# Philosophical Transactions of the Royal Society (1665-1886)/Volume 3/Number 35

Contents:
* Contents
* An Account of an Experiment concerning Deafness.
* A New Discovery touching Vision, made in France.
** To which the main of M. Pecquets Answer is, as followes
* ⁠A letter written to the Publisher concerning some Anatomical Inventions and of Observations, &c.
* Some Observations concerning the Comet, that hath lately appeared in forrain parts, communicated from Italy and Portugal.
* An Account of some Books
** ⁠I. GEOMETRÆ PARS UNIVERSALIS, Quantitatum Curvarum transmutationi & measuræ inserviens, Auth. FAC. GREGORIO, Scoto: Where are inserted some remarks, imparted by the same Author in two Letters written to a member of the R. Society.
** II. AN INTRODUCTION to ALGEBRA, translated out of High Dutch into English: by THO. BRANCKER, M.A; much altered and augmented by D.F.P.
** III. AN ESSAY towards a REAL CHARACTER and a PHILOSOPHICAL LANGUAGE, by JOHN WILKINS, D.D. &c.
** IV. STANISLAI De LUBIENIETZ THEATRUM COMETICUM, &c.
Numb. 35.
PHILOSOPHICAL TRANSACTIONS.
Monday, May, 18. 1668.
The Contents.
An Account
A Young Gentleman, known to divers of the R.Society, was born Deaf, and continued Dumb till his Age of 10. or 11. years. His mother, when she was great with him, received a sudden fright; by occasion whereof, the child's head and face were a little distorted, the whole right side {as I remember) being somewhat elevated, and the left depressed so that ​the passage of his left Ear was quite shut up, and that of the right Ear proportionally distended, and too open. This Gentleman being for some time recommended to my Care, amongst other things, I spent some thoughts in searching the cause of his Deafness in the Ear, whose passage was open. And having found, that the Auditory Nerve was not perished, but that he could hear the sound of a Lute-string, holding one end thereof in his Teeth; and had some perception of any very vehement sound, I supposed the defect to lie in the want of due Tension of the Tympanum of his Ear; whose use I took to be, onely to preserve the Auditory Nerve, and Brain, and inward parts of the Ear from outward injury by cold, Dull, &c and to be no more to Hearing, than glass in the window is in a Room to seeing, i.e. as the one intromits Light without Cold or offence to those in the room, so the other permits Sound to pass, and shuts out what else might offend the Organ; as appears in the Experiment of breaking the Tympanum of a Dog, who hears never the worse for some few weeks, till other causes, as Cold, &c, vitiate the Organ.
But for the Free passage of the Sound into the Ear, it is requisite, that the Tympanum be tense and hard stretched; otherwise the laxness of that membrane will certainly dead and damp the Sound. And because the Tympanum is fixed in the circumference thereof to the Annulus Osseus, and so is not capable of Tension that way, in such manner as a Drum is braced; there remains another way, by drawing it at the Center into a Conoid form. And that is the principal office of the 3. Ossicles, viz, the Malleus, Incus, and Stapes; whereof the Stapes is fixt to the inner Bone, and part of the Malleus, to the Tympanum, and the Incus between them joyn'd on one part to the Malleus, and on the other to the Stapes: by Ginglymoide Joynts, such as in which the upper and lower double Teeth meet one another. And by the help of a Muscle drawing the Incus, these three bones, which otherwise could lye more streight, are brought to a Curved or Arched posture; and the Stapes being fixt unmovable, the Malleus yields, to bring the terms of that line nearer, in proportion as it is curved, and draws the Center of the Tympanum, stretching the surface of it from a Plain to a Conoid figure, within the same ​Circumference. And l conceive, the action of this Muscle does ordinarily and constantly draw the Tympanum to a moderate Tension; but when we have occasion to listen, and give a more particular attention to some sound, the action of that Muscle is then more intense, and the Tympanum is drawn to a more then ordinary tension, so to facilitate the passage of the Sound.
Now as to the case of the young Gentleman before mentioned, I supposed either the Muscle by that convulsive starting Motion in the Womb to be overstrained, and to have lost its Action; or the Membrane by that greater aperture of the Organ to be over-stretched, and afterwards to remain so flaccid, that it was beyond the activity of the Muscle and curviture of the Ossicles to give it a due Tension; or peradventure there was a concurrence of both Causes. Which due tension, if by any remedy it might be restored, I assum'd, that he might recover his hearing in that Ear: To which end, I advised the Excellent Lady his Mother, to consult with Learned Physitians, if by some adstringent Fumes, or otherwise, he might find help.
And for Experiment, I thought of a Temporary Way, by the impulse of any Vehement sound; as of a Drum beaten near him: which sound, during its continuance, must needs give the Tympanum a Tension, by driving and swelling it inwards, as a fresh gale of wind fills the sayles of a ship; and the Experiment succeeded according to my exspectation: For so long as I beat a Drum fast and loud by him, he could hear those who stood behind him, calling him gently by his Name (which he understood, having learned to speak and pronounce it among other words;) and when the Drum ceased, he did not hear the same Persons, when they again very loud called him by his Name. And by this we tryed several times, by beating the Drum again, and ceasing it; and he still heard them, when the Drum beat, and heard them not, when it stopt.
Since that time, a Gentleman about Oxford-shire, sometimes Student of Christ-church, being in a great degree of Deafness, after I had told him of this Experiment, call'd to mind, that he never heard so well and easily, as when he was discoursing with Company in a Coach, whilst it went fast, and made a great rumbling noise in London-streets: by which he was induced to ​believe, that the Impediment of his Hearing was of the like nature with the other.
A New Discovery touching Vision.
HAving often observed in Anatomical Dissections of Men as well as Brutes, that the Optick Nerve does never answer just to the Middle of the bottom of the Eye, i.e. to the place, where is made the picture of the Objects, we directly look on; and that in man it is somewhat higher, and on the side towards the Nose; to make therefore the Rayes of an Object to fall upon the Optick Nerve of my Eye, and to find the consequence thereof, I made this Experiment;
I fastn'd on an obscure Wall, about the hight of my Eye, a small round paper, to serve me for a fixt point of Vision; andl fastned such an other on the side thereof towards my right hand, at the distance of about 2. foot; but somewhat lower than the first, to the end that it might strike the Optick Nerve of my Right Eye, whilst I kept my Left shut. Then I plac'd my self over against the First paper, and drew back by little and little, keeping my Right Eye fixt and very steddy upon the same; and being about 10. foot distant, the second paper totally disappear'd.
That this cannot be imputed to the Oblique position of the second paper, is hence evident. That I can see other Objects further extant on the side of it, so that one would believe, the second paper were by a flight taken away, if one did not soon finde it again by the least flirting of one's Eye.
This Experiment I made often, varying it by different distances, and removing or approaching the Papers to one another proportionally, I made it also with my left Eye, by keeping my Right shut, after I had fastned the Second paper on the Left side of my point of Vision; so that from the Site of the parts of the ​Eye, it cannot be doubted, but that this deficiency of Vision is upon the optick Nerve.
This Discovery I communicated to many of my friends, who found the same thing, though not always just at the same distances; which diversity I adscribed to the different situation of the Optick Nerve.You have made it your self, in his Majesties Library, where I shewed it to those of your Illustrious Assmembly; and you as well as I, found the like variety, there being some, who, at the distances mention'd, lost the sight of a Paper, 8 inch, large, and others, who ceased not to see it, but when it was somewhat less, which appears not how it can be caused but by the differing magnitudes of the Optick Nerve in different Eyes.
This Experiment hath given me cause to doubt, Whether Vision was indeed perform'd in the Retina (as is the Common opinion) or rather in that other Membrane, which at the bottom of the Eye is seen through the Retina, and is called the Choroides. For if Vision were made in the Retina, it seems that then it should be made whereever the Retina is; and since the same covers the whole Nerve, as well as the rest of the bottom of the Eye, there appears no reason to me, why there should be no Vision in the place of the Optick Nerve where it is: on the contrary, if it be in the Choroides that Vision is made, it seems evident, that the reason, why there is none on the Optick Nerve, is, because that that Membrane (the Choroides) parts from the Edges of the said Nerve, and covers not the middle thereof, as it does the rest of the bottom of the Eye.
Upon this, I desire, you would give me your thoughts with freedom, since I am none of those that love to obtrude Conjectures for Demonstrations.
To which the main of M. Pecquets Answer is, as followes;
EVery one wonders, that no person before you hath been aware of this Privation of Sight, which every one now finds, after you have given notice of it. But as to the Sequele, you draw from this Discovery, I see it not cogent, to abandon the Plea of the Retina for being the principal Organ of Vision, For (not to insist here on other considerations) it will be sufficient, now to take notice, that at the place of the Optick Nerve there is ​thing, that may very well cause this loss of the Object. There are the Vessels of the Retina, the trunks whereof are big enough to given hindrance to Vision. These Vessels, which are no other but the ramifications of the Veins and Arteries, are derived from the Heart, and having no communication with the brain, they cannot carry thither the Species of the Objects, If therefore the Visual rays, issuing from an Object, fall on these Vessels at the place of their Trunk or main Body, 'tis certain that the Impression, made thereby, will produce no Vision, and that the picture of that Object will be deficient; as when on a white paper in an obscure Chamber, there is some black spot, or in it some hole considerably bigg: for the more sensible this blackness or hole is, the more of the image of the object it intercepts from our Eyes, It is not so in respect of the small ramifications, that issue from those trunks, and shoot into the Retina, For if they be met with at the place of the bottom of the Eye, where Vision is made distinct, they will not render the image of the Object deficient, because they are so small, as not to be sensible. Thus it is, that in Looking-glasses, when they want lead or tin in any place big enough to be perceived, the image, we there see, appears to have a hole, which happens not, when there is but so small a one, as might be made by the point of a needle.
Thus much being observed as to the deduction, made from this Experiment, I shall further note, That that paper, the sight whereof is lost, must be further or nearer off, according to the diversity of the structure of Eyes. For some loose this paper at the distance of two feet, some at a less, others at at greater distance; some loose it a little higher, others a little lower, according as the trunks of the vessels are situated in respect of the Optick Nerves and some loose more of it than others, according as those vessels are bigger or smaller. And because 'tis hard to determine precisely the place, where the object is lost in all sorts of Eyes we have ground to believe, that this loss is not always made on the extent of the Nerve, where the Retina is, but sometime besides it, where the Chloroides is found. For the trunks of the Vessels of the Retina are big and long enough to extend on this or that side of the Nerve, and so to hide some part of the Chloroides, according to their Magnitude, And in this case it will ​be true, that Vision is not made in all the parts where the Choroides is found, though they be exposed to the light. Which may very well give a check to your opinion, forasmuch as those trunks would hinder the objects, falling on them, from coming to the Choroides which would render the image deficient in that place, in regard that those species would not be able to make an impression on the Organ of Vision through those vessels.
In the mean time, so pretty a discovery, as this is, could not belong without being confirmed. For as the secret of your Experiment consists in contriving, that the picture of an Object may fall just on the Optick Nerve, or thereabout, M. Picard hath devised a way, by which an object is lost keeping both Eyes open, by letting the image of the object fall on both the Optick Nerves at one and the same time, after this manner;
Fasten against a wall a round white paper, of the bigness of an inch or two, and on the side of this paper put two marks one on the right, the other on the left side, each about two foot distant, then place your self directly before the Paper, at the distance of about nine foot, and put the End of your finger over against your both Eyes, so that it may hide from the right Eye the left mark, and from the left Eye, the right mark. If you remain firm in that posture, and look steddily with both Eyes on the end of your finger, the paper, which is not at all cover'd thereby, will altogether disappear; which must be the more surprising, because that without this particular encounter of the Optick Nerves, where no Vision is made, the paper would appear double, as you will finde as often as the finger shall not be placed as it ought to be, or when the sight is carried any thing sideways; whereof the reason is sufficiently known.
The application of this way is easily made to that of yours. For when one looks steddily with both Eyes on the End of one's finger, held before the marks, 'tis the same thing, as if you directed each eye by it self to the place, which is to be looked on to loose the paper; So that one may with both Eyes do the same thing, that you do with one, keeping the other closed, &c.
JAmdudam, Clarissime Oldenburgi, ab Oratore didici, ex omnibus virtutis præmiis, amplissimum esse Gloriam, atque etiam proculdubio omnibus maxime desiderabile, cum hæc unica sit, quæ brevitatem vitæ, posteritatis memoriâ consoletur; quæ efficit, ut absentes adsimus, ut mortui vivamus; & cujus gradibus homines in cœlum videntur adscendere. Humano generi ergo connatus videtur esse gloriæ appetitus, & ejus igniculi in ipsà pueritiâ videntur micare, quibus magna ingenia ad maxime Laudabilia peragenda stimulantur, & minora etiam ad aliquid malus agendum accenduntur. Sed cùm Appetitus hic inordinatus & illicitus evadat, & in parte animi, rationis experte, stabuletur, & uti aliæ cupiditates effrenatæ, flagitia perpetrare audeat; viri etiam it a animo laborantes, non diutis solida & expressa oontenti gloria (viz. Consentiente laude bonorum, & incorrupta voce bene Fudicantium de excellenti virtute) aliorum laudibus obtrectant, corum nomina sugillant, & alien etiam bona, ut sibi propria, arrogare audent. Sed dolendum est, doctam & literatam gentem talibus animi ægritudinibus etiam laborare; cùm penes Philosophum solam sit Animi Medicina, cujus salutaribus præceptis qui paruerint, tranquillitate illa placida quietaque constantia locupletantur, quæ motus turbidos Iræ, & cupidinis inanis gloriæ, rationi contrarios, penitus compescit: unde evenit, quòd qui revera solidam hanc gloriam possident, non inde elatiores evadunt, sed placido, secreto, & tranquillo fruentes Gaudio, non tam præmia sequuntur rectè factorum, quàm ipsa recta facta. Horum Animi eodem perfunduntur gaudio, quando aliquid, humano generi proficuum, vel rei litterariæ ornamentum concilians, vel ab ipsismet vel ab aliis invenitur; aliorum laudea pleno effundent ore, & proprias non avidissimis auribus excipiunt, quin multó malint potiùs, alios splendorem sibi aliquem conciliare plumis & ornamentis conductitiis, quàm ut illimet ipsi ullo ​rum sultu splendere videantur. Verum pauci, quos æquus amavit Jupiter, hanc Animi sanitatem acquisivere, quia plærisque Inculta jacet moralis Philosophia, quæ sola animorum ægritudinibus medelas afferre potest. Hinc evenit, quod Juvenes & Tyrones multi, qui Musarum limen vix adhuc salut averint, nec primas Scientiæ lineas exarare didicerint, Seniores & multo doctiores inani spernunt fastu; nec minus Seniores quans plurimi, eodem fastu laborantes, qui, veterum quorundam verba, fortasse male intelecta, per annos multos solum edidicere, verbosa illa Philosophia tumidissimi facti, injuriis petulantissimis, doctos Juniores, in veræ Philosophiæ indagatione sudantes, infectantur. In Medicina vero præcipue, untriusque hujus generis abundant homines, præter Turbam magnam indoctissimorum, qui, si forte Mechanicam aliqualem Cartesii rationem audiverint & male intellexerint (integum quippe Cartesii Systema, eorum captum longe superat) vel si præstigiis fumivendulorum quorundam ludificati, Carbonum magnum facere dispendium, & quædam male-olentia torrefactione fieri didicerint, se non mode Philosophos, sed solos Sophos esse jactitant, & veræ medicinæ cultiores; inter quos nil nisi Philosophia vel Philosophi per Ignem circumsonat. Sed missis istius farinæ hominibus, si mihi quidem copia sit optandi, libenter velim, ut inter viros vere doctos & medicos res aliter ageretur ꝫ ut scil. Medici seniores, multa lectione & veterum authoritatibus freti, sedulis Junioribus, negandi vel affirmandi arrogantia, languorem ne incuterent; Velim etiam, ut Juniores, qui veræ scientiæ vestigia sequi cupiunt, & quibus casu vel consilio, quædam non ante nota, vel diuturna obscuritate latentia, in lucem producere contigerit; velim, inquam, ut hi etiam, omni seposito fastu, in memoriam revocent per-pauca revera sciri posse & multa sibi necdum nota, senescentem docere ætatem; ideoque summa observantia honores debitos Senioribus deferri omnio debere. Sed intercujusvis ætatis homines ubivis equidem bella moventur, dum invidia, non æmulatio, incitationem accendit. Viri enim volumi nosi, & librorum Heluones, quibus magnum semper est in promptu verborum Armamentarium, in litem studio certaminis parati, quosvis adoriuntur, qui veterum opiniones ullas, quas ipsi longa cogitatione, proprias tandem (uti opinantur,) effecerunt, labefactare audent. Dum enim recordari, illis est Sapere & Scire, ægré ferunt, alios, fortasse Juniores, novis ​experimentis, nuperrime inventis (etsi ex sesuum evidentia petitis) Systema Philosophiæ ab illis tam pulchre effictum, vell deturpare. Hi ergo, magnis argumentorum notionalium copiis apprime instructi, bellum indicunt, non omissis rixarum & covitiorum turpium auxiliis. Alii sunt, qui saniorem ostetant Philosophiam, viz. Experimentalem, sed solum Gloriæ inanis cupidine stimulati, non vero sciendi ardore flagrantes, nomina Authorum, vel rerum Inventaurum, unic amiunt, proindeque, Inventione aliqua nova fortuito audita, statim scripturientibus calamis, mundam credere volunt, se solos illius Inventionis fuisse authores, vel se saltem primos de tali re cogitasse, sed præ aliis quibusdam (magni proculdubio momenti) negotiis impeditos illam in apricum proferre non potuisse; etiamsi vix adhuc animo attente secum expenderint, sitne res reuera consideratu digna, ullumve ex illa emulmentum humano generi, vel rei litterariæ posit afferri: Adhæc, tales inventiones, causu, non consilio, acquisitas, fortunæ imprimis acceptas esse ferendas, easque doctis æque ac indoctis posse contingere. Absit vero, ut de fama virorum doctorum detraham, qui in re Anatomica præsertim insudantes, in magna illa nuperime Inventa fortuito inciderunt. Asellii enim sedulus in Vivorum Anatomia labor summopere est laudandus; unde primam vasorum Lactorum notitiam habuimus; quamvis, teste ipsomet, foruito illa invencrit. Doctissimus Pequetus inventionem illam felicissimam Ductuum Thoracicorum, munus fortunæ, vel potius eximium Dei benificium agnovit. Magnus Bartholinus, ut & Doctissimus Rudbeckins, alia de Lacteis Quærentes, foruito in Vasorum Lymphaticorum notitiam inciderunt. Ac mihi etiam liceat asserere (id quod alii etiam multi, fide digni, sestari mecum poterunt) Jolivium nostrum etiam ante Annum 1652, dum quædam circa Vasa præparantia indagæret, superisius facta ligatura, inferiusque testiculum cum involucris mante tractaret, ut inde vasa turgidiora redderentur, de re tali ne cogitantem quidem, primum Viaia etiam Lymphatica turgescere vidisse.
Quæ quidem haud dicta velim, ut laboribus semper laudandis veletiam felice Bartholini vel Rudbeckii fortunæ quicquam derogem, sed solum ut quod & fortunæ & laboribus solivii nostri debitum erat, & illi redderem. Ille vere, dum supersies manebat, de rebus fortuito inventis rixari nec viro prudenti, nec docto ​medico dignum judicabat, nulla laborans invidia, quod viridaria docti, ejusdam felicis fortunæ participes fuere; libenter etiam agnoscebat corum industriam & fortunam ab omnibus laudandam esse; præsertim cum in suspicionem ne venire quidem posset, ullum horum alteri inventionem clam eripuisse. Absit semper à viris doctis malitia & petulantia eorum, qui veros rerum Inventores sugillant, & inventiones doctorum virorum, sedulo in re litteraria operam navantium, vel nihili faciunt, vel sibimet arrogant, vel aliis adscribunt. Interim homines, talibus animi vitiis laborantes, ubique feriuntur. Nostrates præcipue talia accepere verbera (se tamen verbera sint dicenda, quærisu & dedignatione accipiuntur.) Circulatio Harvatum, res non casu, sed consilio, inventa, cisi sensuum evidentia confirmata, & oculis manibusq; puibusvis rei Anatomicæ pertis, luce meridiana clarior exhibita; frequenter tamen verbosa Philisophia, & ventosis argumentorum machinis, turbata fuit. His vero spretis, immota mansit veritas. Interim alia ab ividia prarantur arma, & inventum hoc nobilissimum cuivis potius, quam vero Inventori, adscribere multis placuit. Clarissimus Bartholinis, qui sua omnia, & aliorum multa quotidie publica facit, non mediocriter in Epistola 47. Centuriæ secundæ Bogdano suo dicata, de talibus conqueritur injuriis: Sed tamen in epistola 26. Centuræ primæ secretum nulli (uti ait) revalandum, toto communicat orbi; viz. Patrem Paulum Venetum, verum sanguinis Circulationis inventorem fuisse. Si defunctus Harveus defensione nostra nunc egeret, facile monstrare possemus, magnum & summe doctum Paulum ab ipso Harveo, (inter hos enim vetusta manebat amicitia) primam Circulationis notitiam (mediante Oratore Vento, hic tunc tempris commorante) recepisse. Interim doleo sane, Venerandum Bartholinum, cujus doctos labores suspicio, & cujus senectutem veneror, ita candoris memoriam demisisse, ut futilem illam Bogdani epistolam 62. Centuiæ secundæ typis mandaret, in qua ille Medicos Loninenses injuriis petulantissimis infectatur. Peregrinus ille à Clarissimo Entie, & aliis nostratium, satis, fortasse nimis comiter exceptus fruit, sed dedignabantur viri docti, quæstiunculis ineptis tamtenuis Emissarii satisfacere; hic iratum animalculum sibilando ingenium prodere cœpit. Sed non est meum, calumniatores redarguere contumeliis litterato orbi statis notum est, Philosophos & Medicos Anglic ​non multa inepta vel inconcocta divulgasse, nec corum adeo multos scripturiendi pruritu laborare. Verulamius, et Gilbertus, Philosophiæ venæ magna edidere Specimina; et Medici nosrates, Harueius, Glissonius, Entius, Whartonus, Willisius, et alii, res nonnisi demonstrativas utplurimum publicas fecere; nec festinando cœrcos parturiere catulos. Affirmandi sane arrogantiam, in rebus præsertim conjecturalibus, ubique, putem vitavere, & (spero) vitabunt, temeritatemque fugient, satis gnari, quantis in tenebris laboremus. Oruitur vero, et tantum non pessundatur res-publica litteriaria, dum popularis auræ aucupatores multi, nec veritati, nec humani generis commodo litantes, puotidie res suas insulsas, et male intellectas, fortasse vix intelligibiles mundo protrudunt: unde nimis præcocia ingenia notionibus non intelligendis insanire videntur. Agyrtæ vero, fumivenduli, et circumforanei, quasi de rebus nunquam assequendis certam haberent Scientiam, audacter de his pronunciant, atque insolentia et audacia, à Sapientibus semper irridenda, Veritatem et Scientiam sibi solis vendicant, quum nec quid sit scibile norint, nec quicquam veri sapiant. Interim vero, æstu quodam ignorantiæ, in altum gradisonantis hujus dementiæ admirationem plebs indocta rapitur. Pergat sane gens utraque, bona doctorum omnium venia, ubivis et in quovis decipi, et insanire, modo à Medicinæ praxi abstineant, nec de humana pelle tam temere ludant. Per duo annorum millia, ab experientia adhuc crescit Medicina; at null fit in praxi experientia utilis isi summa adhibita ratione, et debite simul quibusvis collatis circumstatiis. Metuenda ergo sunt, quæcunque in medicinæ praxi nova; et caute admodum cum illis procedendum, doneo evidenti et multiplici experientia, confirmata fuerint. Mihi enim non liquet, ulla remedia hominibus fuisse revelata; sed omnia ab experimentis diversimode factis, mutuo communicatis, simil collatis, et tandem a Viris doctis congestis, mundo draditia fuere. Hodierni vero novatores non erebescunt asserere, se magnum aliquod remidium novum, nec sibimet nec aliis antea no'um, jam nunc invenisse; et statim insignes ejus prædicant virtutes, à nemine tamen utplurimum percipiendas unquam. Seniores vero sapientiores, et bene exercitati Medici, vix, ni fallor, credent, illum dia inter multos et multifarie ægrotos versatum fuisse, qui audacter de peculiarium remidorum virtutibus, nonquam fallentibus, ad experientium provocat. Insurgunt tamen puotidie ​bemines quidam, qui re aliqua, ipsis fortasse nova, fortuito auditæ, vel lecta, & male ut plurimum intellecta, eam statim novitatis solum causâ in arotissimos recipiunt amplexus, phantasia diligenter fevent, & verborum fortasse sesquipedalium mangonio in molem aliqualem sufflare nituntur, & deinde supposititia hæc pro suis mundo obtrudunt, & statim Authorum & Inventorum nomina usurpantes, minus doctos Tyronesque credulos in vevios errores agunt.
Sed aliter proculdubio agendum est illis, qui ad veram scientiam promovendam, operam strenue navant. Insulsa & indigesta non statim evulganda sunt, & diu etiam de rerum in lucem emittendarum vertate, ceritudine & utilitate pensitandum. Si enim subacto judicio, quæ typis sunt mandata, composita fuissent, veri literati non tanta librorum inutilium lole fatigarentur.
His consideratis, Doctissime Oldenburgi, mea qualiacunque fuerint, vix typis digna judicare possum. Et si enim per plus quam duo annorum lustra præterita, diligenter in miscendis variis cum Animalium viventium sanguine liquoribus sudaverim, nec solum potulenta diversa, usque ad libras duas, in massam sanguineam infundi & misceri curaverim, sed etiam Emetica, Catharica, diuretica, Cardiaca & Opiata isto modo exhibuerim; proviriti etiam eorum effecta notaverim, præterea sanguinis etiam ipsius Transfusionem sæpius tentaverim; agnoscotamen me de hujismodi experimentorum utilitate multum adhuc dubitare. Nosti tutemet, doctissimevir, me ante quinque circiter abhinc annos horum experimentorum viria, Societati Regiæ communicasse, cujus hortatu ea typis tunc temporis mandare decreveram: sed dum alia hujesmodi experimenta repeterem, ut certius possem de eorum usu & utilitate statuere, varia sæpenumero occurebant phœnomena, quæ me morbos sanandos applicari. Veruntamen agnosco, me opinari hactenus, posseres Anotomicæ, & naturæ sanguinis melius expiscandæ, infusiones diversorum liquorum in vexas animalium viventium, inservire. Putem insuper, Transfusionem sanguinis in magnis & subitaneis sanguinis profusionibus, ad vires subito instaurandas, fortasse multum posse conducere. Tutemet obiscum vidisti, Vir Amicissime, animal larga sanguinis profusione fere exsangue redditum, & convulsiombus lethalibus plane moribundum, sanguine ​alterius animalis, non ejusdem speciei, in illum transfuso, intra septem horæ minuta, adpristinum & perfectum vigorem restitutum. Ex repetitis tamen experientis dubia mecum manent diversa, possintne morbi ulli ex Transfusionibus talibus sanari, vel etiam in ætate senili, juventutis vigor aliquatenus instaurari; specierumve vel individuorum ingenia vel dotes ita alterari, ut à nativis diversatandem evadant. Jam scimus, alterationes diversas, quas sæpius in animalibus & eorum sanguine, ex liquoribus variis infusis, factas opservavimus; sed, ni fallor, ut aliquid in verum animalis commodum verti possit, illud, quicquid sit, quod com massa sanguinea misceri debet, præviam illam, in primis concoctionibus alterationem & dispositionem requirit, quæ hoc apium natum ad tales usus reddat.
Sed, Deodante, promissa tandem exsolvam & aliquas ex Observationibus illis, quas peregi, publicas faciam. Quod moram adhuc injicit, præter negotia & statum vitæ nimis valetudinarium, est, quod quædam, quæ de sanguinis Natalitiis primis, mihi observasse majorem certitudinem reducere velim: Polliceor quippe pauca illa, que alii à me evulgatu digna judicavêre, fore nonnisi facta & observata quædam, perspicue & fideliter recitata; quæque de iis ratiocinari ausus fuerim, ex evidentia sensus pro virili deducta.
Cæterum, cum Tu ita velis, doctissime Vir, & quod ita fieri oporteat credas, fideliter Originem Transfusionis sanguinis, ut ea apud nos saltem se habet, enarrabo. Missotestimonio illo, quod a viro fide digno & Regalis Societatis cosorte, penes Te etiamnum reperitur, vis Rever. Dominum Potter, Theologum insignem, trignta ab hinc annis, consideratà Cirulatione. Harveana, focio huic nostro & aliis viris doctis, sæpius sanguinis Transfusionem proposuisse; Ego Circa finem Anni 1656. aut circiter, Mathematicus ille insignissimus, D.D. Chistophorus Wren primus infusionem variorum liquorum in Massam sanuineam viventium animalium excogitavit & Oxonii peregit. Anno sequenti, viz. 1657 idem mihi tunc temporis, sanguinis naturam provirili inaaganti, quæ ipse sicerat, etiam communicavit, ex quo tempore diligenter ad diversa hujusmodi experimenta facienda me accingebam: & inter alia, quæ tunc temporis agenda decrevi, quas, cerevisias cujusvis generis, lac, ​serum lactis, jusoula, vinæ, Sp. Vini, & aimalium diversorum sanguinem, injicienda mecum statui. Et præter fistulas alias, ad varias operationes adaptatas, quasdam Figuræ tertiæ in modum, factas habui, ut uno extremo in arteriam unius animalis immisse, altero in venam alterius, sanguis ab uno animali in alterum facilius transfundi posset: & ut docto cuivis, quod debitum est, reddam, D. Dr. Henshaw, etiam è Societate Regia, vel ante hoc, vel circa idem tempus (uti & egomet) incassum tamen, eadem methodo, sanguinis Transfusionem tentavit. Hinc fuit, quod com in Regali Societate, inter alia Experimenta (quod ex Archivis illius satis liquet) sanguinis Transfusio proponeretur, alii viri docti mecum opinabantur, ex operatione tali nil forte asse sperandum; atque ipsemet difficultates recivavi, quæ mihi hanc operationem peragenti contigerant. Dehinc res denuo tentata, boiscum non successit, noec Doctissimus & Exercitatissimus Anatomicus, D. Dr. Lower, Oxonii, Anno 1666. rem feliciter conficeret. Quo factotuemet, sub ejusdem anni finem, totam rem cum operationis methodo, publicam fecisti. Anno sequenti, ex Gallia etiam de hac operatione audivimus. Fateor, me totum gaudio perfusum fuisse, quum certus redderer, fiduciam Gallicam illud aggressam esse, quod timor vel ignavia forasse nostra, vix tentare quidem ausa fuerat. Scis, doctissime vir, quantocum applausu Clarissimo Denisio assurexi, qui non solum ingeniosissime talem experimentorum defensionem suscepit, fed in Hominibus etiam postea celebravit.
At tanti mihi non videtur, Eruditum illum Gallum tam strenue & animose de prima Transfusionis sanguinis origine contendere; vel me etiam primam ejus Inventionem nobis ipsis vendicare. Tutemet, ni fallor, D. Oldenburgi, hunc Gallum in errorem duxisti. In Philosophicis enim tuis Transactionibus, Mense Decembri, Anno 1665. editis, ubi de origine Infusionis variorum liquorum in venas, rationem reddidisti inquis; Sex ab illo tempore retro annis ad minimum, D. D. Christopherum Wren Infusionem illam primum omnium tentasse.
Nemo forasse dubit abit, quin, si quis de hoc Experimento promovendo serio cogitaret, & de variis cum sanguine miscendis attente meditaretur, mixtio sanguinis diversorum animalium facillime tali meditationi sit occursura. Cum igitur Infusio, secundum calculum tuum; circa Annum 1659. inventa fuerit, & propositio illa de ​sanguinis Transfusione in ædibus Dn. Monmori facta dicatur Anno 1658. vel a clarissimo Abbate Bourdelot, vel a docto Benedictino Roberto de Gabetts (de primo enim Prepositore necdum convenit) facile quivis in illam duci potuit sententiam, quod Galliæ experimenti hujus mentio prima saltem debeatur. Sed illa operatio, cujus in dictis illis Transactionibus mentionem fecisti, infusiæ scil. vini Emetici in massam sanguineam, per venam brachii servi cujusdam, in ædibus Legati alicujus peregrini, Londini tunc temporis commorantis, peracta, facta suit Anno 1657. in ædibus Gailici Oratoris D. de Bourdeaux, adstante D. Colladon, Equite Aurato, & hodie Reginæ Matri Medica Ordinario. Quodque multa talia experimenta eodem anno à nobis repetita fuerint, mecum multi viri testari possunt, quorum aliqua in ædibus Illustrissimi Marchionis Dorcestriæ peracta etiam fuerunt. Notatu etiam dignum est, quod tota illa methodus facilis D. Loweii, Transfusionis peragendæ, Mense Decembri, Anno 1666. à Te edita fuit, & non nisi mense Martii anni sequentis de tali operatione è Gallia andivimus. Verosimile ergo, ni fallor, videtur palmam hujus inventionis (si modo palmam mereatur) Anglis quàm Gallis potius debiri.
Cætera, libenter scirem, quibus rationibus ductus Romanus ille doctissimus Manfredi judicatit, hanc inventionem in Germania primo conceptam fuisse. Nobis enim adbuc nihil omnino occurrit, quod vel in minimam ejusmodi suspicionem ducere potuerit. Tribus vel quatuor abhinc annis Major quidam, Medicus Hamburgensis, schedis quibusdam publice emissis persuadere orbi literato nisus est, se ante biennium de tali re cogitasse. Sed proculdubio male bac de re edoctus fuit vir Eruditus, & nimis festinanter suas propalavit cogitationes, Dicit emim, se andivisse, talem operationem, viz. exhibitionem Medicamenti Cathartici per infusionem in venam coram Principe quodam Palatino in Germania peractam fuisse; cum revera hoc à me in aula nostra Regia coram Celfissimo Principe Palatino Ruperto, præstitam fuerit, unde postea facile Germanis potuit communicari. Præterea, ni fallor, ex ipsis ejusdem scriptus satis liquet, illum tunc temporis tale experimentum ne tentasse quidem. Si ego memet novi, tantum abest, ut aliis debitas eripere laudes velim, vel aliena Mihi aut Nostratibus arrogare, ut mea potius aliis concederem. Quin si penes me præclara aliqua ​inventa viri jam mortui, nulli nota, manerent, mortuo sane quæ ipsius erent, redderem, & Manibus ejus debitos honores deferrem. De hac re etiam, nisi te hortante, altum egissem silentium, nec adhuc ejus Inventionem tanti judico, ut de ejus origine rixas cum ullo inire velim. Rem fideliter, temporum secutus ordinem, enarravi; etsi ante id tempus monstrare quis possit, de tali re fe cogitasse, sint & illi etiam quas meruit laudes. Hoc tamen audacter assero, Nos in Anglia Inventionem hanc à nullo accepisse peregrino. Si igitur Epistolam hanc in publicum mittis, cave Tibi, D. Oldenburgi; nam hac de re nunquam serram reciprocabo.
Denique, quoniam Tu ita vis, tibi etiam mitto figuram vasorum deferentium & vesicularum seminalium, sicut illa ab Exercitatissino Lowero & à me ipso è corpore humano execta fuere, quæque, ut tutemet nosti, adhuc arida & inflata mecum manent, Gratulor Doctissimo Regnero de Graaf, vel potius mihimet, quod eandem veritatem, ni fallor, invenimus & asserismus: commnnio enim illa vasorum deferentium cum vesiculis seminalibus ita manifeste se prodit, ut illi, qui per syphonem liquores aliques in vas deferens injici curraverit, ne guttula liquoris injecti perforamen in urethram exire videatur, priusquam extremum superius vesivclarum feminalium attigerit, In Angulo enim A. ita communio ista construitur, ut vesiculæ feminales prius totæ impleantur, quam liquor ullus in urethram possit exire. Agnosco etiam, per duo formina semen in urethram injici, sed vix doctissimo viro possum concedere, unam solumodo esse materiam seminis: se enim Testis, Mechanicâ structurâ, colore & substantia ab Epididymide disserat, sicut Epididymis à Parastata; si etiam in his succi diversi & substantia & colore inveniantur, diversæ proculdubio seminis materiæ in illis conficiuntur.
Quod asserit etiam cum illo Doctisimus Van Horne; viz. Testis substantiam non esse nisi Conglomerationem aliquam quorundam quasi funiculorum, vel potius vasorum minutissimorum; non solum hoc jam dudum constabat Nobis; sed jam ante etiam Celeberrimo Rolano & aliis.
Addam quoque, ope Microscopii fubiculos istos videri ubicunque per minutissimas glandulas tansire; unde similitudinem Pultacæ cujusdam substantiæ refert testis. Tametu vero in aliqualem longitudinem funiculi bi protrabi possint, totam ​tamen ejus substantiam, quasi lanam factam, è fuso explicari posse, nunquam adhuc potui experiri. Sed de his in præsentiarum satis. Dixi ea, ut ipse scias, & sciant etiam Doctissimi illi viri, (si modo ita tibi visum fuerit,) Medicos Anglicanos non omnino in Anatomicis feriari Brevi, Deo volente, observationes nostras de Partibus generationi dicatis, unà cum illis, quas per annos aliquot de Hominis Generatione observavimus, non solum in abortibus, primo, secundo, tertio, & quarto imprægnationis mense; factis, sed in cadaveribus etiam mulierum divesarum imprægnatarum dissectis: Ni fallor, à primis quatuordecim diebus (testibus quibusdam fide dignissimis adstantibus) usque ad septimum & octavum mensem.
Fortassis Epistolæ Limites sum egressus; interim quod tam prolixe te interpellaverim, tutemet in culpa es, & debito hoc supplicio culpam Luis; uti & ego, quod tam tarde hæc Tibi miserim, severa satis supplicia perferam, si publicam hanc Epistolam feceris. Vale.
Explicatio Figurarum, quarum sit in hac Epistla mentio.
Figura I, exhibetur Pars Vasis deferentis, cum vesicis seminalibus unius lateris; sicut in Corpore, antequam execta illa sue e, appa ebant.
A. Angulus Communionis.
B. Extremum superius Vesicularum seminalium.
C. Vas deferens, ubi Syphonem parvum inseruimu'.
D. Foramen apertum in Urethram.
a a a. Pars vasis Deferentis.b b b. Vesiculæ feminales.
c c c. Ductus à Vesiculis in Urethram.
Figura II, repræsntatur pars vasis deferentis cum vesiculis feminalibus alterius lateris, sicut execta, inflata & arida asservatur, ut in Fig. I. notant literæ.
Some Observations Concerning the Comet, that hath lately appear'd in forain parts, communicated from Italy and Portugal. The Italian Account, given by Gio. Domen. Cassini, we thus English.
ANno 1668. the 10th of March h.I. of the following night, (after the Italian way of counting) at Bononio, I observed a path of Light extended from the Whale through Eridanus; which I judged to be the Train of a Comet, both by the Figure and Colour, as also because that the direction of it, being by the Fancy continued, seem'd to proceed unto the 21. degr. of Pisces, where the Sun then was, and so tended to the part opposit to the Sun, like other Comets. By its extreme point it reached to that Star in Eridanus, which is called the Fourteenth by Bayerus: But it issued out of the Horizontal Clouds, so that I thought, the Head of the Comet was either vailed by them, or hid under the Horizon. It followed the Motion of diurnal revolution Westward, and it was to be seen about the second hour of the night; for then it was demersed in the mists of the Horizon.
Not far from its pointed end Eastward, there appeared a Star, equal to the brightest of the Fourth magnitude, almost in the same place, where was observ'd the Comet of A. 1664. Decemb. 31. which Star was not then seen, nor at other times elsewhere, nor is described in any Catalogue, on any Globe or Map, that I can learn; which therefore I deem to be a New one, that is, of new appearance.
March 11:at even the Horizon was in the West overcast with thin Clouds; among which after one hour of the night, there was seen a Brightness in the Whale, at least for half an hour, which was very like the splendour of Venus, likewise vailed by thin clouds.
March 12.at night, the lower parts of the Heavens in the West were clouded, and when the Great Dog-star was in the Mid-heaven, the same Tail appear'd again. It passed through the Star in Eridanus, which Bayerus calls the 15th, and left to the ​Southward the 14th, where it did terminate March 10. Being by the imagination drawn out to about 3. degrees and further, it tended to that Southern Star, which preceds the Ear of Lepus. It was therefore more Northerly, than the day before yesterday, and more Easterly; and it also reacht to the opposit part of the Sun. Towards the West it came out of the Clouds, and left us doubtful, whether its head was hid by them, or under the Horizon. But the Line from Jupiter to the extremity of the said Tayle in the Clouds was perpendicular to that Tayle; So that it was in the Whale, and the apparent part of the Train reached out in length about 32. degrees.
So far the Italian relation; that of Portugal from Lisbon is this;
Various are the Discourses of the newly discover'd Comet, seen here the first time (according to the general report of our Observers;)
March 5. ft. n. But for as much as it seems to follow the Regular course of the Sun, and sets few hours after it, there could hitherto be taken no considerable observations of it. The Body thereof is not seen, because it remains hid in the Horizon. Its Train is of a stupendious length, extended in appearance over almost the 4th part of the visible Heaven, from West to East; its apparent breadth is of a good Palm, and its splendor very great, but it lasts but a few hours. In time there will be discourses written upon this Subject, like to be more particular and exact, which I shall transmit to you, to compare with the Observations, made in your parts.
An Account of some Books.
Numb. 30., We gave an account of a small Tract, entitul'd Quadratura Circuli & Hyperboæ in Propria sua Proportionis specie inventa & demonstrata, á Jac. Gregorio Scoto; and intimated, that it would be reprinted here, and accordingly the Impression was begun; but since then, the Author writing to a member of the 'R. Society, signifies, that it is now reprinting at Venice (and possibly not without some enlargement;) which hath caused the design to be laid aside here. Mean time, the same Author hath sent over his other Book of his own composure also: in the Preface whereof he observes, That the defect of Algebra (which is most manifest in the Mensuration of Curved quantities) may in some manner be supplyed, if out of some essential property of any Figure thence be given be given a method of changing it into another Figure (equal thereto) that hath known properties, and of that into another add so forward, until at last you change it into some known quantity: And he modestly faith, that his own Treatise hath so far pursued this Method, that it refuseth no particular figure yet consider'd by Geometry.
After this, he answers such objections, as either have been, or such as himself could conceive might be made against: his former Book of the Quadrature of the Circle and Hyperbola.
For such, as would square a Circle organically, or divide an Angle in a given ratio, he supposeth, that there is no easier way of doing it, then by the common Linea Quadratrix, (the properties whereof are largely handled in Leotandi Cyclomathia, Lugduni, 1663. in quarto.)
Then he discourseth, that all things concerning Logarithmes and the Composition of Ratio's may be perform'd by help of a Curved Line, drawn through the Tops of a Rank of Lines in continual Proportion, (landing as Perpendiculars on a right line and at equal distance; that the Operations perform'd thereby are not to ​be accounted a-geometrical, because they are not perform'd by the Sole aid of Ruler and Compass; which he suggests to be well observ'd à Subtilissimo Mathemetico D. Carolo Reinaldino in Geometra suo promoto, dum tractat de novis illis Lineis, quas Mediceas appellat: Concerning which Author, he faith thus, p, 132. Qui autem desiderat plenum Analyseos & Æquationum doctrinam, expectet absolutissimum Caroli Reinaldini Opus de Resolutione & Compositione Mathematica, quod nunc sub prælo est. It seems, that the Book will be three large Volums in folio; the first whereof, being Introductory, and containing the Algebra of the Antients, is already in England.
And for the Confirmation of what hath been asserted, the Author thus demonstrates, that no Cubick Æquation (that is irreducible to a Quadratick) can be resolv'd by the sole aid of Ruler and Compass. For every Cubick Æquation hath either but one or three real roots, which if they could be found by the said sole aid of Rule and Compass, or by the Intersection of a Circle and a Right Line, then a Right Line should cut a Circle either in one Point or three; either of which is most absurd. And for the like reason a Cubick Æquation, having three real roots, can never be reduced to a pure Æquation, which hath but one onely root; for in these Æquations, Reduction shall no wise profit, forasmuch as 'tis impossible, by aid thereof to change an Imaginary root into areal one, and the Converse.
As to the Argument of the Book it self, it contains these several Heads.
1. The Mensuration of sundry Solids, with General Methods to that purpose; concerning which the Author faith, p. 123. Totus namque Archimedis Tractatus de Sphæra & Cylindro facilè demonstratur ex hujus 3. ad modum hujus 46. & aliquot sequentium. Liber de Conoidibus & Sphæeroidibus, & tota Lucæ Valerii doctrina, ex hujus 21. Tota Guldini, Johannis de la Faille, & AndreæTacqueti doctrina, ex hujus 35. & aliquot sequentium. And as a Corollary of Prop. 62. he Cubeth or measureth either of the Segments of a Parabolical Conoid cut with a Plain, parallel to the Axis. Hence we observe, that supposing such a Segment, again cut with a Plain, erect to the former Plain, the Proposition may be well apply'd to the Gauging of Cask part out, ​when the Liquor falls between the heads, which are supposed erect to the Horizon.
2. The Mensuration or Plaining of the Surfaces of divers Solids and Spiral Spaces, unknown to Antiquty, and not treated of by any modern Authors, till of very late years; from whom the Author differs in his Method: Particularly he finds a Circle equal to the Surface of
| A | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Parabolical | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | Conoid, resembling a Cup or Bowl; viz. when the Revolution is about their Axes, Prop. 46. & 49. |
| An | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Hyperbolical | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | Conoid, resembling a Cup or Bowl; viz. when the Revolution is about their Axes, Prop. 46. & 49. |
| The Parabolical Hour-Glass or Solid when the Revolution is about a Touch-line passing through the Vertex, Prop. 52. |||||
| A | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Long | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | Sphæroid, Prop. 47. 48. |
| A | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Broad | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | Sphæroid, Prop. 47. 48. |
Generally Prop., 36. The Surface of every Round Solid is equal to a Rectangle, whose Base is the Circumference of the Figure, by the Rotation whereof the Solid is begot, and the Height equal to the Circumference, which the Center of Gravity of the Perimeter of the Figure describeth.
3. A Method for strenghtening of Curved lines in the first 6 propositions; and in particular he finds a Right line equal to a parabolical Curve, Prop. 51
4. Divers Optick Propositions towards the end of the Book, concerning the Imperfection of the Eye, and the Confusion of the Sight; the apparent Magnitude of the Sun, low and high; the Tails of Comets; what Proportion the Earths illumination by the Sun at the Full of the Moon bears to the illumination of the Earth by the Moon; and the like comparison between the Sun and Sirius; That vision by aid of a Telescope or Microscope, is not deceitful: And an Observation of the likeness between the Earth and the Moon.
This same Author in his Letter to Mr F. C. suggests, that Cassini hath observed the Motion of Jupiter about his Axis in 10 hours; of Mars in 23 hours; that Venus hath the like Rotations: but the precise period not yet known; that Cassini ​hath publish'd Tables of the Motion of the Safellits of Jupiter, with an Ephemeris of the same for this present year: All which are there much applauded. The like Tables have been formerly publish'd by the Learn'd John Baptist Hodinera at Rome about 1656. which we intimate, because that and other Works of that knowing Author are here scarcely known nomine tenus.
In another Letter of this Author to the same F. C. (which is an answer to a Quære, whether Antimo Fabry, by some suppos'd to be Hon. Fabry, the Author of a Tract entituled "Opusculum Geometricum de linea Sinuum & Cycloide", printed at Rome An. 1659. had publisht the Treatises promised in the Preface thereof, viz, a Century de Maximis & Minimis; and some other Geometrical Tracts, as precursory to his, intended General Body of Geometry) he answers, that none of these Treatises are extant; that Mich. Angeo Ricci only, (since Viviani) hath written de Maximis & Minimis in two sheets, but to extraordinary good purpose. The Argument, doubtless, concerns either the Limits of Geometrical Problems, or of Æquation. Concerning the latter; we shall here intimate, that Erasmus Bartholinus hath well handled the same in his Treatise, entitul'd, Dioristice five Methodus Æquationum prima & secunda, Hafniæ, 1663; which are different from those of de Beaune formerly publisht: At the end of which Treatise the said Bartholinus prorniseth a General Body of Algebra, wherein the Precepts shall be explain'd by Examples. The same Author hath publisht other Treatises, which we do not find to have been brought over; as one, De Arte Analytica inveniendi omnia Problemata Proportionalium maximé Harmonicorum, Hafniæ, 1657. in 4°, Another, de Problematibus Mathematicis ibid. A. 1665. in 4°.
II. AN INTRODUCTION TO ALGEBRA, Translated out of High-Dutch into English by THO. BRANKER. M. A. much alter'd and augmented. Dr. J. P. Also a Table of such odd Numbers, as are less than one hundred thousand, shewing those that are Incomposit, and resolving the rest into their Factors or Coefficients. Printed at London in 4°
First, as to the Method of this Book, it is New, such as ​obtains much in a little, each distinct step of Ratiocination or Operation hath a distinct Line: the Author putting small Letters for unknown Quantities, and great Letters for known ones; and the Method is such, that most of the Book, if not all, may be understood by those not vers'd in the English Tongue, that are vers'd in Specious Algebra; most of the Questions being propounded in Symbols, and the progress of the work so described by the Marginal quotations, that for those exercised in Algebra, that would transcribe a Problem in this Method, it were sufficient, only to take the Margent, omitting the works it self, till farther leisure is afforded to perform it.
Next, as to the Matter, the Book consists of many excellent Problems; some whereof are such, as Bachet (that famous Commentator on Diophantus) either confesseth he did not attain, or at least left obscure: and others of them are such, as the celebrated DesCartes and Van Schooten have left doubtful, as not being by them, thoroughly understood. And some of them are such, as being unlimited, have for their Answers certain ranks or Series of all possible whole or rational Numbers, whereby the Student may be accomplisht for the resolution of other Questions of the like Nature.
Thirdly, as to the Table of Incomposits, no Book but this, extends it to above Ten thousands; some of the uses whereof are declared in the Title, others in the Book; and even in Common Arithmetick, it is of excellent Use for the Abbreviation of Fractions, and for giving of all the aliquot parts of a Number proposed, useful for the Depression and Resolution of Æquations, as is taught by Albert Gerard, and Van Schooten. Besides, it is observable in this Treatise, that the Author declineth the Exegesis numerosa of Vieta, which following Writers use for the finding of the Roots of Æquations.
As to the Remaining part of the Book, as it was published by John Henry Rohn in High Dutch, reasons may be given, why it was omitted in this English Edition.
The First Part of it handles the Taction of Circles; about which Argument some Epistles of Descartes are published in the Third Volume of his Posthumous Letters.
​The Second Part of it treates of the Geometrical Composition or Delineation of Æquations by aid of a Circle and Parabola, wherein the Author seemes to have followed Descartes About this Subject see an Excellent Tract Intitled Mesolabum, sive Duæ mediæ inter extremas datas infinitis modis exhibitæ, Auctore Renato Francisco Stusio Canonico Leodiensi (cujus nomen subticetur) Leodri Eburomum 1659 4°, which Book the Learned Author thereof promiseth to reprint and enlarge this Summer.
The Third Part of it contains 105 Theoremes about Sines, Tangents, Secants, &c, the Doctrine whereof, together with what else is omitted in this Edition, and other considerable matters about Æquations, may be hoped for from the Pen of that excellent Person, that is mentioned in the Epistle to the Reader.
III.AN ESSAY towards a REAL CHARACTER and a PHILOSOPHICAL LANGUAGE, by JOHN WILKINS D. D. Dean of Ripon, and Fellow of the R. Society.
The Reverend and Learned Author of this well-consider'd Work hath digested the things, which to him seem'd most proper and material to be said of this Subject, into four parts.
In the First, he premises some things as Præognita, concerning such Tongues and Letters as are already in being, particularly concerning those various defects and imperfections in them, which ought to be supply'd and provided against, in any such Language or Character, as is to be invented according to the Rules of Art.
The Second contains that which is the great Foundation of the thing here designed, viz. a regular Enumeration and Description of all those Things and Notions, to which Markes or Names ought to be assigned according to their respective natures; which may be stiled the Scientifical Part, comprehending Universal Philosophy: It being the proper End and Design of the several branches of Philosophy, to reduce all things and notions unto such a frame, as may express their natural order, dependence, and ​relations. All these things or notions he represents in a Scheme, and reduces them to forty Genus's.
The Third part treats of such helps and lnstruments, as are requisite for the framing of these more simple Notions into continued Speech or Discourse; which may therefore be stiled the Organical or Instrumental Part, and doth comprehend the Art of Natural or Philosophical Grammar.
In the Fourth, he shews, How these more general Rules may be applyed to particular kinds of Characters, and Languages giving an Instance of each. To which he adjoyns, by way of Appendix, a Discourse shewing the advantage of such a kind of Philosophical Character and Langnage, above any of those which are now known; more particularly above that, which is of most general use in these parts of the World, namely, the Latine.
Lastly, There is added a Dictionary of the English Tongue, in which is shewn, How all the words of this Language, according to the various equivocal senses of them, may be sufficiently expressed by the Philosophical Tables here proposed.
This is the Method, in which the Author hath treated of this considerable subject; concerning which he addresses his desires to the R. Society, to whom he dedicateth this Book, that they would appoint some of their Number, thoroughly to examine and consider the whole, and to suggest, what they judge fit to be amended in it. Which desire of his hath already been so farr entertain'd, that several of the Fellows of that Society have been nominated, and desired to peruse the Book with attention, and thereupon to make a Report accordingly, for the furthering and facilitating the Practice of what is therein aimed at.
IV. STANISLAI De LUBIENIETZ THEATRUM COMETICUM, duabus partibus constans; quarum Altera, Cometas A. 1664 & 1665, vaiis Virorum per Europam Clarissimorum, cum quibus Author de hoc Argumento contulit, Observationibus, dissertationibus, animadversionibus, descriptos & 59. Figuris æneis illustratos, fos, exhibet: Ahera, continet Historam 415. Cometarum, à tempore Diluvii ad A. 1665. cum 25. Figuris, & accurato ​eulo non tantum tristium, sed & lætorum Eventuum, eos secutorum: in qua simul Synopsis quædam Historiæ Universailis proponitur; & Theatri Cometici Exitus sive de. significatione Cometarum. Opus Mathematicum, Physicum, Historicum, Politicum, Ethcum, Oeconomicum, Chronologicum. Amstelodami A. 1668. in Fol.
ERRATA.
PAge 667. l. 5. r. Tympanum p. 681. l. 13. r. execta. p. 685. l. 17. r. thence be given. p. 688. l. 14. r. he answers.
FINIS.
In the SAVOY,
Printed by T.N. for John Martyn, Printer to the Royal Society and are to be sold at the Bell a little without Temple-Bar, 1668.
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Cite error: <ref> tags exist for a group named "errata", but no corresponding <references group="errata"/> tag was found
Errata
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