An Account of Some Books

An Account of some Books. I. ELEMENTS de GEOMETRIE; par le P. Ignace Gaston Pardies, dela Comp. de l. A Paris 1671, in 12°. The Learned Author of this Tract declareth, that in it he hath given a short and easy Method to learn what is necessary to be known of Euclid, Archimedes, Apollonius, and of the best Inventions of the Ancient and Modern Geometrians. Of which Method he hath now publish't the first 9 Books; reserving to another time the remaining seven, which, he faith, are to explain the more profound and sublime inventions of this Science, but are not so necessary to those, that have a mind to begin the Study of it; for whose greater conveniency he seems to have taken the pains to divulge this first part, In which he treateth of what he thought most considerable in the 15 Books of Euclid; and besides, What Archimedes hath demonstrated of the Quadrature of the Circle, as also the Doctrine of Logarithms, of Sinus's, &c. He shews the admirable proprieties of the Numbers, which Euclid hath demonstrated in the 7, 8, and 9th. of his Elements. He affirms, to have found a new way of Teaching the Doctrine of Incommensurables, and given Directions in four or five small pages, perfectly to comprehend what very few persons, even of those that meddle with Geometry, are able to understand. Besides this, he treateth of divers kinds of Progressions, chiefly insisting on the Two most famous ones, viz. the Geometrical and Arithmetical; and comparing them one with another, he treateth of Logarithms, and shews the Art of them by the means of a Geometrick Line, by him esteem'd very useful for the Resolution of all sorts of Algebraical Problems; by the help of which he faith to have formerly squared the Hyperbola. He concludeth this first Part with a short Practical Geometry; wherein, besides the more easy and more common Operations Operations, he faith he hath delivered the Principles not only of measuring the Magnitudes and Distances of places Inaccessible; of making the Map of a place or a province; of finding the Sinus's, Tangents and Secants of all Angles; but in short, of coming to the Knowledge of what ever appertains to this part of Geometry. In his Preface he promiseth to give us, next, his Algebra, his Doctrine of Conical Sections, Sphericks and Staticks; but, above all, to establish Five or six General Rules, whence afterwards, by way of Corollaries, may be drawn the demonstration of an Infinity of Propositions, which pass for great ones in Geometry: Where, he adds, shall be found the nature and measure of Asymptotick spaces, as the most admirable knowledge in the World; those spaces being of an extent actually infinite, comprised between two lines, which being infinitely prolonged do never meet; but of which yet it may be demonstrated, that they are equal to a Circle or another determined figure; so that Infinite itself, as immense and innumerable as it is, may notwithstanding be reduced to a calculus and to a Geometrical measure, and that the Mind of Man, being greater than it, is capable to comprehend it; For since Imagination cannot attain so far as to represent unto us what is Infinite; the demonstration, we make of the nature and proprieties of this immense and infinite Alymptotick extension, convinceth us at the same time, that we have within us a power capable to represent unto us this infinite Extension. For, faith he, as, for measuring with a Rule and Compass a Figure represented upon paper, I must have this Figure present to mine eyes and hands, that so, by applying the Instruments to its angles and sides, I may take all the dimensions of it, and so determine its Magnitude; even so, for taking with the rule of my Reason the measures of this Asymptotick space, I must have an Idea thereof inwardly presented to my Mind, and this Mind by applying it self, as it were, to this Idea and Interior figure, must take the dimensions of it, determine its bigness, and demonstrate all its proprieties, &c. In the same Preface the Author deduceth largely, wherein his Method of Teaching Geometry differs from the Methods of others, as to facility and intelligibleness: which we forbear to transcribe, because it would take up too much of that room, which we shall need for giving some account of Two other Authors. II. Regnerus de Graaf de SVCCO PANCREATICO. Lugduni Batavorum, An. 1671, in 12°. That the Reader may not think, we twice serve up the same matter, forasmuch as we may seem to have described this very Tract long ago, viz. in Numb. 10. p. 178; we must inform him, that this Edition is by the Author himself esteem'd to deserve in a manner the Name of a New Treatise, by reason of several New Observations added, and divers Objections solved therein. Besides, that there is annexed to it the Author's Ingenious Letter to D. Lucas Schacht, Professor of Physick at Leyden, de Partibus Genitalibus Mulierum; of which subject he therein summarily delivers, what he intends to compose hereafter a Book of. De quo quidem Argumento ne nihil dicamus, linguâ minus communi rem totam, ab Authore hic traditam, compendificare studebimus. Ait itaque, Vasa praeparantia Mulierum breviora esse quam Virorum: Testes Muliebres nullam cum Virilibus similitudinem obtinere, cum non sint vascula seminaria, sed perfectissima ova in se continent, ad que vasa praeparantia excurrant: Ova in Testibus illis contenta facunda reddi, quatenus seminalis Aura, ex Utero per patentes ejus Tubas ad Testes pervadens, in Ovis inibi latitantibus fermentationem excitat; obque ipso Testiculorum substantiam ad expellenda Ova disponit, qua à simbría, Tubarum extremitate, excepta, per Tubas ad Uterum transeant: Ligamenta Uteri nil aliudeesse quam membranas multos vasculis refertas quorum extremitates in pinguedine Pubis terminentur & evanescant: Arterias Hypogastricas, plures disseminare propagines ad Uterum, quam ad Vaginam ejus; earum, qua ad Uterum excurrunt, praecipuam mira miro ductu utrinque ad Uteri fundum pertingere, atque Arteriis praeparantibus sive spermaticis tam affabre uniri, ut peritiores etiam Anatomici dubitare possint, utrum ab Hypogastricis, an vero à Praeparantibus Arteriis sanguinem suum arteriosum Testes ac Tubae hauriant: Venas Hypogastricas, etiam ad Uterum, Vaginae & reliquas partes tendentes, sibi invicem tot támque patentibus nexibus copulari, ut inflatâ vel minimâ venulâ protinus totius Uteri, Vaginae, Tubarum atque Testium vena distendantur: Utero secundum longitudinem per medium diviso, dissectorum vasorum orificio quamplurima conspicis, atque Uteri cavitatem tantum unicam reperiri, eámque ab interno Uteri osculo usque ad magnam suam capacitatem rugosam esse, pluribusque foraminulis praeditam, ex quibus, presso Utero, pituitosa & viscida materia prodeat: Adhæc, in rugosa Vaginae tunica hinc inde etiam porulos conspicis, sed longè pauciores ac minores, quàm in collo Uteri, nisi prope Vagina orificium, ubi, in Superiori inprimis parte, prope meatum urinarium, & in ipso, tam magni ductus sive lacunæ reperiantur, ut stylum crassum sculum admittant, ex quibus in salaciioribus, non minus quàm ex iis, qui sunt in Uteri collo, materia sero pituitosa (impropriè femen vocata) cum impetu erumpit. Denique, Clitoridi, ut Membro virili, arterias, venas & nervos communicari, & quoad substantiam cum Pene virili aliquam similitudinem habere; carere tamen Urethrae, & duobus tantum Musculis instrui, licet plerique quatuor numerent; sub horum Musculorum carnosis expansionibus (spongiosum quoddam reperiri corpus, ex multis vasculis & fibrillis conflatum, quod proprià membranà cingatur, & ad latera Vaginae, propè ejus orificium, ab inferiori parte ad membranosam usque Clitoridis substantiam utrinque ascendet, uti, si infletur, conspicendum se præbeat. Haecenus Industrius juxta ac Doctus hic Author, Cujus ampliorem de hac materia Dissertationem, fide Observationibus & Experimentis nixam, impensè desideramus; inprimis vero, ut liquidius, quàm haecenus factum, ostendatur, quo scil. meatu Ova ista quarumvis fæmellarum è Testibus in Tubas, & per Tubas, quae aliquà sui parte imperivia habentur, in Uterum devolvantur. Spes interim haud levis me fovet, Controversiam hanc de mulierum Ovariis, quàm ea hoc ipso tempore Peritissimorum quorumque in Anglia Anglia, Gallia, Belgio, &c. Anatomicorum tribunali se stiterit, brevi ab ipso, in rei Anatomicae incrementum, penitus elucidatum iri? Vid. Numb. 70. p. 2136. III. Physico Mathesis de LUMINE, COLORIBUS & IRLDE, &c. Auth. Franc. Maria Grimaldo s.j. Bologna, 1665. in 4°. This Learned Treatise was not to be altogether omitted in these Philosophical Occurrences, though an Account of it hath been deferr'd (too long,) it being but lately fallen into the Publisher's hands. The Author then finding, that much obscurity was left in the Doctrine of Light, and esteeming it rather commendable than presumptuous, to endeavor the clearing of it, especially if that be done by Experiments (which he judgeth an exceedingly conducive way for the Improvement of all Natural Knowledge;) undertaketh in Two parts to deliver his Tryals and Meditations on this Subject: In the First are contained the several Experiments, which may favour the Doctrine of the Substantiality of Light, together with the Ratiocinations thence arising. In the Second is represented, What may be answered to all those Arguments, so as to save the Peripatetick Opinion of the Accidentality of Light: Which yet is done in such a manner, as that the Author leaveth a liberty to the Judicious Reader, to embrace which of these two Opinions he shall think the more probable. But, more particularly, in the former part he explains, How many ways Light is propagated or diffused, viz. not only directly, and by refraction, and reflexion, but also by diffraction; which last, according to him, is done, when the parts of Light, separated by a manifold dissection, do in the same medium proceed in different ways. Next, he considers the Nature of Light, as also Daphaneity, and Opacity; and taketh notice, that most Bodies, whether Solid or Fluid, are porous; on which occasion he ventures to explain almost the whole Philosophy of Magneticks. Then he discusseth the Question, Whether the diffusion of Light be Instantaneous, and concludeth it in the Negative, though the Duration of it be imperceptible. This done, he examines the nature of Reflexion and Refraction, and seems to acknowledge, that, supposing Light to be a Substance very fluid and very subtile, an account may easily be given, why it is reflected and re- fracted, and why it observes such Laws in its reflexion and refraction, as really it doth. Further, he discourseth of Colours, and considers, How Light is changed into Colour, sometimes by Reflexion alone, sometimes by Refraction alone, sometimes without either and without the change of the Medium, vid. by Diffraction. He explains also, How Light by the sole intrinsick modifica- tion of it self, passeth sometimes into a colour that is com- monly called Apparent: Where he declareth, that the reason, why Light passeth into an Apparent colour, is not some de- terminate Angle, at which the rays amongst themselves are inclined; but that that Colour is produced by the intension and density of Light. He teaches also, That to the Vision of things permanently colour'd, there are not required any intentional species, transmitted from them, and contradistinct to Light; but that the Light, which is diffused, or at least re- flected from things colour'd, is sufficient; yet with such a Mo- dification, as is to be found in Light apparently coloured: On which occasion many particulars are delivered concerning Reflex Vision, together with an Explication of that Quere, How the Place of the thing seen is perceived? &c. To all which is added, that the Modification of Light, by which it is both permanently, and (as they speak) apparently coloured, or made sensible under the representation of Colour, may not improbably be said to be a determinate and most finely fur- row'd Undulation of the same, and a kind of tremulous dif- fusion, with a certain very subtle floating, whereby it doth, in a peculiar way of application, affect the Organ of Vision: Which is illustrated and confirmed by what is by Philosophers taught: taught of Sound and Hearing. Upon which 'tis inferr'd, that Colours are not anything permanent in visible things, not of themselves lucid, when they are not illuminated; but that they are the Light itself, under some peculiar Modification made sensible by the Sight. Lastly, This first part is ended with a large Discourse of the Rainbow, its Colours and their Order, its Circular figure, the Concentricness of Rainbows, &c. Concluding upon the whole, that a Rainbow, both the Primary and Secondary, is generated from the Solar rays, reflected and refracted by the drops of a rorid cloud, so that the Primary is represented by the rays that are once reflected within those drops; but the Secondary, by the rays twice reflected, and which after a double refraction in both cases pass to the Eye, placed in the axis of the Rainbow. The Second Part is dispatched in Six Propositions; in which the Author taketh pains, notwithstanding all what he hath delivered before, to abet Aristotle's opinion, importing, that Light is an Accident; though he dissembleth not, that that Philosopher seems to have somewhere favour'd the contrary Opinion; as he also acknowledgeth, that the Experiments and the Reasons thence deduced for the Substantiality of Light, approach very near to a Physico-Mathematical evidence, especially with such men as have, either skilfully and carefully made those Experiments, themselves, or attentively beheld them, when made by others. However, he maketh a shift to say something by way of Answer to all the Arguments, produced in the first place for the proof of Lights being a Substance: yet denying, that, though Light were an Accident, it would follow, that Colours, call'd Permanent, are something distinct from Light, and residing in Bodies when Light is absent. IV. Marci IV. Marci Meibomii de Fabrica TRIREMIVM Liber, Amstelodami 1671. in 4°. This Discourse treats first of the Occasion and Original of Shipping, and relates, that it began with Oars, and then was improved by Sails, and at last was practised with the use of both. In the beginning, for Celerity and Fight, they multiplied Oares, and, for some strength, they fortified their ships with strong Beaks, as Birds of prey have strong Wings and a sharp Beak. He ascribes to the Sidonians the first invention of Building long Ships for War, and the contrivance of filling them with Oares in such a manner, that no void spaces might be left. As broader and shorter Ships were built for burthen. Gallies he distinguishes into Monocrota, wherein one or more rows of men do sit in the same level or plain; and Polycrota, in which the Rowers sit in divers heights, one above another, as in Amphitheaters; whence the Biremis, Trireme, Quadrireme, and so on to the Tesseracanteris, the biggest that we read of, and recorded to have been made by Philopater. In the Monocrota he considers the manner of the Sitting of the Rowers; and the Intercalmium, or the space between the two Oares of the same Versus or Row; referring the Transfixa to the Polycrota Gallies; where he hath occasion to examine the measure of the great and Roman foot and cubit; as also to give the meaning of the words Versus (Gr. στιχός) or στιχός) and Ordo (Gr. ὁρός). Next he endeavors to explain in the Gallies that are Polycrota of 3, 4, 5, or more tires of Rowers, seated in different heights, how those men could be placed. And here he pretends to have been the first, that hath perfected the way of lessening the height of the ancient Gallies, by devising these two Expedients; by the first of which (said to have been published by him 22 years since) he affirms to have shewed, so to place the the Lateral Rowers, as that he that sits behind an other, may move his hands and Oar under the feet of the rower sitting next before him: By which means three lateral Rowers, which, according to Scaliger's way, would require the height of $13\frac{1}{2}$ feet, will be content with the space of $7\frac{1}{2}$ feet. By the other Invention, which he now adds, he pretends to have found a new place in those Ships for almost half the number of Rowers; forasmuch as on the side of the aforeaid Rowers, he placeth others in the middle of the Ship, in transtria or traverse Seats, which, as he imagines, (how consonantly to use and practice, the Intelligent soon will judge) may thrust out their Oars under the Seats of the Lateral Rowers. By which contrivance he thinks is gain'd in a Quinqueremis the space of nine feet in height: which, he saith, Scaliger, if alive, would admire. And to all this he subjoyns some passages out of ancient Authors, which he conceives do much strengthen the fitness of these Inventions of his, concerning both the placing of the Lateral Rowers, and those that sit in transtria. Here he inserts the Explication of those names of Thalamita, Zygita, and Thrana, in the Trireme; the first signifying him that sits in the lowest row; the second, him that sits in Transtria; the third, him that sits uppermost. After this, he inquireth, Whether ever such great Vessels of so many tires of Oars, sitting in so many different heights, were ever actually built? And, if they were, Whether they ever came abroad to Fight? Especially such an one as that of Philopaters is recorded to have been, of forty tires, requiring above four thousand Rowers; and that of Ptolemaeus Philadelphus, of thirty tires, having more than three thousand Rowers; and another of twenty rows, requiring two thousand. Hereupon our Author scruples not to affirm all to be true, what is written of such vast Ships; adding, that he hath made it intelligible, how it may be so, by finding places for the Zygite, and a conveniency of moving their Oars under the Seats of those that sate next before them. And here he shews at large, of what determinate bigness those Vessels were, according to his supposition and contrivance; vance; beginning from a Trireme, and shewing, how many Oars and Sea-men it contained, namely two hundred, of which one hundred and eighty were Rowers, and the rest Marriners. So that in the Athenian Fleet, of which Cono was General, consisting of one hundred and eighty Triremes, there were six and thirty thousand Men. Then proceeding to a Quinquereme, with four hundred and twenty Men apiece; of which there were Rowers three hundred, and Souldiers one hundred and twenty. So that three things were stupendi- ous in that Roman Fleet at Messina, and the Carthaginian at Lilybicum; one is, that the former consisted of three hundred and thirty, and the latter of three hundred and fifty Ships, most Quinqueremes, that is, an hundred and fifty feet long; the second, that the number of Men, they contained, was one hundred and thirty thousand, and one hundred and fifty thousand Men; the third, the apparatus and provision necessary: Yet all this affirmed by one of the best of the ancient Historians, Polybius; who himself wonders at such a vast Equipage. Here the Author undertaketh, out of Polybius, Plutarch, and Livy, to refute Salmasius, affirming, that hardly any Gal- leys were built or equipped bigger than of Nine Tires, called Hence he proceeds to the Ships of Eleven Rows (Εξακινάρης;) and of Fifteen Rows (Πεντακινάρης;) and to one of Sixteen (Σεκσακινάρης.) Having dispatched these particulars (of which we leave Curious and Learned Antiquaries, and good Naval Architects to judge) he proposeth the Usefulness of these his Inventions, after that, by the means of them, both the Structure and Or- dering of Ancient Shipping hath been explained; and is of opinion, that the Modern Galley and Galleasses might, ac- cording to his Model, be more conveniently built, both for celerity, strength, and lesser expences. He thinks, that the Modern form would be better, if in the Structure the pro- portion of the long Ships of the Antients were observed. And he conceiveth also, that Five men sitting at one Oar in the Modern Galeasses, much strength is wasted to no purpose, because they sit too near to the tide or stay (the fulcrum;) whereas a lesser number of Rowers, at a greater distance from the said Stay, would give more strength for more swiftness, and require less charge. To which he adds, that these Galleys are of great use both in Rivers and Un-deep Seas, and therefore convenient for the Baltick and Britannick, as well as the Mediterranean Seas. Further, that they are very serviceable for transporting great Forces. Occasionally (to add that by the by,) he shews out of Josephus lib.8.c.7. what is meant by the Almyggim Wood in Sacred Writ, 1 Reg.10.11, 2 Chron.11.8, &c. אַלְמִיָגִים, namely, the Indian Pine or Fir-tree, brought out of Ophir, excellent both for a shining Whiteness and for Levity; whence very proper for Musical Instruments. LONDON Printed for John Martyn, Printer to the Royal Society. 1674.