Philosophical Transactions/Volume 1/Number 1

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PHILOSOPHICAL


TRANSACTIONS.




Munday, March 6. 1664/5.




The Contents.

An Introduction to this Tract. An Accompt of the Improvement of Optick Glasses at Rome. Of the Observation made in England, of a Spot in one of the Belts of the Planet Jupiter. Of the motion of the late Comet prædicted. The Heads of many New Observations and Experiments, in order to an Experimental History of Cold; together with some Thermometrical Discourses and Experiments. A Relation of a very odd Monstrous Calf. Of a peculiar Lead-Ore in Germany, very useful for Essays. Of an Hungarian Bolus, of the same effect with the Bolus Armenus. Of the New American Whale-fishing about the Bermudas. A Narative concerning the success of the Pendulum-watches at Sea for the Longitudes; and the Grant of a Patent thereupon. A Catalogue of the Philosophical Books publisht by Monsieur de Fermat, Counſellour at Tholouse, lately dead.

The Introduction.


WHereas there is nothing more necessary for promoting the improvement of Philosophical Matters, than the communicating to such, as apply their Studies and Endeavours that way, such things as are discovered or put in practise by others; it is therefore thought fit to employ the Press, as the most proper way to gratifie those, whose engagement in such Studies, and delight in the advancement of Learning and profitable Discoveries, doth entitle them to the knowledge of what this Kingdom, or other parts of the World, do, from time to time, afford, as well of the progress of the Studies, Labours, and attempts of the Curious and learned in things of this kind, as of their compleat Discoveries and performances: To the end, that such Productions being clearly and truly communicated, desires after solid and usefull knowledge may be further entertained, ingenious Endeavours and Undertakings cherished, and those, addicted to and conversant in such matters, may be invited and encouraged to search, try, and find out new things, impart their knowledge to one another, and contribute what they can to the Grand design of improving Natural knowledge, and perfecting all Philosophical Arts, and Sciences. All for the Glory of God, the Honour and Advantage of these Kingdoms, and the Universal Good of Mankind.

An Accompt of the improvement of Optick Glasses.

There came lately from Paris a Relation, concerning the Improvement of Optick Glasses, not long since attempted at Rome by Signor Giuseppe Campani, and by him discoursed of, in a Book Entituled, Ragguaglio di nuoue Oss}ervationi, lately printed in the said City, but not yet transmitted into these parts; wherein these following particulars, according to the Intelligence, which was sent hither, are contained.

The First regardeth the excellency of the long Telescopes, made by the said Campani, who pretends to have found a way to work great Optick Glasses with a Turne-tool, without any Mould: And whereas hitherto it hath been found by Experience, that small Glasses are in proportion better to see with, upon the Earth, than the great ones; that Author affirms, that his are equally good for the Earth, and for making Observations in the Heavens. Besides, he useth three Eye-Glasses for his great Telescopes, without finding any Iris, or such Rain-bow colours, as do usually appear in ordinary Glasses, and prove an impediment to Observations.

The Second, concerns the Circle of Saturn, in which he hath observed nothing, but what confirms Monsieur Christian Huygens de Zulichem his Systeme of that Planet, published by that worthy Gentleman in the year, 1659.

The Third, respects Jupiter, wherein Campani affirms he hath observed by the goodness of his Glasses, certain protuberancies and inequalities, much greater than those that have been seen therein hitherto. He addeth, that he is now observing, whether those sallies in the said Planet do not change their scituation, which if they should be found to do, he judgeth, that Jupiter might then be said to turn upon his Axe; which, in his opinion, would serve much to confirm the opinion of Copernicus. Besides this, he affirms, he hath remarked in the Belts of Jupiter, the shaddows of his Satellites, and followed them, and at length seen them emerge out of his Disk.

A Spot in one of the Belts of Jupiter.

The Ingenious Mr. Hook did, some moneths since, intimate to a friend of his, that he had, with an excellent twelve foot Telescope, observed, some days before, he than spoke of it, (videl. on the ninth of May, 1664, about 9 of the clock at night) a small Spot in the biggest of the 3 obscurer Belts of Jupiter, and that, observing it from time to time, he found, that within 2 hours after, the said Spot had moved from East to West, about half the length of the Diameter of Jupiter.

The Motion of the late Comet prædicted.

There was lately sent to one of the Secretaries of the Royal Society a Packet, containing some Copies of a Printed Paper, Entituled, The Ephemerides of the Comet, made by the same Person, that sent it, called Monsieur Auzout, a French Gentleman of no ordinary Merit and Learning, who desired, that a couple of them might be recommended to the said Society, and one to their President, and another to his Highness Prince Rupert, and the rest to some other Persons, nominated by him in a Letter that accompanied this present, and known abroad for their singular abilities and knowledge in Philosophical Matters. The end of the Communication of this Paper was, That, the motion of the Comet, that hath lately appeared, having been prædicted by said Monsieur Auzout after he had seen it (as himself affirms) but 4 or 5 times: the Virtuosi of England, among others, might compare also their Observations with his Ephemerides; either to confirm the hypothesis, upon which the Author had before hand calculated the way of this Star, or to undeceive him, if he be in a mistake. The said Author Dedicateth these his conceptions to the most Christian King, telling him, that he presents Him with design, which never yet was undertaken by any Astronomer, all the World having been hitherto perswaded, that the motions of Comets were so irregular, that they could not be reduced to any Laws, and men having contented themselves, to observe exactly the places, through which they did pass; but no man, that he knows, having been so bold as to venture to foretel the places, through which they should pass, and where they should cease to appear. Whereas he exhibits here the Ephemerides, determining day by day, in what place of the Heavens this Comet shall be, at what hour it shall be in its Meridian, and at what hour it shall set; untill its too great remoteness, or the approach of the Sun, hide it from our eyes. Descending to particulars, he saith, that this Star, being disengaged from the beams of the Sun might have been observed, if his conjectures be good, ever since it hath been of 17 or 18 degrees Southern Latitude, and that about the middle of November last, and sooner, unless it have been too small: That however it hath been seen in Holland ever since the 2d. of December last, at which time according to his reckoning, the Diurnal motion of the Comet should already amount to 17 or 18 minutes. He finds, that this Star moveth just enough in the Plan of a Great Circle, which inclineth to the Equinoctial about 30 degrees, and to the Ecliptick about 49d. or 491/2 cutting the equator at about 45d1/2 , and the Ecliptick at the 28d. of Aries, or a little more. He saith just enough, because he thinks, there may perhaps be some parallaxe, which he wisheth could be determined.

Hence, (so he goes on) every one who pleaseth, may see, in tracing the Comet upon the Globe, through, or by which Stars it hath passed and shall pass; adding, that there will be neither cause to wonder, that having descended to about 6. deg. beneath the Tropick of Capricorn, he hath remounted afterwards, and shall go on ascending so, as to pass the Æquinoctial, and perhaps proceed to 15. degrees Northern Declination, if it do not disappear before that time, by reason of its remoteness: Nor to believe, that there have been two Comets, upon its being seen again the 31 of December; since, according to him, it ought to have been so, if it continue to move in a Great Circle.

Having hereupon shewed, how the motion is to be traced upon the Globe, he finds, that, according to his Calculation, this Comet was to pass the Tropick of Capricorn about the 16 of December, and being entred into the Sign of Virgo on the 20. of the same month, and having been in Quadrat with the Sun, it should still descend, until the 26 of December in the morning, and then enter into Leo; that having entred, the 28. of the same month, into Cancer, and been, a little after that time, in its greatest Inclination to the Ecliptick, vid. in the 28. degree of Leo, it was to repass the Southern Tropick, over against the little Dogg, on the 29. of December about 9 or 10 of the clock in the morning; after it had been opposite to the Sun 2. or 3. hours before; and that on the 29. of December in the evening it should be in Gemini; and at the very beginning of the New year, enter into Taurus.

After this, our Author finds, that this Comet according to his account, should pass the Æquator, on the 4. of January before noon, and that about 5. or 6. of the clock in the evening of that day it was to come into the jaw of the Whale, and the 9. of the same, at 6. of the clock, it should come close to the small Star of the Whale, which is in its way, a little below. At length he finds that it was to enter into Aries on the 12. of January, and to cut the Ecliptick on the 16. of the same month about noon, at which time it was to be again in Quadrat with the Sun, whence drawing a little to above the Northern Line of Pisces, it should in his opinion cease to appear a little beyond that place, without going as far as to the middle of Aries, if so be that its remoteness make it not disappear sooner.

He continueth, and saith, that this Comet shall not arrive to the place over against the Line of Pisces till the 10 of February, & that then its Diurnal motion shall not exceed 8 minutes, and not 5 minutes about the 20 of the same month: and that in the beginning of March, if we see it so long, the said motion shall not exceed 4 minutes, and so shall be still diminishing; except the Comet become Retrograde, which, as very important, he would have well observed; as also, whether it motion will be about the end more or less swift, than he hath calculated it.

He subjoyneth, that the greatest way, which this Star could make in 24 hours, hath been 13.d.25'; and in one houre, about 34's and thinking it probable, that about the time, when it made so much way, it should be nearest to the Earth, he concludeth that its motion in 24. hours must be, in its least distance from the Earth, as about 3. to 14, or 1. to 42/3, and that its motion in one hour was to be to the same least distance, as about 1. to 1021/7.

But that, which he judgeth most rewarkable, is, that he found by his Calculation, that the said least distance should be on the 29. of December, when the Comet was opposite to the Suns which he does not know whether it may not serve to decide the grand Question concerning the Motion of the Earth.

He taketh further notice, that the Tayl of the Comet was to turn Westward, with a point to the North, until the 29. of December, at which time it was to be opposite to the Sun, and that then the said Tayl was to look directly North; but that, after that time, the Tayl was to turn Eastward, and continure to do so, until it disappear; and that it shall draw a little towards the North, until the 8. or 10. of February, at which time the Tayl is to be parallel to the Æquator, as if the Comet be yet seen for some time after, the Tayl shall go a little lower towards the South, but grow smaller.

He finds by his Hypothesis, that on the 2. of December, which is the first observation, that he hath heard of, this Star was to be about 7. times more remote from the Earth, than when it was in its Perigeum; and that it will be again in an equall remoteness from the Earth, on the 27. of January, so that he is of opinion, that in case this Comet have not been seen before the 2 of December, it will not be seen any more after the 27. of January.

He wishes above all things, that it might be very exactly observed, at what Angle the way of the Comet cuts the Æquator, and, most of all, the Ecliptick, that so it may be seen, whether there hath not been some Parallaxe in the Circle of his Motion; as also, that some observations could be had of its greatest descent beneath the Tropick of Capricorn in the more Southern parts, where he saith it would have been without Refractions; Moreover of the Time, when it hath been in Quadrat with the Sun about the 20 of December; and that also very exact Observation might be made of the time of its being again in Quadrat with the Sun, which, according to him, was to be January 16.

He wishes also, that some in Madagascar may have observed this Star; Seeing that it began to appear over the middle of that Island, and passed twice over their heads; he judgeth, that they have seen it before us. And he wisheth lastly, that there were some intelligent person in Guiana to observe it there, seeing that within a few daies, according to his reckoning, it will pass over their Heads, and will not remove from thence but 8 or 10 degrees Northward, where he saith, it will disappear; thinking it improbable, that it can still appear, after the Sun shall have passed it.

This Account beareth date of the 2. January, new stile, 1665. and the Author thereof addeth this Note, That, seeing it could not be printed nor distributed so soon as he desired, he hath had the opportunity to verifie it by some Observations, from which he affirms he hath found no sensible difference; or, if there be, that it proceeds only from thence, that the Stars have advanced, since his Globe was made. He concludeth, that if this continue, and the first Observations do likewise agree, or that the differences do arrive within the Times, ghessed by him, that he hopes, he shall determine both the Distance and the Magnitude of this Comet; and that perhaps one may be enabled to decide the Question of the Motion of the Earth. In the interim, he assureth, that he hath not changed the least numbers in his Calculations, and that Monsieur Huygens, and several French Gentlemen, to whom he saith, he hath given them long since, can bear him witness that he hath done so; as also many other friends of his, who saw upon his Globe, several daies before, the way of the Comet from day to day.

Thus for the Parisian Account of the Comet, which is here inserted at large, that the intelligent and curious in England may compare their Observations therewith, either to verifie these Prœdictions, or to shew wherein they differ; which is (as was also hinted above) the design of this Philisophical Prophet in dispersing his Conceptions, who declareth himself ready, in case he be mistaken in his reckoning, to learn another Hypothesis, to explicate these admirable appearances by.

An Experimental History of Cold.

There is in the Press, a New Treatise, entituled, New Observations and Experiments in order to an Experimental History of Cold, begun by that Noble Philosopher, Mr. Robert Boyle, and in great part already Printed; He did lately very obligingly present several Copies of so much as was Printed, to the Royal Society, with a desire that some of the Members thereof might be engaged to peruse the Book, and select out of it for trial, the hints of such Experiments, as the Author there wisheth might be either yet made or prosecuted. The Heads thereof are,

  1. Experiments touching Bodies capable of Freezing others.
  2. Experiments and Observations touching Bodies Disposed to be Frozen.
  3. Experiments touching Bodies, Indisposed to be Frozen.
  4. Experiments and Observations touching the Degrees of Cold in several Bodies.
  5. Experiments touching the Tendency of Cold Upwards or Downwards.
  6. Experiments and Observation touching the Preservation and Destruction of (Eggs, Apples, and other) Bodies by Cold.
  7. Experiments touching the Expansion of Water and Aqueous Liquors by Freezing.
  8. Experiments touching the Contraction of Liquours by Cold.
  9. Experiments in Consort, touching the Bubbles, from which the Levity of Ice is supposed to proceed.
  10. Experiments about the Measure of the Expansion and the Contraction of Liquors by Cold.
  11. Experiments touching the Expansive Force of Freezing Water.
  12. Experiments touching a New way of estimating the Expansive force of Congelation, and highly compressing Air without Engines.
    • Experiments and Observations touching the Sphere of Activity of Cold.
    • Experiments touching differing Mediums, through which Cold may be diffused.
    • Experiments and Observations touching Ice.
    • Experiments and Observations touching the duration of Ice and Snow, and the destroying of them by the Air, and several Liquors.
    • Considerations and Experiments touching the Primum Frigidum.
    • Experiments and Observations touching the Coldness and Temperature of the Air.
    • Of the strange Effects of Cold.
    • Experiments touching the weight of Bodies frozen and unfrozen.
    • Promiscuous Experiments and Observations concerning Cold.
    • This Treatise will be dispatched within a very short time, and would have been so, ere this, if the extremity of the late Frost had not stopt the Press. It will be accompanied with some Discourses of the same Author, concerning New Thermometrical Experiments and Thoughts, as also, with an Exercitation about the Doctrine of the Antiperistasis: In the former whereof is first proposed this Paradox, That not only our Senses, but common Weather glasses, may misinform us about Cold. Next, there are contained in this part, New Observations about the deficiencies of Weather-glasses, together with some considerations touching the New or Hermetrical Thermometers. Lastly, they deliver another Paradox, touching the cause of the Condensation of the Air, and Ascent of water by cold in common Weather-glasses. The latter piece of this part contains an Examen of Antiperistasis, as it is wont to be taught and proved; Of all which there will, perhaps, a fuller account be given by the Next.

      An Account of a very odd Monstrous Calf.

      By the same Noble person was lately communicated to the Royal Society an Account of a very Odd Monstrous Birth, produced at Limmington in Hampshire, where a Butcher, having caused a Cow (which cast her Calf the year before) to be covered, that she might the sooner be fatted, killed her when fat, and opening the Womb, which he found heavy to admiration, saw in it a Calf, which had begun to have hair, whose hinder Leggs had no Joynts, and whose Tongue was, Cerberus-like, triple, to each side of his Mouth one, and one in the midst: Between the Fore-leggs and the Hinder-leggs was a great Stone, on which the Calf rid: The Sternum, or that part of the Breast, where the Ribs lye, was also perfect Stone; and the Stone, on which it rid, weighed twenty pounds and a half; the outside of the Stone was of Grenish colour, but some small parts being broken off, it appeared a perfect Free-stone. The Stone, according to the Letter of Mr. David Thomas, who sent this Account to Mr. Boyle, is with Doctor Haughteyn of Salisbury, to whom he also referreth for further Information.

      Of a peculiar Lead-Ore of Germany, and the Use thereof.

      There was, not long since, sent hither out of Germany from an inquisitive Physician, a List of several Minerals and Earths of that Country, and of Hungary, together with a Specimen of each of them: among which there was a kind of Lead-Ore which is more considerable than all the rest, because of its singular use for Essays upon the Coppell, seeing that there is not any other Mettal mixed with it. 'Tis found in the Upper Palatinate, at a place called Freyung and there are two sorts of it, whereof one is a kind of Crystalline Stone, and almost all good Leads the other not so rich, and more farinaceous. By the information, coming along with it, they are fetcht, not from under the ground, but, the Mines of that place having lain long neglected, by reason of the Wars of Germany and the increase of Waters, the people, living there-about take it from what their Forefathers had thrown away, and had lain long in the open Air. The use above mentioned being considerable, the person, who sent it, hath been intreated, to inform what quantities may be had of it, if there should be occasion to send for some.

      Of an Hungarian Bolus, of the same Effect with the Bolus Armenus.

      The same person gave notice also, that, besides the Bolus Armenus, and the Terra Silesiaca, there is an Earth to be found in Hungary about the River Tockay, thence called Bolus Tockaviensis, having as good effects in Physick, as either of the former two, and commended by experience in those parts, as much as it is by Sennertus out of Crato, for its goodness.

      Of the New American Whale-fishing about the Bermudas.

      Here follows a Relation, somewhat more divertising, than the precedent Accounts, which is about the new Whale-fishing in the West-Indies about the Bermudas, as it was delivered by an understanding and hardy Sea-man, who affirmed he had been at the killing work himself. His account, as far as remembred, was this; that though hitherto all Attempts of mastering the Whales of those Seas had been unsuccesful, by reason of the extraordinary fierceness and swiftness of these monstrous Animals; yet the enterprise being lately renewed, and such persons chosen and sent thither for the work, as were resolved not to be baffled by a Sea-monster, they did prosper so far in this undertaking, that, having been out at Sea, near the said Isle of Bermudas, seventeen times, and fastned their Weapons a dozen times, they killed in these expeditions 2 old Female-Whales, and 3 Cubs, whereof one of the old ones, from the head to the extremity of the Tayl, was 88. Foot in length, by measure; its Tayl being 23. Foot broad, the swimming Finn 26. Foot long, and the Gills three Foot long: having great bends underneath from the Nose to the Navil; upon her after-part, a Finn on the backs being within paved (this was the plain Sea-man's phrase) with fat, like the Cawl of a Hog.

      The other old one, he said, was some 60. Foot long. Of the Cubs, one was 33. the other two, much about 25 or 26. Foot long.

      The shape of the Fish, he said, was very sharp behind, like the ridge of a house; the head pretty bluff, and full of bumps on both sides; the back perfectly black, and the belly white.

      Their celerity and force he affirmed to be wonderful, insomuch that one of those Creatures, which he struck himself, towed the boat wherein he was, after him, for the space of six or seven Leagues, in 3/4 of an hours time. Being wounded, he saith, they make a hideous roaring, at which, all of that kind that are within hearing, come towards that place, where the Animal is, yet without striking, or doing any harm to the wary.

      He added, that they struck one of a prodigious bigness, and by guess of above 100 foot long. He is of opinion, that this Fish comes nearest to that sort of Whales, which they call the Jubartes; they are without teeth, and longer than the Greenland-Whales, but not so thick.

      He said further, that they fed much upon Grass, growing at the bottom of the Sea; which, he affirmed, was seen by cutting up the great Bag of Maw, wherein he had found in one of them about two or three Hogsheads of a greenish grassy matter.

      As to the quantity and nature of the Oyl which they yield, he thought, that the largest sort of these Whales might afford seven or eight Tuns if well husbanded, although they had lost much this first time, for want of a good Cooper; having brought home but eleven Tuns. The Cubbs, by his relation, do yield but little, and that is but a kind of a Jelly. That which the old ones render, doth candy like Porks Grease, yet burneth very well. He observed, that the Oyl of the Blubber is as clear and fair as any Whey: but that which is boyled out of the Lean, interlarded, becomes as hard as Tallow, spattering in the burning and that which is made of the Cawl, resembleth Hoggs grease.

      One, but scarce credible, quality of this Oyl, he affirms to be, that though it be boiling, yet one may run ones hand into it without scalding; to which he adds, that it hath a very healing Vertue for cuttings, lameness, &c., the part affected being anointed therewith. One thing more he related, not to be omitted, which is, that having told, that the time of catching these Fishes was from the beginning of March, to the end of May, after which time they appeared no more in that part of the Sea: he did, when asked, whither they then retired, give this Answer, That it was thought, they went into the Weed-beds of the Gulf of Florida, it having been observed, that upon their Fins and Tails they have store of Clams or Barnacles, upon which, he said, Rock-weed or Sea-tangle did grow a hand long; many of them having been taken of them, of the bigness of great Oyster-shels, and hung upon the Governour of Bermudas his Pales.

      A Narrative concerning the success of Pendulum-Watches at Sea for the Longitudes.

      The Relation lately made by Major Holmes, concerning the success of the Pendulum-Watches at Sea (two whereof were committed to his Care and Observation in his last voyage to Guiny by some of our Eminent Virtuosi, and Grand Promoters of Navigation) is as followeth;

      The said Major having left that Coast, and being come to the Isle of St. Thomas under the Line accompanied with four Vessels, having there adjusted his Watches, put to Sea, and sailed Westward, seven or eight hundred Leagues, without changing his course; after which, finding the Wind favourable, he steered towards the Coast of Africk, North-North-East. But having sailed upon that Line a matter of two or three hundred Leagues, the Masters of the other Ships, under his Conduct, apprehending that they should want Water, before they could reach that Coast, did propose to him to steer their Course to the Barbadoes, to supply themselves with Water there. Whereupon the said Major, having called the Master and Pilots together, and caused them to produce their Journals and Calculations, it was found, that those Pilots did differ in their reckonings from that of the Major, one of them eighty Leagues, another about an hundred, and the third, more; but the Major judging by his Pendulum-Watches, that they were only some thirty Leagues distant from the Isle of Fuego, which is one of the Isles of Cape Verde, and that they might reach it next day, and having a great confidence in the said Watches, resolved to steer their Course thither, and having given order so to do, they got the very next day about Noon a sight of the said Isle of Fuego, finding themselves to sail directly upon it, and so arrived at it that Afternoon, as he had said. These Watches having been first Invented by the Excellent Monsieur Christian Hugens of Zulichem, and fitted to go at Sea, by the Right Honourable, the Earl of Kincardin, both Fellows of the Royal Society, are now brought by a New addition to a wonderful perfection. The said Monsieur Hugens, having been informed of the success of the Experiment, made by Major Holmes, wrought to a friend at Paris a Letter to this effect;

      Major Holmes at his return, hath made a relation concerning the usefulness of Pendulums, which surpasseth my expectation: I did not imagine that the Watches of this first Structure would succeed so well, and I had reserved my main hopes for the New ones. But seeing that those have already served so succesfully, and that the other are yet more just and exact, I have the more reason to believe, that the Invention of Longitudes will come to its perfection. In the mean time I shall tell you, that the States did receive my Proposition, when I desired of them a Patent for these new Watches, and the recompense set a-part for the invention in case of success; and that without any difficulty they have granted my request, commanding me to bring one of these Watches into their Assembly, to explicate unto them the Invention, and the application thereof to the Longitudes; which I have done to their contentment. I have this week published, that the said Watches shall be exposed to sale, together with an Information necessary to use them at Sea: and thus I have broken the Ice. The same Objection, that hath been made in your parts against the exactness of these Pendulums, hath also been made here; to wit, that though they should agree together, they might fail both of them, by reason that the Air at one time might be thicker, than at another. But I have answered, that this difference, if there be any, will not be at all perceived in the Penduls, seeing that the continuall Observations, made in Winter from day to day, until Summer, have shewed me that they have always agreed with the Sun. As to the Printing of the Figure of my New Watch, I shall defer that yet a while: but it shall in time appear with all the Demonstrations thereof, together with a Treatise of Pendulums, written by me some days since, which is of a very subtile Speculation.

      The Character, lately published beyond the Seas, of an Eminent person, not long since dead at Tholouse, where he was a Councellor of Parliament.

      It is the deservedly famous Monsieur de Fermat, who was, (saith the Author of the Letter) one of the most Excellent Men of this Age, a Genius so universal, and of so vast an extent, that if very knowing and learned Men had not given testimony of his extraordinary merit, what with truth can be said of him, would hardly be believed. He entertained a constant correspondence with many of the most Illustrious Mathematicians of Europe, and did excel in all the parts of Mathematical Science: a Testimony whereof he hath left behind him in the following Books.

      A Method for the Quadrature of Parabola's of all degrees.

      A Book De Maximis & Minimis, which serveth not only for the determination of Problems of Plains and Solids, but also for the invention of Tangents and Curve Lines, and of the Centres of Gravity in Solids; and likewise for Numerical Questions.

      An Introduction to the Doctrine of Plains and Solids, which is an Analytical Treatise, concerning the solution of Plains and Solids, which has been seen (as the Advertiser affirms) before Monsieur Des Cartes had publish'd any thing upon this Subject.

      A Treatise De Contactibus Sphæricis, where he hath demonstrated in Solids, what Mr. Viet, Master of Requests, had but demonstrated in Plains.

      Another Treatise, wherein he establisheth and demonstrateth the two Books of Apollonius Pergæus, of Plains.

      And a General Method for the dimension of Curve Lines, &c. Besides, having a perfect knowledge in Antiquity, he was consulted from all parts upon the difficulties that did emerge therein: he hath explained abundance of obscure places, that are found in the Antients. There have been lately printed some of his Observations upon Athenæus; and he that hath interpreted Benedetto Castelli, of the Measure of running waters, hath thence inserted in his Work a very handsome one upon an Epistle of Synesius, which was so difficult, that the Jesuit Petavius, who hath commented upon this Author, acknowledges, that he could not understand it.

      He hath also made many Observations upon Theon of Smyrne, and upon other Antient Authors: but most part of them are not found but scattered in his Epistles, because he did not write much upon these kinds of Subjects, but to satisfie the curiosity of his friends.

      All these Mathematical Works, and all these curious searches in Antiquity, did not hinder this great Virtuoso from discharging the duties of his place with much assiduity, and with so much ability, that he hath had the reputation of one of the greatest Civilians of his Age.

      But that, which is most of all surprising to many, is, that with all that strength of understanding, which was requisite to make good these rare qualities, lately mentioned, he had so polite and delicate parts, that he composed Latin, French, and Spanish Verses with the same elegancy, as if he had lived in the time of Augustus, and passed the greatest part of his life at the Courts of France and Spain.

      More particulars will perhaps be mention'd of the Works of this Rare person, when all things, that he hath publish'd, shall be recovered, and when liberty shall be obtained of his Worthy Son, to impart unto the World the rest of his Writings, hitherto unpublished.

       

       

      Printed with Licence, For John Martin, and James Allistry, Printers to the Royal-Society.