVITATIS Ejusque CALCULO: Auth. Johanne Wallis, SS. Th. D., Geometriae Profess. Saviliano in Celeberr. Acad. Oxoniensi; Regalis Societ. Sodali, & Regiae Majestati à Sacris. Londini, Impensis Mosis Pitt in Vico vocato Little Britain, 1670. in 4°. In this Second Part (amongst many other things, in this and the foregoing Part, Demonstrated, which are wont to be Postulated, but should be Proved;) the Excellent Author demonstrates the Center of Gravity to be (which hath not been done formerly, that we know of, by any;) and that, as to all Ponderation, the whole weight may justly be reputed There to be, where is its Center of Gravity; and so much to be mov'd: with other general Affections thereof. He shews also, from General Principles, How, by Calculation, to determine, as well the Magnitude, as the Center of Gravity, in innumerable sorts of Lines, Surfaces, and Solids, (and the Aggregates or Differences of such.) As, in all Right-lined Figures whatsoever; in all Solids bounded by Plains; in Cones also and Cylinders: And in Curve-lined Figures innumerable; not only (with Archimedes) in the Parabolar Figure, but likewise in all Paraboloids whatever (and the parts of such;) together with their Ungular Solids insisting on them; and their Conoecids or other Solids made by the Conversion (perfect, or imperfect,) of those Plains (or their Parts) about any Axe in the same Plain assigned; and the Center of Gravity of all these Solids. And the like also in other Figures Reciprocal to these Paraboloids, infinitely continued between such Curves and their Asymptotes: Shewing, which of those Figures (infinitely Long) are of Finit magnitude, (and what that is;) which, of Infinit: and, which of them have, which have not, Centers of Gravity; and, in those which have, how to Assign them: And the like of the Unguls appertaining to them, and the Solids made by their Conversion about an Axe: In many of which, the Magnitude of the Vngle or Solid is shew'd to be but Finit, where the Magnitude of the respective Plain (on which they stand, or by whose conversion they be made) is Infinit: and (contrary-wise) in Others, the Magnitude of the Vngle or Solid to be Infinit, where that of the Plain is but Finit. He gives also General Methods, How, from the Center of Gravity of a Plain (or of Lines described in a Plain) whose Magnitude is also known; to find the Magnitude of the Vngles, and Solids made by Conversion thereof about assigned Axes; and, from These, to find That: with other like Processes, from Plains to Solids, and so onward. He shews not only (with Archimedes) the Solidity and Surface of the Sphere and Cylinder; but of their Segments and Portions, cut off by a Plain, or any number of Plains, in what mannersoever; and the Center of Gravity of the same: most of which (as to the Solidity and Center of Gravity) is in like manner applicable to the Spheroid; useful in Guaging Vessels, and otherwise. He shews particularly, that the Scalene Cylindrick Surface, is to the Erect, as the Perimeter of an Ellipse to that of a Circle. He shews the Center of Gravity of all Arches of Circles, with their Superficial Vnguls, and the Surfaces made by the Conversion of such Arches about assigned Axes. And the like, of the Sectors, Segments, and other Portions of Circles, (which are applicable also to those of Ellipses;) with the Vnguls, and Solids made by such Conversion; and their Centers of Gravity. He doth the like in the Cycloid, shewing the length of the Curve, and of the Portions thereof, with their Centers of Gravity, and their several Superficial Vnguls, and Surfaces, made by Conversion, and the Centers of Gravity of all these. As likewise the Magnitude of the Plain, as well of the Primary Cycloid, as of the Secundary, whether Contracted or Protracted; with their several Tangents: and of the Segments and Portions of those Plains; with their several Vnguls, and Solids made by their Conversion (Perfect, or Imperfect,) and the Centers of Gravity of all these: Wherein in he prosecutes at large, what was delivered in his Book De Cycloide, formerly publish't; continuing his Calculations (which were there begun) to a great number of Particular Cases, which (for reasons then assigned) were there omitted, and which have not by any hitherto been computed. He doth the like, in the Figure of Right-Sines, in the Figure of Versed Sines, and of Arches; assigning the Magnitude of those Figures, and of their Segments and Portions; with their Unguls, and Solids by Conversion; and the Centers of Gravity of all these. Whence (amongst many other things) are deduced the sums of the Right-sines, Versed Sines, and Arches, appertaining to any assigned Portion of a Circle; and the sums of their Squares, Cubes, or other Powers. He doth the like in Spiral Figures, as well that of Archimedes, as an infinite number of other Spirals; shewing the Magnitude of the several Parts or Sectors; with their Centers of Gravity; (all applicable also to their respective Scalar Solids;) and the respective Paraboloids with which they Symbolize, and by whose Convolution they are made; their Tangents also, with much more concerning them. He prosecutes the same in part, but more briefly, in the Cissoid, and Conchoeid, and the Figure of Tangents; as to the Magnitude of those Figures, and the Parts thereof; their Unguls, Solids, and Centers of Gravity. He shews particularly as to the Cissoid, how it doth symbolize with the Cycloid, the parts of the one figure being equal to the respective parts of the other: And, as to the Conchoeid, That its Plain is in Magnitude (as well as Longitude) Infinite; yet a Solid made by its Conversion, equal to a finite Cylinder. He shews also the Quadrature of the Hyperbola, and parts thereof; their Unguls, solids, and Centers of Gravity: As also, an Hyperbolical Solid, made by the Conversion of a Straight Line about an Axis not in the same Plain; shewing the Magnitude of that Solid, and of its Parts, and their Centers of Gravity; and the several Sections of that Solid made by Plains in any assigned position; being Parabola's, Hyperboles, Ellipses, Circles, Parallelograms, and Triangles; according to the different Positions of the Cutting Plains: With many many other particulars, too many to be here rehearsed. In short, you have here well nigh All or the Greatest part of the most abstruse and intricate Speculations, as well of the Antient as the Moderns Geometers, hitherto discover'd, (with many new Additionals,) briefly and clearly deduced from Peculiar Principles and Methods of his own; (especially those of his *Arithmetica Infinitorum*;) which are also in like manner applicable to Innumerable other Cases, as occasion shall require. And his Method (in this and the former part) deducing all from the first principles, doth scarce depend upon any other Treatises as necessary to the understanding; save only the knowledge of some very ordinary things in common Geometry, and some few Propositions out of his own *Arithmetick of Infinity*, with some skill in the practice of Numerous and Specious Arithmetick. II. *EXERCITATIONES MECHANICÆ*, Alexandri Marchetti. Piss, 1669. in 4°. To be found at Mr. Starky's near Temple Bar. This Author declareth, that though many Eminent men have already treated of the Subject of this his Book, as Aristotle, Archimedes, Lucas Valerius, Guldinus, Galileus and others; yet hath he not been deterred from writing of the same Argument, esteeming, that he hath handled it more largely, more distinctly, and more clearly and easily: which, how he does actually perform, we leave to Mathematical Mechanicians to Judge. III. *The Natural History of NITER, or, a Philosophical Discourse of the Nature, Generation, Place, and Artificial Extraction of NITER, with its Vertues and Uses*, by WILLIAM CLARKE. London, 1670. in 8°. The Author of this Tract, esteeming, that most, who have known this Mineral Body, seem to have had but a partial knowledge of it, undertaketh to deliver here its Compleat History; And therefore First, describeth Niter by its properties, Figure (like that of Needles,) Taste (salt, sharp and cooling,) and Inflammability, Secondly, giveth some Chymical Analysis of Niter, both by calcination, in which he faith that it burns almost all away if refined; and by Distillation in a Retort, which maketh it yield a little. Flegme, then a Spirit, first in the form of a white, and soon after in that of a red vapour, corrosive and fetid, leaving a Caput mortuum behind. Where the Author giveth us his opinion, that this Body being thus analysed is rendered incapable of Redintegration; (concerning which the Reader may consult that Noble and Experienced Philosopher Mr. Boyle, in his Essay containing an Experiment with some Considerations touching the differing parts and Redintegration of Salt-petre; Printed 1661.) Thirdly, examines the Question; whether this Niter is the same with the Niter of the Antients; and resolveth it in the Affirmative. Fourthly, enquireth into the Generation and Place of Niter; Where he discusseth that Inquiry, whether in Houses, or Walls, Earthen floars, &c. Niter be generated, or separated and drawn from the Air by the heat and dryness of the Places; observing, that the dryer the places, where Niter is, are kept, there is more Niter. Whereupon he discourseth largely of the Niter in the Air, and making it not only a Meteor itself, and particularly a cause of lightning and thunder, but a general cause of Meteors, jointly with Sulphur. Fifthly, he declareth the Use of Niter to Animals and Vegetables; affirming first, that the life of Animals, being a burning Sulphur, is, as't were, kindled by the Nitrous Air received into the Lungs and communicated to the Heart; and adding that as without Air, which is the life of Fire, the innate animal-heat would extinguish; so that Air, being Nitrous, not only inflames it, but from its Coolness so allays the same, that it doth not too much prey upon our Radical moisture, and keeps our life in its due Fermentation; and moreover, by its dissolving nature renders the humors of the Body more fluid, and so more apt to perform their Circular motions, for the entertaining of life. Secondly, that without this Nitrosity the Sulphur of Seeds would lie dormant in the the Earth, be scorched up and wither'd, nor pass into the pores of Plants: Sixthly, he delivers the Artificial manner of Extracting and Refining of Niter; after he had first inform'd his Reader, How it may be known, whether a place be impregnated with Niter or no? Seventhly, he giveth the Vertues and Uses of Niter; first in Physick; where he affirms it to be not only Cooling, at least by removing hot humors, whereby the Body may become cooler; but also Resolving, Purgative and Diuretical: Upon the score of all which properties 'tis used not only in Burning Fevers, in the form of the Lapis prunella; (the preparation of which he describeth;) but also in those Diseases, in which are to be discharged by siege and Urine, hot, sharp, choleric and obstructive humors. Having dispatched this Medicinal use, he proceeds next to the use of Niter in Chymistry; where he observeth that by it may be made a pleasant and cooling Acid; or a hot and burning Corrosive: that sometimes it revives the Vomitive and Purgative vertue of Antimony, sometimes it kills the Vomitive, and reviveth only the Purgative; and sometimes it destroyes both, and quickens neither the Diuretick or Diaphoretick, &c. besides that it Calcineth, Sublimeth and Dissolveth Minerals and Metals. Thirdly, he adds the Use of Niter in Artillery; where he discourses of the reason of the Composition and Force of Gun-powder, together with the Use and Office of every Ingredient of the same. Fourthly and lastly, he sets down the Uses of Niter for Refiners, Dyers and Cooks. ADVERTISEMENT. The Author of the Discourse concerning Mineral waters, in Numb. 60, beginning p. 1074, desireth, that these lines may be inserted p. 1081, after the word Dysenteries, l. 19. viz. Neither do I think this water any thing the worse because of the Alone, but much the better for it in Hypochondriack maladies: For by its adstringency it defends the Tone of the Liver and the other natural parts, which otherwise are apt to be debilitated by purging and penetrating medicines; it being, according to Galen's advice, ever necessary to intermix some Adstringents with Hepatick remedies; in Art. Med. c. 95. to which agree very good writers, antient and modern. Errat. p. 1096. l. 2. r. if he hit. LONDON, Printed by T.R. for John Martyn, Printer to the Royal-Society. 1670.