An Account of Some Books

there being so vast a deal of room, that 40000 People may shelter themselves in it. And he that would attempt to seek them out in this vast Wilderness of Walks and Pillars, without an expert Guide, would not only be in hazard of loosing his way, but of being knock't in the head at the Corner of every Pillar, where people lurking in the dark with their Carabins and Fowling pieces, would have fair opportunity to shoot them by the light of their own Torches. In this vast Grotto 'tis remarkable, that there is but little Rubbish: which shews both the goodness of the Stone, and the carefulness of the Workmen. And in divers places there are little Pools of Water, perhaps made on purpose for Beasts to drink, and to serve for other uses in time of need: For in no place almost are there any Droppings to be seen; nor are the Walks at all wet under-foot; only it seems, that Rain gets in by the Air-shafts, which, for saving of labour, and perhaps too, to make these Pools, are let down from such places commonly, as are the Pools thereabout; and so the Rain, that falls on the higher grounds, does easily find the way thither. An Account of some Books. I. TRACTS written by the Honourable Robert Boyle, of a Discovery of the Admirable RAREFACTION of the AIR (even without Heat:) New Observations about the DURATION of the SPRING of the AIR: New Experiments touching the CONDENSATION of the Air by meer COLD; and its COMPRES- SION without Mechanical Engins: And the admirably DIFFERING EXTENSION of the same Quantity of Air rarified and compressed. London, for H. Herringman, 1670. in 4°. The main drift of these Excellent Tracts is, to invite the Curious to observe the stupendious Mutability of the Air, as to Rarity and Density, whereby the same Quantity of Air, being sometimes compres'd, sometimes dilated, may change its Dimensions to a degree, that seems almost to transcend the power of Nature and Art, and might be look't upon as incredible, if it were abruptly and nakedly proposed, or by a person of only common skill in these matters. It will then appear by the Experiments and Calculation, made by our Noble Author, that, according to the least Estimate of any recited in them, the Extension of the same Quantity of Air, is as 1. to 2744, or thereabouts: And if, instead of the moderatest, there be taken the greatest Expansion of the Air; being as about 13000 to 1, when the uncomprest Air was highly rarify'd, that number being multiplyed by 40, because of the great Compression of the Air, effected by Cold (as appears in the Third of these Tracts,) will amount to 520000, for the number of times, by which the Air at one time exceeds the same portion of Air at another time: Which is an Expansion so great, that it will easily keep the Reader from thinking the Title of this Discourse, where the Rarefaction of the Air is call'd Admirable, immodest. It will also appear by these Tracts, that the Air may by the Intervention of Art and Instruments be much more expanded, than it has yet been found to be by the bare application of External Heat, though it were that of an Intense Fire itself. The Natural Philosopher will doubtless, upon the reading of this strange Expansion of the Air, be excited to consider, when he shall look on one of our Author's well exhausted Receivers, How small a proportion the Common Aereal particles, which are very sparingly dispers'd there, bear to the whole Cavity of the Vessel, which, before it was exhausted, was thought to be replenish't with Air alone. Certainly both the Cartesians and Epicureans will find themselves highly concern'd in this matter. The former will endeavor thereby to establish the necessity of their Materia subtilis, to maintain the Plenitude of the World, and the Circle they attribute to Moving Bodies. The latter will think, they have cause here to triumph, as believing to have met with a more illustrious Instance, than ever, of their Vacuum Coacervatum within the World; since here is an impenetrable Vessel, out of which 'tis manifest, that an almost incredible proportion of Aerial substance hath been made to issue; whereas 'tis no ways manifest to any of our senses, that any other Body hath got into succeed in its room. II. ELEMENTA GEOMETRIÆ PLANÆ. Authore Ægidio Francisco de Gottignies Bruxellensis, Soc. Jesu in Collegio Romano Matheæos Professore, Romæ 1669. in 12. This Author, in a Monitum to the Students of Geometry, intimates, that he hath read Mathematicks more than 7 years at Rome; that it hath been his custome to advise his Scholars, first to read over the Definitions, the Titles of Propositions, and to exercise themselves in the Construction of Problems, without being solicitous of the truth of the Propositions or Constructions, until they become familiar; and after they are somewhat conversant with the Geometrick Assertions and Phrases, then to doubt of their truth as much as they please, and study their Demonstration. The same, in the Proeme thinking it convenient to begin with Quantity, treats of it abstractly, as void of such affections and modes as are congruent thereto. 1. In his first Chapter he giveth Definitions, Postulates, and Axiomes. 2. In the second, because one quantity in relation to another is said to have a Ratio or Proportion, he treats of Ratio’s, and delivers the doctrine of the fifth Book of Euclid; to which are annexed 7 questions about Geometrical Proportions with their Solutions, clearing up the debates, that through the mistakes of some late Authors have risen about Ratio’s. 3. He treats of Angles, and of the affections of Angles in plain Right-lined Figures. And at the end of this Chapter he states the question, Whether an Angle be a Quantity shewing, that Clavius affirms all Angles to be quantities; Peletarius denies the Angle of Contact to be a quantity; Tacquet condemns both, denying any Angle to be a quantity, to whom our Author assents, and on this Hypothesis removeth 5 Paradoxes, that are natural to the other assertion. And whereas a late Writer alledgedeth, that it may be pleaded to be the opinion of the Antients, he saith, that among the Learned moderns, it is now refuted, herein siding with Gregory of St. Vincent, Aynscott, Tacquet, and Dr. Wallis. 4. He treats of Rectangles. 5. Of Triangles and Right-lined Figures. 6. Of Circles, where he delivers the Doctrine of the third Book of Euclid; and, imitating Archimedes, enlargeth this Chapter with other propertys, which he had first shewn to be congruent to Right-lined Figures. 7. He treats of Problemes, by which a Preparation is made to pass from Speculation to Use and Practice. The Author having thus altered Euclid's order, giveth an Index, to shew where the Propositions of the 1, 2, 3, 5 and 6th. Book of Euclid are to be found in these Elements. He hath passed over all the Propositions of the 4th. Book of Euclid, as superfluous in his method: In that Book, 'tis known, that Euclid teacheth, How to Inscribe or Circumscribe some, but not any Regular Figures about a Circle: Of this he treats at the end of the 7th. Chapter. This Doctrine is either necessary for Practice, as in Fortification; or in order to the Construction of the Canon of Sines. He intends to treat of Trigonometry and Practical Geometry elsewhere, saying in his Dedication: Euclidem ex novo adornare studui, brevi tamen scriptione concinnatum, ut esset opportunior. Ex quo tanquam ex fundamento pendet reliqua mearum doctrina tractationum, quas prae lo paratas me habere probè nosti. As to his method of Demonstration, he faith, Demonstrations vix alias pono, quàm affirmativas, ut discentibus constet ea qua proponuntur non tantum vera esse, sed etiam cur vera sint: in Euclide non paucia per negativas demonstratio-nes probantur, vel in his probandis negative tantum probata as- sumuntur; & An recte omnia, nonnulli controvertunt. III. SYNOPSI GEOMETRICA cum Tribus Opusculis, De LINEA SINUUM & CYCLOIDE; De MAXIMIS & MI- NIMIS, Centuria; Et SYNOPSI GEOMETRIÆ PLANÆ, Auth.Honor.Fabry S.Jesu. Lugduni Galliarum 1669 in 12°. This Author in this Geometrical Synopsis hath endeavoured, as M. Gottignies, (just now taken notice of,) promiseth to do in his New Euclid, to render Geometry clearer and easier by delivering such Demonstrations, as prove the thing in hand by direct and intrinsick Principles, not such as are indirect, and leading ad absurdum & impossible, whereby 'tis only concluded, that the thing cannot be false, but not shewn, why it is and must be true. In reference to which, he considers, that, whereas Geo- N n metry consists in demonstrating the proprieties of Quantity, there is no such propriety, but it belongs to it by some genuine and intrinsic principle, easily to be found out by the Analysis or Genesis of Quantity. By which way he Judgeth, that Geometry may be exceedingly contracted, forasmuch as very many things, separately demonstrated in the received way, may then be evinced jointly by one plain and easy Demonstration; considering that, where the same propriety belongs to various quantities and figures from the same intrinsic Principle, whether they be Plain, or Solid, or Right-lined, or Curve, or Mixt; nothing hinders, but that propriety may be Demonstrated of them all by one only Demonstration. And hence this Author is inclinable to lay aside those many Divisions of Geometry, as are made by Authors, viz. into Trigonometry, Planometry and Stereometry; and peculiar and prolix Treatises of Conical Sections; of the Sphere and Cylinder; of Lines of divers kinds; of Plain and Spherical Triangles; of a Solid Angle; of Proportions and Proportionalties, &c: esteeming, that a more convenient Division will serve his Design; whence he compriseth this whole Synopsis in two parts. The first treats of the Elements for Beginners, and contains 6 parts: In the first whereof are delivered the Definitions and Explications of Terms, the Axioms, and Postulata. In the second, are explain'd the Genesis and Analysis of Figures, and their different Classes. In the third, are demonstrated the Elements of Lines and Angles. In the fourth, is treated of Ratio's and Proportions. In the fifth, are considered the Products of the Segments of a Line, multiplied into one another. In the sixth, are handled the remaining Elements. In the Other, he proceeds to the Demonstration of higher and abstruser things; and this part he divideth into several Classes, each of which contains all its homogenal figures, Right-lin'd or Curve, Solid or not Solid; there being so many several Ranks, as there are different ways of their Generation. These Classes are here distributed into two sorts, the one contains those Figures, whose Generating quantity is drawn either into the whole Altitude, or into its Rational or Commensurable Segment, for the Equation of the Figure; the other is of those, whose Generating quantity can only be drawn into an Irratio- nal Line, for Equation. But he adds, that it often falls out, that one and the same Figure belongs to several Classes, in regard that it may be resolved into divers Elements, or have more than one Genitrix, and therefore, according to the variety of the Genitrix, may be diversly generated. And this, he esteems, doth very much commend his Method, in regard that there is the same Equation of the same Figure, whether it be demonstrated in this or that Classis by this Intrinsick Principle. Meantime this Author denyeth not, that this kind of direct Method was before him deliver'd and publish'd by Bonaventura Cavalieri, but adds, that it was done with such difficulties and obscurities, as deterred young Students from it; which in this Synopsis are said to be avoided, or removed. As to the Three Opuscula, adjoyned to the Synopsis, the Author affirms of the First, that it was publish't Eleven years since, but uncorrectedly; now Re-printed more carefully, and with a design, to give a Specimen of his new Method in that abstruse Argument; adding withal, that, for ought he knows, he is the first that hath written of this Subject; only he had seen some few things concerning the Cycloid in Torricellius, in that Appendix, which he subjoyn'd to the Problem of the Dimension of the Parabola, where he very well demonstrates, that the Space contained by the Cycloid and Basis, is Triplicate to the Generating Circle. But our Author affirms to have here added many new Demonstrations, alledging, that Torricellius in the said Appendix hath demonstrated nothing else, but that one thing just now recited. And though the same in his First Book De Motu Gravium doth propose many excellent things of the Cycloid, yet our Author observeth, that he hath demonstrated none of those. Concerning the second Opuscle, viz. the Century of his Propositions De Maximis & Minimis, he affirms, to have written them, for his divertisement, many years ago. And the third, which is a short piece of Trigonometry, he saith to have hastily Composed at the sollicitation of an Ingenious Friend, to serve Mathematical Beginners. IV. DIALOGI PHYSICI, quorum Primus de Lumine; Secundus & Tertius De VI PERCUSSIONIS & MOTU; Quartus De HUMORIS ELEVATIONE per CANALICULUM; Quintus Quintus & Sextus De Variis Selectis. Auth Honor. Fabry, s. Jesu, Lugduni Galliarum. 1669. in 8°. His Learn'd Jesuit in those Dialogues writeth against Grimaldi, Alphonsus Borelli, and Montanari, who in divers things differ from what he hath written: Against the first, concerning Light, and that great controverted point, Whether it be a Body? And whether Reflection, and Refraction prove it to be such? &c. Against the second he writeth, about Motion and Percussion, where many things are discussed; as, Whether motion be produced, or traduced? Whether the impetus of the least Body may move the greatest Body? Whether the Force of Percussion be a certain action of Compression in the Impellent Body? What are the Laws of two Projected Bodies; equal, or unequal; of equal, or unequal velocity? Whether the Times of the Vibrations of different Pendulums are in a sub-duplicate proportion of their Lengths? Whether a Body impelled, being reflected by a Springy and Compressed Body, restoring itself, be moved and carried back with that Impetus only, which it received from the same? Whether a Body Horizontally projected will at the same time come to the ground, as if it had of itself fallen down Perpendicularly? Why Bricks are broken by the percussions of an Hammer, though they remain whole under the weight of a vast and bulky Body? And why an Hatchet cleaveth Wood, whereas a very heavy weight laid on an Hatcher fixed in Wood, doth not? What is the Principle of the Motion of Restitution? And many more. Against the third he writeth, about the Ascent of Liquors in slender Tubes; to wit, whether that Rising proceeds from the Gravitation of the Air, or from its Compression only, prescinded from its weight? Whether Liquors do rise equally high, in longer and shorter Tubes, but of equal bore? &c. The Two last Dialogues contain Miscellanies: As, of the Impetus innate in Bodies, assigned them by Nature to attain their respective Ends; of the Gravitation of the Air and its pressure downwards, to make Vapors ascend; of the Variety of Motion in Heavier and Lighter Balls moved on Longer or Shorter, thicker or slenderer strings; of new Mechanical Powers; of an Hypothesis for solving the Phenomena of the Tides by the Pressure of the Atmosphere, importing, that the Tides do do vary according to the inequality, or the various Circles of the Air's pressure, and the several Tracts of those Circles, in re- spect of their Scite and Extent; so that if all the Circles of that pressure of the Air were free, that is, if the water did cover the whole Surface of the Earth, it would rise much higher in the Tydes; (See pag. 406, 407:) Besides, of a Question, Whe- ther in a Ship moved, all the motions of the people carried in it will be made after the same manner, as if made in a Ship not moved; Of the 7 Rules of Motion deliver'd by M. Huygens, with some considerations thereon, p. 411; Of the great Com- pression of the Air, in reference to what Mr. Boyle hath pub- lish't on that Subje&., p. 436; Of the Controversy, Whether the Mercury in the Torricell. Experiment be sustain'd by the exte- nal Air, or by a Tense matter within; Of the cause of the Glass- drops shiver'd in small pieces by breaking off the tail of them, p. 467; Of Electricity, p. 475, &c. But whether our Author have the better of those, against whom he writes, I shall not take upon me to Judge, but leave it to the Reader to think as he shall see cause. V. ANTONII MOLINETTI, Phil. & Med. Veneti, &c. DIS- SSERTATIONES ANATOMICÆ & PATHOLOGICÆ de Sen- sibus & eorum Organis. Patavii, 1669. in 4°. In this Learned Treatise of the Senses, the Author begins from the consideration of the Touch, discoursing of the genuin Organ thereof, which he maketh to be the soft substance of the Nerve only. Next, he treats of the Sight and its Organ; where he largely discusseth the old Controversy of the manner how Vision is made, whether by the Reception of the Species or visible rays of the Object, or by the Emission of the Spirits of the Eye; maintaining the former, and refusing the latter. Then he pro- ceedeth; 1. To speak of the nature of Light and Colours, e- steeming the distinction of Colours into Real and Apparent to be puerile. 2. To treat of the Three Refractions of the Lumi- nous rays made in the Eye, by the several humors thereof. 3. To assign the different apertures of the Pupil according to the distance of the object, and the degrees of its illumination; as also the respective offices of the Chrystillin, Vitreous, and Aqueous humors; and the reason of their position, and confi- guration, 4. To give the History of the Tunicles and Muscles of the Eye, asserting the Retina to be the formal organ of Vision; and Seven Muscles to perform all the motions therein; and observing the curious structure and apparatus in all. 5. To discourse of the various Distempers of Eyes, and to observe, that there is scarce any particle of that organ, not subject to some peculiar distemper; which he very learnedly and accurately specifies and enlarges upon. Thirdly, he treats of Hearing and its Organ: having premised, that the difference of the several Senses consists only in the different apparatus, by which all the sensible Objects are received in one and the same formal organ, of the same kind; as also, what Analogy there is in the structure of the Eye and Ear; the Cornea of the one answering the Membran of the other; the Water within the Cornea, to the Air within the Tympanum; the Ciliar ligaments of the Eye, relaxing or straightening the Pupil, to the Stapes of the Ear, capable to be easily moved inward, and a little outward. Now of this Sense of Hearing he observeth, 1. The Air-reflecting organ (answerable to the Refractive organ in the Eye) and remarketh the admirableness of its fabric; as also how exactly every vibration of the Air, made upon the Drum by the outward Air, is by the Labyrinth of the Eye distinguish'd from one another. 2. The manner, how Hearing is performed; where occur divers un-common Observations about the Malleus, Incus, and Stapes; and the three Holes in the Drum; as also of the passage, by which the cavity of the Drum hath a consent with the Palat, &c. 3. The many distempers of this Organ, very accurately described. Fourthly, concerning the Sense of smelling, he 1. Taketh notice, that Vesalius was the first, that rightly observed the Olfactory Nerves. 2. He observeth the Analogy of this Sense to those of Seeing and Hearing. 3. Giveth the reason, why Doggs, Horses, and some other Animals excel the rest in the strength of Smelling. 4. Affirms, that moisture falls into the Nose, not by the Holes of the Os Ethmoides, but by those that are in the inward corners of the Eyes. 4. The Diseases of this Sense; where the Author taketh occasion to commend the Art of Talizacotius in restoring lost Noses, and to confirm the truth of that Practice, performed by his own Father, Fifthly, Fifthly, touching the Taste, he 1. Maketh the Tongue the Organ of it, as it is made up of such a kind of Porous Flesh, covered with such a coat, and very plentifully enterwoven with such nerves; furnish't with a fine Saliva, which being mixed with the meat and drink, sinks it into the nerves through the pores of the Coat, and so gives different kinds of Taste. 2. Compareth this Sense with all the former, by observing the Analogy betwixt them. 3. Assigneth the difference between Taste and simple Touch. 4. Enumerateth the Affections of the Tongue, and insists especially upon the Convulsion and Palsy, which it is subject to. Having dispatched his Dissertation about the Five Senses, he proceeds to the consideration of the Brain, whereof he 1. Explains the admirable structure, connexion and dependency of its parts. 2. Shews the difference of the Animals Spirits from the Vital; which he esteems to be only this, That the Animal Spirits are Vital Spirits highly rectified, refined and perfected in and by the Brain, for Sensation. 3. Lays open the origine of the Nerves, proceeding from that part of the Brain, call'd Pons Cerebri, which he makes to be nothing else but a Congeries or Heap of innumerable Filaments, divaricated out of the Solider substance of the Brain; whence all the Nerves (many of those threds being joyned together) take their rise; which in their issue out of the Bones, either those of the Skull or the Vertebra's, are invested by both Membrans, which contain them as well, as they do the Brain it self. 4. Declares, that in the said Pons Cerebri, from whence all the Nerves proceed, is transacted the Common Sensation; confidently affirming, that whatever motions are made in the Organs of Sense by the Spirits that are in the Nerves, they must needs be conveyed into the Principle of the Nerves (which, in his judgment, is the Pons;) and that performed in a moment of time, by reason of the continuity of the Spirits from the Sensories to the said common Source. 5. Distinguisheth the Operations of the Common Sense from those of the Phancy, and Memory; and withal teacheth, how the Rational Soul differenceth the Apprehensions of things from those made by Brutes. 6. Determines not, whether, for the Memory, the vestigia of things are imprelled in the Brain; or whether the substance of the Brain be so framed, that according to the different agitation of the Spirits it may be contracted or dilated; or else, whether the Pores or minute Passages sages between the medullar Filaments be open'd, or shut, and that more or less; or lastly, whether it be, that the Spirits are variously disposed, whilst the Medulla of the Brain remains in the same state? 7. Discourseth of Sleep and Waking; where he very curiously observeth, first, How far there is in Sleep a Cessation of Sense and Motion; and how Night-walkings and Respiration (two very strong Motions) are performed in Sleep: Secondly, What is the immediate cause of that Cessation, viz., a scanty and alter'd influx of the Spirits into the Organs of outward Sense. 8. Affirbeth the exact knowledge of the Medulla Spinalis to that excellent English Physitian and Anatomist Dr. Willis. 9. Explains the order in which the several Combinations of the Nerves do proceed, out of the Medullar Mass of the Brain, into and through the whole Body. 10. Concludeth the whole with an Explication of the Affections and Diseases of the Brain; and shews, first, How the various Head-aches are caused by the various qualities of the parts that compose the Blood, which being either bilious, sulphureous, salin, aqueous, or terrestrial, do accordingly cause lacera ting, pricking, vellicating, or heavy pains: Secondly, How the Dropsy of the Brain is caused by the copious ferocities gather'd between the Membrans of it. Thirdly, How Ulcers, Obstructions, and Inflammations are produced. Fourthly, How those many Perturbations and Symptoms are occasioned in the Brain, as Sadness, Fear, Sleepiness, Madness, Forgetfulness; Epilepsy's, Apoplexy's, among which two last he finds this difference, that an Epilepsy is not necessarily preceded by any Obstruction; an irritation and an offensive afflux to the Sensible parts, being able to produce it alone; whereas an Apoplexy never comes without an Obstruction of the Spirits. Fifthly, How Palpy's are caused, viz., by an influx of impure Spirits from the Origine of the Nerves into the beginnings of the same. Sixthly, How overmuch Watching is occasioned, namely by over-hot Spirits; as an Un-natural Sleep is produced by thick, torpid and cold vapors, intermingled with the Spirits, &c. Errata. In Numb.65,p.2014.l.17.del.first,and read, were started. Besides, the Reader is desired, not to be offended at the oversight of the Printer, who in this same Tract of N 65, when he should have numbered page 2107, did print 2007; whereby some confusion would arise in the Index, that is to follow, if therein the Publisher did not intend to prevent it in some measure by quoting as well the Number of these Tracts, as the page. In this Numb.67,p.2040.l.17. del. Farewell. London, Printed for John Martyn, Printer to the Royal Society.