# Philosophical Transactions of the Royal Society (1665-1886)/Volume 2/Number 30

Contents:
* Contents
* An Account of the Experiment of Transfusion, practised upon a Man in London.
* A Relation of some Trials of the same Operation, lately made in France.
* Some new Experiments of injecting Medicated Liquors into Veins, together with the considerable Cures perform'd thereby.
* An Extract of a Letter, written from the Bermudas, giving an account of the Course of the Tides there; of Wells both salt and sweet, digg'd near the Sea; of the Whale-fishing there practised anew, and of such Whales as have the Sperma Ceti in them.
* A Method for finding the Number of the Julian Period for any Year assign'd, the Number of the Cycle of the Sun, the Cycle of the Moon, and of the Indictions for the same year, being given; together with the Demonstration of that Method.
* An Account of some Books.
** I. Petri Lambecii Lib. Primus Prodromi Historiæ Literariæ, &c.——
** II. Thomæ Cornelii Consentini Progymnasmata Physica
** Les Essays Physiques du Sieur de Launay, Liv. premier.
** IV. Francisci du Laurens Speciminia Mathematica, duobus Libris comprehensa.
* Errata, forgot to be corrected sooner.
Numb. 30.
PHILOSOPHICAL
TRANSACTIONS.
Monday, December. 9. 1667.
The Contents.
An Account Of the Experiment of Transfusion, practised upon a Man in London.
This was perform'd, Novemb. 23. 1667. upon one Mr. Arthur Coga, at Arundel-house, in the presence of many considerable and intelligent persons, by the management of those two Learned Physicians and dextrous Anatomists Dr. Richard Lower, and Dr. Edmund King, the latter of whom communicated the Relation of it, as followeth.
The Experiment of Transfusion of Blood into an humane Vein was made by Us in this manner. Having prepared ​the Carotid Artery in at young Sheep, we inserted a Silver-Pipe into the Quills to let the Blood run through it into a Porringer, and in the space of almost a minute, about 12 ounces of the Sheeps bloud ran through the Pipe into the Porringer; which was somewhat to direct us in the quantity of Bloud now to be transfus'd into the Man. Which done, when we came to prepare the Vein in the Man's Arm, the Vein seem'd too small for that Pipe, which we intended to insert into it; so that we imployed another, about one third part less, at the little end. Then we made an incision in the Vein, after the method formerly publisht, Numb. 28; which method we observ'd without any other alteration, but in the shape of one of our Pipes; which we found more convenient for our purpose. And, having open'd the Vein in the Man's Arm, with as much ease as in the common way of Venæ-seetion, we let thence run out 6 or 7 ounces of Blood. Then we planted our silver Pipe into the said Incision, and inserted Quills between the two Pipes already advanced in the two subjects, to convey the Arterial bloud from the Sheep into the Vein of the Man. But this Blood was near a minute, before it had past through the Pipes and Quills into the Arm; and then it ran freely into the Man's Vein for the space of 2 minutes at least; so that we could feel a Pulse in the said Vein just beyond the end of the silver Pipe; though the Patient said, he did not feel the Blood hot, (as we reported of the subject in the French Experiment) which may very well be imputed to the length of the Pipes, through which the blood passed, losing thereby so much of its heat, as to come in a temper very agreeable to Venal Blood. And as to the quantity of Blood receiv'd into the Man's Vein, we judge, there was about 9 or 10 ounces: For, allowing this Pipe ⅓ less than that, through which 12 ounces pass'd in one minute before, we may very well suppose, it might in 2 minutes convey as much blood into the Vein, as the other did in the Porringer in one minute; granting withall, that the Blood did not run so vigorously the second minute, as it did the first, nor the third, as the second, &c. But, that the Blood did run all the time of those two minutes, we conclude from thence; First, because we felt a Pulse during that time. Secondly, because when upon the Man's saying, ​He thought, he had enough, we drew the Pipe out of his Vein, the Sheeps blood ran through it with a full stream; which it had not done, if there had been any (top before, in the space of those two minutes; the blood being so very apt to coagulate in the Pipes upon the least stop, especially the Pipes being so long as three Qulls.
The Man after this operation, as well as in it, found himself very well, and hath given in his own Narrative under his own hand, enlarging more upon the benefit, he thinks, he hath received by it, than we think fit to own as yet. He urg'd us to have the Experiment repeated upon him within 3 or 4 days after this; but it was thought advisable, to put it off somewhat longer. And the next time, we hope to be more exact, especially in Weighing the Emittent Animal before and after the Operation, to have a more just account of the quantity of Blood, it shall have lost.
A Relation
Of some Trials of the same Operation, lately made in France.
1. M. Denys, Professor of the Mathematicks and Natural Philosophy at Paris, in a Letter of his to the Publisher relateth, That they had lately transmitted the Blood of four Weathers into a Horse of 26 years old, and that this Horse had thence received much strength, and more than an ordinary stomach.
2. The same person was pleased to lend to the same hand a printed Letter, written to the Abbot Bourdelot by M. Gadroys, being an Answer to a Paper of one M. Lamy, and confirming the Transfusion of Blood by new Experiments. In this Answer the Author is vindicating the Transfusion from Objections; where first he takes notice, That, whereas the Objector undertakes to refute the Experiments made, by simple Ratiocinations, it ought to be considered, that the Quodlibetical Learning of the Schools is capable enough to find Arguments for and against all sorts of Opinions, but that there is nothing, but Experience, that is able to ​give the Verdict and the last Decision, especially in matters of Natural Philosophy and Physick: That a hundred years ago, there were no Arguments wanting to prove, that Antimony or the Vinum Emeticum was poyson; the use of it being then forbidden by a Decree of the Faculty of Physicians; and that at this day there are no Arguments wanting, to prove the contrary, and to assert, That it is a Purgative of great importance, follow'd with wonderful effects, the same Faculty having publish'd a Decree the last year, by which it permits, and even ordains the use thereof. So that it ought to be said, that Sole Experience hath determin'd this matter, and that the Recovery of many persons, and amongst them, of the Most Christian King himself, hath more conduced to convince Men of its usefulness, than all the bare Ratiocinations, that could be employed to defend it. And so it is with all Remedies, there being not one, that is not approved by some Physician or other, who thinks to have reason on his side, and disapprov'd at the same time by others of that Profession, who conceive to have it on theirs: Whereas He certainly is to be esteemed the most Rational, that in these matters is guided by good Experience. And since the Transfusion of Blood is a new thing (unknown for ought we know) to all former Ages, ingenious Men, and lovers of the Increase of the Stock, serving for the relief and conveniences of Human Life, do no more, in this particular, than propose and recommend it to generous and unprejudicate Physicians, to judge of its agreeableness to Human Bodies, and to make trials of it accordingly; themselves esteeming, that since it concerns the Health and Life of Man, it cannot be examin'd too severely; though at the same time they conceive, that 'tis unequal to stand herein to the verdict of such arrogant Men, who from a self conceit of knowing all things already, are very impatient at any thing discover'd, which they have not thought on themselves: Those Men being the best advised and the most to be relied on, who do not precipitate their Judgment, but stay for many Experiments, carefully made, to conclude themselves by. For which purpose, the Author wishes, that Persons in power would cause a good number of Experiments of this Invention to be made, and examin them either themselves, or give order to prudent and free-spirited Physicians and Chirugeons to do so.
​Among the Objections, (which the Author finds to be generally grounded upon inconsiderations, mistakes, and a supposition, as if peremptory Affirmations touching the effects of this Transfusion were obtruded, whereas all is left to the success of Experiments faithfully made) there is one, directed against the effects of that operation, which appeared in the young Man, who (by Mr. Denys's Relation in his printed Letter to Monsieur De Montmor) after he had received the Arterial Blood of a Lamb, was cured of an extraordinary Lethargy, consequent to a violent Feaver wherein he had been let blood 20 times. And the Objection is, That the lively apprehension the said young Man had of a remedy so unusual, and whereof the success could not but appear very dubious to him, and so render him exceedingly anxious, did so rouse his spirits, and put them into such motion, as to disengage from that embarasment, which hundred their diffusion; upon which disentanglement follow'd all the other good effects, that are imputed to the Transfusion.
To this Conceit the Answerer replies, That if the Apprehension could have cured this young Man, the Cure would doubtless have been effected 24 hours before the Transfusion, because he then happen'd to have a very great one by falling down stairs; as was also observed in Mr. Denys his Relation of this Experiment. Besides, that this Patient was noted to be so far from apprehending or fearing this Operation, that he did not so much as know, what the Transfusion was; but thought, the Lamb was only applied to his Arm, to suck from him his ill Blood, as he was made to believe, after an ancient and usual way.
To that Objection, wherein some put weight, viz, That there is a great difference between the Flesh we eat for food, and the Blood that is transmitted immediately into the Veins; the former undergoing a great Alteration, which the latter does nor: Our Author replies, That of, the three principal Digestions of the Aliment, that have been always distinguish'd by Authors, the First, which is made in the Stomach, is not considerable in comparison of the two others, which are made of the Chyle and the Blood, in the Heart, the Liver, and generally in all the parts that receive nutrition, which he illustrates by this: That as the Concoction, which is made of the Juices of the Earth in the Root ​and Heart of the Trunk of a Tree, does not so much serve to the production of this or that Fruit, as the last Filtration that is made of those Juyces in the small Fibres of the Grafts; so also all those Digestions, which are supposed to be made in the Stomach and the Heart or the Liver of Animals, do not so much serve to give the particles of the Aliment those Figures, which they require to be converted into the substance of Man, as the diversity of Pores, that strain them last of all, and differ in the Bones, Flesh, Cartilages, and other parts; in which the Ancients for this reason did admit as many different Assimilating faculties. Now, saith he, though the new Blood, which is given in the Transfusion, undergoes not the first Concoction, made in the Stomach, yet it suffers the two others, in making many Circulations together with the native blood; and that therefore nothing hinders, but it may be fit to be changed into the substance of Man, without inconvenience.
The rest of the Objections, here alledged, seeming to be of no moment, though answer'd by our Author, we shall here pass by, and, for a general answer to all, employ Experience, and the several successful Transfusions, he relates; as those of Lambs-blood into Dogs, which, after the space of several months from the time of the Operation, do not only live, but are very well, and some of them grown fatter than they were before; and of Kids blood into a little Spaniel bitch of 12 years of age, which, a little while after the Operation, grew vigorous and active, and even proud in less than eight days. To which, he adds a considerable Experiment, lately made upon a person, that had been for three weeks affected with the complicated Distempers of an Hepatick Flux, a Lientery, and a bilious Diarrhæa, accompanied with-a, very violent Feaver; and had been attended by four Physicians, who having blouded, purged, and clystered him, as much as they thought fit, he grew at last so weak, that he was unable to stir, lost his speech and senses, and vomited all he took: whereupon they altogether despairing of and abandoning the Patient, and declaring that they did so, in the presence of divers persons of honor, consented to have the Experiment of Transfusion made upon the Patient, which his Relations had proposed, as the last Refuge; very unwilling to omit any thing, that might seem probable to rescue a dying ​man. M. Denys and M. Emmerey were besought to employ this last succours. But they, seeing the deplored state of the Sick, absolutely refused to make the tryal, alledging, that the Transfusion was not a means to restore either the solid parts, or to cure a Gangrene, which was apparently in his Intestines; they should have used it sooner, and at the very time, when the great evacuations of blood were made in the Patient. But, notwithstanding all this, they were exceedingly press'd to comply with their desires, and not to let their Friend dye without trying all means possible. They, being overcome by this importunity, and having secured their honour and safety, by the declaration above mentioned of the Physicians. and by their consent to the tryal of this Experiment, transfused into his Veins a small quantity of Calves blood in a morning; whereupon. though this Patient was already in a Lethargy, and convulsive, and had a very low and creeping pulse, yet, behold, an unexpected change happen'd to him. His pulse grew higher in an instant, and became more vigorous, his Convulsions ceased, he look'd fixedly on the By-standers, spoke pertinently, and in divers Languages to those that spoke to him, and fell into a very quiet sleep. Awakening three quarters of an hour after, he took several Broaths for the rest of the day, not vomiting at all, nor having any stool, although for three days before he could take nothing at the Mouth, nor had had any intermission of his loosness since the very beginning of his sickness. Having thus remained for 24 hours, his forces began to diminish again, and his pulse to grow low, and the loosness to return. His Friends then urged a second Transfusion, which being at last performed the next morning, the Patient indeed recover'd some vigour again, but that was of a short duration. For though then also he took his broath well, without vomiting. yet he voided still by stool, and at noon he began to decline, and about 5 at night he died, without the appearance of any convulsions. His body being open'd before the Physicians, the Ileon was found return'd into it self from the top to the bottom, and below that knot unto the anus the Bowels were all livid, gangren'd, and of an unsupportable steach. His Pancreas was extraordinarily hard, and so obstructed, that the Pancreatick Juice had no liberty to diffuse it self into the Guts. ​His Spleen was very thick, and his Liver big, and in some places livid. The Heart very dry, and, as 'twere, burnt. And having found the Vein, by which the Transfusion had been made, there was, from the place of the opening of the Arm, to the Heart, almost no blood found in it, no more than in the other Veins, nor in the Ventricles of the Heart, for as much as that little, he received, had been imbibed by his hot and dry Flesh. All which this Author assures, can be attested both by a dozen persons of great veracity; who were present at this dissection, and confirmed by the Certificates given by the Physicians themselves, to be sent to the Parents of the deceased Stranger; who is the very same with him, of whom a less punctual account was given, Numb. 28. p. 519.
Some new Experiments
This was lately communicated in a Letter from Dantzick written by Dr. Fabritius, Physician in Ordinary to that City, which out of the Latin we thus English.
Forasmuch as we had a great desire to experiment; what would be the effects of the Chirurgery of injecting Liquors into Humane Veins, three fit Subjects presenting themselves in our Hospital, we thought good to make the Tryal upon them. But seeing little ground to hope for a manifest operation from only Altering Medicines, we esteemed, the Experiment would be more convenient and conspicuous from Laxatives; which made us inject by a Syphon about two Drachms of such a kind of Physick into the Median Vein of the right Arm. The Patients were these. One was a lusty robust Souldier dangerously infected with the Venereal Disease, and suffering grievous protuberatings of the bones in his Arms. He, when the purgative Liquor was infused into him, complained of great pains in his Elbows, and the little valves of his Arm did swell so visibly, that it was necessary by a gentle compression of-ones fingers to stroke up that swelling towards the Patients shoulders. Some 4 hours after, it began to work, not very troublesomly; and so it did the next day, insomuch that the Man had five good stools after it. Without any ​other remedies those protuberances were gone, nor are there any footsteps left of the above mentioned Disease.
The two other Trials were made upon the other Sex. A married Woman of 35, and a serving Maid of 20 years of age, had been both of them from their Birth very grievously afflicted with Epileptick fits, so that there was little hopes left to cure them. They both underwent this operation, and there was injected into their Veins a Laxative Rosin, dissolved in an Anti-Epilectical Spirit. The first of these had gentle stools, some hours after the Injection, and the next day the fits recurring now and then, but much milder, are since altogether vanish'd. As for the other, viz. the Maid, the went the same day to stool four times, and several times the next; but by going into the Air, and taking cold, and not observing any diet, cast her self away.
'Tis remarkable, that it was common to all three to vomit soon after the injection, and that extreamly and frequently;. the reason whereof we leave to intelligent Physicians to assign.
An Extract
This Letter was written June 18. 1667. by that intelligent Gentleman Mr. Richard Norwood, living upon the place, and relating as follows.
SIR,
I Received your Letter of October 24. 1666. but, whereas you mention another formerly sent, that never came to my hands: Neither had I, before the receipt of yours, the least intelligence of the Institution of the Royal Society, founded by the King; but am very glad, that God hath put into the heart of his Majesty, to advance such a noble Design, and should rejoyce, I were able to add my Mite for the furtherance of it. As to the particulars you recommend to me, I shall answer to them, as I can, in the order I find them.
First, touching the Conjunction of Mercury with the Sun, ​which you say you gave me notice of in your first, not received, and which happened Octob. 25. 1664. I had also notice of it from Mr. Street, and had provided in some measure to observe it; but the sky was so overcast, that the Sun could scarce be discerned all that day.
Next, concerning the Tides, I have only taken a general notice of them; as, that it is high water about 7 of the clock on the Change day (in some Creeks an hour or two later.) The water riseth but little, as about 4 foot at a high water; but at the Spring-tides it may be a foot more. The Tides without are very various in their setting. Sometimes the Tide of Floud sets to the Eastward, sometimes to the Westward: but in fair, calm, and setled weather, the said Tide sets from the South-east toward the North-west, as they say.
We dig Wells, of fresh water sometimes within 20 yards of the Sea or less, which rise and Fall upon the Floud, and ebb as the Sea doth; and so do most of the Wells in the Country, though further up (as I am inform'd.) Wheresoever they digg Wells here, they digg till they come almost to a Level with the superficies of the Sea, and then they find either fresh water or salt. If it be fresh, yet if they digg two or three foot deeper, or often less, they come to salt water. If it be a sandy ground, or a sandy crumbling Stone, that the water soaks gently through, they find usually fresh water; but if they be hard Limestone Rocks, which the water cannot soak through, but passeth in chinks or clefts between them, the water is salt or brackish. Yet (to mention that by the by) I never saw any Sand in the Country such as will grind Glass, or whet Knives, &c. as in England, but a substance like Sand, though much softer; neither have we any Peble-stones or Flint.
A Method
In these Transactions, N° 18. p. 324. is a Theorem for finding the Year of the Julian Period by a new and very easie Method, which was taken out of the Journal des Scavans, N° 36. as it had been proposed and communicated by the Learned Jesuit De Bill.
Multiply the
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Solar | $\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,$ | Cycle | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Lunar | $\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,$ | Cycle | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Indication | | | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
by
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 4845. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 4200. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 6916. | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
Then divide the sum of the Products by 7980 (the Julian Period) the Remainder of the Division, without having regard to the Quotient, shall be the Year inquired after.
Some Learned Mathematicians of Paris, to whom the said P. de Billy did propose this Problem, have found the Demonstration thereof as the same Journal intimates.
There being no further Elucidation of the said Theorem since publish'd, Mr. John Collins, now a Member of the Royal Society, communicated what follows, viz.
That the Julian Period is a Basis, whereon to found Chronology not liable to Controversie, as the Age of the World is: And 'tis the Number abovesaid, to wit, 7980, which-is. the Product of
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 28 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 19 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 15 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
the
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Solar | $\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,$ | Cycle |
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Lunar | $\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,$ | Cycle |
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Indication |
Concerning this Julian Period, the late Archbishop of Armagh, Usher, in the Preface to his Learned Annals, advertiseth, that Robert Lotharing, Bishop of Hereford, first observed the Conveniencics thereof; 500 years after whom, it was fitted for Chronological uses by Joseph Scaliger, and is now embraced by the Learned as such a limit to Chronology, that within the space of 7980 Years, the Number of the Sun's Cycle, the Prime, and the year of the Roman Indiction (which relates to their ancient Laws ​and Records) can never happen alike. And these Remarques being given, the year of the Julian Period is by the former Rule infallibly found.
This Period is used by the said Archbishop in his Annals, and is by him accounted to exceed the Age of the World 709 years. Those that desire further satisfaction about Æra's, Epocha's, and Periods, may repair to many Authors, and among them to Gregory's Posthuma in English, Helvici Chronologia, Ægidii Strauchii Breviarium Chronologicum, who is one of the latest Authors.
Now as to the Problem it self, it may be thus proposed:
Any number of Divisors, together with their Remainders after Division, being proposed, to find the Dividend.
This thus generally proposed is no new Problem, and was resolved long since, by John Geysius, by the help of particular Multipliers, such as those above-mentioned, and publish'd by Alstedius in his Encyclopedia in Ann. 1630. and by Van Schooten his Miscellanies.
We shall clear up, what Authors have omitted concerning the Definition and Demonstration of such fixed Multipliers, &c. And therefore say, that each Multiplier is relative to the Divisor, to which it belongs, and thus define it;
It is such a Number, as divided by the rest of the Divisors, or their Product, the Remainder is 0; but divided by its own Divisor, the Remainder is an Unit.
We require the Divisors proposed to be Primitive each to other, i.e. that no two or more of them can be reduced to lesser terms by any common Divisor: For if so, the Question may be possible in it self, but not revolvable by help of such Multipliers, such being impossible to be found. The reason is, because the Product of an Odd and Even Number is always Even, and that divided by an Even Number, leaves either Nothing, or an Even Number.
Divisors
| 28 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
| 19 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
| 15 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
The Multipliers relative thereto are
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 4845 |
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 4200 |
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 6916 |
The Definition affords light enough for the discovery of these Numbers. To instance in the first: The Product of 19 and 15
| 4845 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
| 4200 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
| 6916 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ |
is equal to the Solid or Product of
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 19, 15, 17 |
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 28, 15, 10 |
| $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 28, 19, 13 |
More easie ways of performing this postulatum, are to be found in Van Schooten's Miscellanies, and Tacquet's Arithmetick, which perchance are not so obvious to every understanding.
For illustration of the Rule proposed, take this Example.
| In the year 1668. | Cyclus Solis | 25 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | The Multipliers | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 4845 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | Products | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 121125 |
| In the year 1668. | Cyclus Lunæ | 16 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | The Multipliers | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 4200 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | Products | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 67200 |
| In the year 1668. | Indictio | 6 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | The Multipliers | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 6916 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | Products | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 41496 |
| | | | The Sum of the Products | The Sum of the Products | The Sum of the Products | The Sum of the Products | The Sum of the Products | The Sum of the Products | The Sum of the Products | 229821 |
The which divided by 7980, the remainder is 6381, for the year of the Julian Period; from which subtracting 709, there remains 5622, for the Age of the World, according to Archbishop Usher.
For Demonstration of this Rule we thus argue:
1. Each Multiplier multiplied by its Remainder, is measured or divided by its own Divisor, leaving such a Remainder as is proposed.
For before, each Multiplier was defined to be a Multiplex of its own Divisor, plus an Unit: Wherefore multiplying it by any Remainder, it doth only render it a greater Multiplex in the said Divisor, plus an Unit, multiplied by the Remainder, which is no other than the Remainder it self; but if 0 remain, that Product is destroyed.
2. The Sum of the Products, divided by each respective Divisor, have the Remainder assigned.
For concerning the first Product, it is by the first Section ​measur'd by its own Divisor, leaving the remainder proposed; and if we add the rest of the Products thereto, we only add a Multiplex of its own Divisor, which in Division enlargeth the Quote, but not the Remainder.
Particularly the second Multiplier is 28 + 15 + 10 + Remainder, all which is but a Multiplex of 28.
And so the third Product is 28 + 19 + 13 + Remainder.
And what hath been said concerning the sum of the Products, being divided by the first Divisor, and leaving the Remainder thereto assign'd, may be said of each respectively.
3 The sum of the Products divided by the solid of the three Divisors, leaves a Remainder so qualified as the said Sum.
For concerning the said Sum, 'tis evident by the second hereof, that it is no other than the first Product; increas'd by adding a just Multiplex of the first Divisor, that thereby we did only enlarge the Quote, not alter the Remainder. By the like reason, the subtracting a just Multiplex thereof, doth only alter the Quote, not the Remainder; but the Solid of all three Divisors, multiplied here by the Quote, as there by the Remainder, is no other than a just Multiplex of the first Divisor. Wherefore the Remainder, after this Division is perform'd, is of the same Quality as the sum of the Products, and divided by the first Divisor; leaves the Remainder proper thereto. And the like may be said concerning each Divisor.
As in the Method hitherto deliver'd, we requir'd the Divisors be Primitive to each other; so, if we take the Problem as generally proposed, in the Preface to Helvicus his Chronologia, we are told, common Arithmetick fails in the solution thereof, and Tacquet denies it to be performable by the Regula Falsi, and being unlimited, we must do it by Tryals. Wherefore,
When any two Divisors with their Remainders are proposed, try the Multiplices of one of them, increased by its Remainder, and divide by the other: If you find such Remainders as are not for the purpose, and that they are repeated, the Problem is impossible.
Example.
| Divisors | 6. | Remainders | 3. |
| Divisors | 8. | Remainders | 5. |
| The Multiplices of 8, increased by 5, are | 13. | 21. | 29. | 37. | 45. | 53. |
| Those divided by 6, the Remainders are. | 1. | 3. | 5. | 1. | 3. | 5. |
Here you see 21 and 45 for the purpose, and take the Progression, adding the common Difference 24 (which is the least Dividend measured by 6 and 8) and you have 21. 45. 69. 93, 117. 141.
Admit, the Question had concerned these three Divisors:
| 6 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | the Remainders being | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 3 | Then dividing the former Progression by 9, the Remainders are 3. 0. 6. 3. 0. 6. |
| 8 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | the Remainders being | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 5 | Then dividing the former Progression by 9, the Remainders are 3. 0. 6. 3. 0. 6. |
| 9 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | the Remainders being | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 6 | Then dividing the former Progression by 9, the Remainders are 3. 0. 6. 3. 0. 6. |
Wherefore I conclude, that the third and sixth of these Numbers are those sought, to wit, 69 or 141, and so on progressively; whereas, if you had propounded the Remainder of 9 to have been any other Number than 3, 0, 6, the Problem, as concerning all these, had not been possible
Some easie Cases of the Problem are these:
When the Remainder of some Divisor is 0, and of each of the rest of the Divisors, an Unit, or less by an Unit, than the Divisor.
In which Cafes you are to find such a Multiplex of the Produéft or least Dividend measurable by those Divisors that have Remainders, which increas'd or diminish'd by an Unit, may be a just Multiplex of that Divisor that hath no Remainder. These Cases are handled by Tacquet, and Bachet in his Problemes plaisans & delectables.
PROBLEM.
To find the Year of the Julian Period for any year of our Lord proposed.
It is necessary to be furnished with the Sun's Cycle, the Prime Number, and the Number of the Roman Indiction, which the industrious Mr. Street thus performs:
When 1. 9. 3. to the Year hath added been, Divide by 19. 28, fifteen.
The Remainders are the Numbers sought. And hereby We found them for the year 1668. in the former Example
The use of the Prime is, to find the Epact, and thereby the Moons Age, time of High Water, &c.
A farther use of the Suns Cycle is, to attain the Dominical Letter, and thereby to know the Day of the Week, on which any Day of the Month happens. But this is more easily and with less caution obtain'd, by finding on what Day of the Week the first of March happens for ever, according to such Rules and Verses as I have elsewhere published. In brief thus:
| To the Number | 2. |
| Add the Year of our Lord, suppose | 1669. |
| $\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,$ And its even 4th part, neglecting what remains, if any | 417. |
| The Sum | 2088. |
Divide by 7, noting the Remainder, which shews the Number of the Day of the Week, accounting Sunday first. If 0 remain, the first of March falls on a Saturday. In this Example there remains 2, shewing the first of March to fall on Monday.
If it were required to perform this for years preceding our Saviour's Nativity, then take this Rule:
To the Year add its even fourth part, the Sum divide by 7, the Remainder shews the Day of the Week, accounting Sunday first, Saturday second, and so backward.
PROBLEM.
To find what day of the Month in the first Week of each Month, happens to be on the same day of the Week as the first of March.
Use the (plain) following Verses, in which the twelve Words relate to the twelve Months of the Year, accounting March the first:
    Ask endless Comfort, God enough bestows,
    From Divine Axioms Faith confirmed grows. ​The Alphabetical Number of the first Letter of the word, proper to the Month proposed, is the Answer.
Example.
If the Month were April, the word proper thereto is Endless, and E is the fifth Letter in the Alphabet. Wherefore conclude, That the first of March and fifth of April do for ever happen on the same day of the Week; which for the year 1669. will be on Monday.
PROBLEM.
To find on what day of the Week the first day of each Month happeneth.
Supposing the first of March known, it might be reckoned from the former Problem, but the following Verse, beginning with March, as the former, is more ready for the purpose:
    A dreadful Fire, Beholders daily Gaze,
    Chastized England. Ah cruel fatal Blaze.
In the Year 1669, the first of March is Monday; I would know on what day of the week the first of October happens. The word proper to the Month is England; then count Alphabetically to E, viz. A. Monday, B. Tuesday, C..Wednesday, D. Thursday, E. Friday, which is the day sought. Whence conclude, that the 1st, 8th, 15th, 22th, 29th days of October are all Fridays. Thence it is, easie to reckon, on what day of the Week any day of that Month happened; and so for all other Months.
PROBLEM.
To find on what Day of the Month the Sun enters into any Sign of the Zodiack.
For this, ex super abundanti, we give the following Verse:
    Charles brought Content, divers Effects ensue,
    Envy, Fear, Dolour, Danger, bids adieu.
Hear again the twelve Words relate to the twelve Months, March being the first.
​To the number of the Letter of the Alphabet the word begins with, add 7.
Example. Fear is the word for October, and F the sixth Letter: Wherefore the Sun enters into the 8th Sign, to wit, Scorpio, on the 13th of October.
An Account of some Books.
The Author of this Book is now the Historiographer and Library-keeper to the Emperour. He publish'd this Volume some few years ago at Hamburgh, the place of his Birth, (whence an Exemplar was but lately lent to the Publisher.) He was excited to this Work by the complaint made by the illustrious Lord Verulam, (Lib. 2. cap. 4. de Augm. Scientiarum) of the want of a compleat History of Learning, that might give a satisfactory Account of the Rise, Progress, Transmigrations, Interruptions, Declinations, and Restaurations of all kind of Learning, Sciences, Arts, and Inventions; together with the occasion of Inventions through all Arts; the method of teaching, and the manner of improving and advancing them: Adding the various Sects, and the most famous Controversies among the Learned; the Encouragements they received; the chief Writings they composed; their Schools, Academies, Societies, Colledges, Successions, Orders, and whatever belongs to the state of Learning.
This grand Desideratum our Author undertakes to supply the World with, and in order thereunto, hath given us the first Book of the Prodromus of this History, and with it the four first Chapters of the Second Book, together with an Appendix, containing a Summary of the chief Persons and Things he intends more fully and accurately to treat of in the remaining 32 Chapters, designed for the same second Book: To which, he subjoins two Tables of Universal Chronology, in the first whereof he exhibits the succession of all Ages from the Creation of the World to the beginning of the common Christian Account; in the other, a Continuation of them from the beginning of the said Account unto this present Age: In which Tables he gives a general Idea of the Connexion of all Ages, as they are computed in respect of the ​Vulgar Christian account, either by ascending to the Creation of the World, or by descending to our Age: He also for the sake of this Work acquaints the Reader, that he betook himself to the Explication and Castigation of the Bibliotheca Chronologica Classicorum Authorum Johannis Jacobi Frisii Tigurini; substituting, as he affirms, a true Calculation in the place of the false one; reducing the Authors, there enumerated, to the true time of their Age, distinguishing what is supposititious from genuine, and adding many things that were unhappily omitted. Which done, he saith, he proceeded from this Account of the Succession of the illustrious Writers, to the History of the Origin, Increase, Nature, and Constitution of all Professions, Sciences, and Arts, chusing the Eight Books of Polydore Virgil de rerum Inventioribus; and Diogenes Laertius, De Vitis, & Dogmatibus veteris Græciæ Philosophorum; as also, the Eight Books of Johannes Middendorpius De Celebribus Universi Orbis Academiis.
He excuseth himself for having made no further progress in this desirable Work, alledging the difficulty and trouble of the Undertaking, the unavoidable interruptions he hath met with, and the narrowness of a private Man's fortune to carry on so chargeable an Attempt, requiring a Royal encouragement and assistance.
This Author, a Friend to the Cartesian Philosophy, entertains the Curious in this Book with seven Exercitations, viz.
1. De Ratione Philosophandi: Where in the genuine Students of Natural Philosophy he first requires the study of Mathematicks, to accustom their Minds to a fixed Attention, and to strict Reasoning; and next directs them to study Nature it self, and to labour after a true History of Nature: recommending lastly and particularly the use of Chymistry, as an excellent key to open her Treasures, and the study of Mechanical Principles, as nearly allied to those of Nature.
​2. De Rerum Naturalium Initiis: Where he mentions the several Hypotheses and Principles of Philosophers, and approves of the Cartesian, esteeming, that none ever looked so like truth, as those; though he thinks them defective in this, that how well soever they shew the production of things out of Matter variously modified, yet they seem not to have sufficiently accounted for the efficient power thereof.
3. De Universitate: Where he seems to be in a Maze, and thinks, That the Structure of the Universe hath not been understood hitherto, nor will easily be hereafter.
4. De Sole: Which Lumuniary he is inclin'd to believe to be a kind of flaming Fire, appearing in a Telescope like a Caldron full of boyling Metal; Where also he discourses of the nature of Light, Heat, and Flame; and affirms Light (as other sensible Qualities) to be not in the Object but the Sentient; as Pain is not in the Sword, but in the Animal wounded by the Sword.
5. De Generatione Hominis: Where, distinguishing between Genitura and Semen, and making the former to be that substance, which either Sex furnishes to the Fœtus, and the latter, the Concrete of both Parents, He is of opinion, that that which he calls Genitura, consists of two things. Vid. a Crasse liquor, manifest to sense, and of a very subtil and refined substance, containing all the virtue of Generation, and lodged in the formes as its receptacle: Which having establish'd, he affirms, that grosser part of the Geniture not to be Blood elaborated, but a Juice, secreted from the Blood, and being strained through the Corpus varicosum or plexus pampiniformis (wherein the seminal Arteries are by innumerable Anastomoses so combined and interwoven with Veins, that very hardly any naked eye can discern a Vein from an Artery) it passeth into peculiar fit Vessels, and is of a colour like that of the White of an Egg. As to the Formation of the Fœtus, he esteems That, before the appearance of any Blood, or the framing of any Member, there are form'd all the Lineaments of the Animal to come, though indiscernibly; which he endeavours to make out very particularly, interweaving some Animadversions on Authors of differing sentiments, and mentioning several not unphilosophical Hints.
6. De Nutricatione: Here the Author observes some things in ​the Structure of the Stomach, which he thinks highly considerable for the understanding of the action and use of this Viscus, and hitherto not taken notice of by others that he knows. Then he teacheth, that time Food is not digested in the Stomach by Heat, nor by acid dissolving Juices only, but that many Causes concurring to that digestion, the Aliment is there fermented, both by the warmth of the Stomach it self, and of the neighbouring parts, but especially by the acrimonious steams that pass through the Gastrick and Splenick Arteries into the Stomach, which advances also its Concoction by its compressing and relaxing motions, and is assisted by an apt Liquor, bedewing, dissolving, and diluting the Meat, and so converting it into a Pulse or Cream-like substance. Next, he teacheth, that the Chyle passeth not through the milky Veins (so called by Asellius) to the Liver, nor all of it through the Channel of Pecquet to the Heart, but a great part of it through the common Veins of the Stomach and the Mesentery, to the Liver. Nor will he admit, that the Sanguification is performed in any one part of the Animal, as the peculiar Shop or Elaboratory of it, whether Liver, Heart, Spleen, &c. Nor that the parts are increased and nourished by the red part of the Blood, but that, as to the former action, it is done by the means of a Liquor, and by hot steams, giving the red colour to the Chyle, as Chymists use to change white juices into red, by the affusion of Oyl of Sulphur, or the like Liquors; that redness being much advanced by the motion and agitation of the blood in the Veins and Arteries. But as to the latter, vid. the Nutrition, it is performed by that whitish Juice, which is mixed with the Blood, and separated from it by the straining Glandules of the Body.
To these particulars he adds several not unconsiderable remarks touching the Gall, Spleen, Lymphatick Vessels, &c. Observing also, that the whole kind of Birds is destitute of milky Vessels; and occasionally taking notice, that Worms are bred in almost all the parts of Animal Bodies; of which he alledges very odd Observations and Histories.
7. De Vita: This he affirms to consist in the continued motion of the Blood, depending from that of the Heart; yet so, that this latter proceeds not from the heat of the Blood (as Des ​Cartes would have it) but the moist steams and expirations of the Heart.
As for Respiration, he thinks it a vain opinion, that thereby the heat of the Blood is temper'd and allay'd; but affirms, that it is therefore necessary, because that the Blood, which out of the right Ventricle of the Heart is propelled into the Lungs, in such Animals, as are furnish'd with them, cannot pals into the left, unless the Air, breathed in, do swell and distend the small branches of the Windpipe; it being from thence, that the ramifications of the Arterial Vein, through which the blood must pass, are compress'd, and the blood therein inclosed is protruded into the branches of the venal Artery: For the proof of which, he alledges divers Observations. Adding withall, that since Animals, whilst they are. in the Womb, respire not, there being peculiar ductus's by which the blood passeth into the Aorta, without passing through the Lungs, as it always doth in Animals destitute of Lungs; he doubts not, but that with art and care those Channels may be preserved unabolisht, and made to grow and to be perfected with the other parts of the Animal, so that grown men may be brought to live the life of Amphibious Creatures. Nor dot he think this very difficult, in regard, that if their mouths and noses were from their very infancy often stopt every day, and their breath so long intercepted, while the blood passeth through those Ductus's into the left Ventricle of the Heart and the great Artery, the said passages would' never be dried up: To confirm the possibility whereof, he alledges Examples of divers, who from their Childhood being given to swimming and diving and so to the holding of their breath, did thereby so preserve those Channels from being dried up, that upon occasion they could stay a great while under water, as Amphibiums use to do.
This Learned Man having proposed to himself to go through the. whole Body of Natural Philosophy, by the way of Essays, divides that System into three Parts; whereof
The First being General, is to treat of what is common to all ​Bodies, both Superiour and Inferiour; and is divided again into six Books, whereof the first considers the Universe in general; the second is to discourse of Place, Vacuum, and Time, things as general as the World; the third, of the material Principles of all Bodies; the fourth, of their efficient Cause; the fifth, of their natural Qualities; and the sixth, of Motion, Generation, and Corruption of Bodies inanimate and animate.
The second part is to examine the Celestial Bodies. The third shall treat of the Terrestrial, viz. the Elements, Meteors, Minerals, Plants, Brutes, Men.
Of this Work is now printed the first Book of the first Part, consisting of five Dissertations.
The first is about the preliminary Questions of Physiology. The second inquireth whether the Universe is compounded of many Worlds. The third is of the System of the World, its Magnitude, and Figure. The fourth examins, whether the World be animated? The fifth, whether it hath been or could be from Eternity? The sixth is concerning the End of the World.
Horum Prior, Syntheticus, agit de Genuinis Matheseos Principiis in genere; in specie autem de Veris Geometriæ Elementis hucusque nondum traditis.
Posterior, Analyticus, de Methodo Compositionis, atque Resolutionis fuse differit; & multa nova complectitur, quæ subtilissimam Analyseos Artem mirum in modum promovent.
Errata, forgot to be corrected sooner.
In № 28. Pag. 521. lin. 22, 23. r. She took dog (even before the wound was heal'd up) was with puppy. P. 525. l. 8. r. Answers that shall. ibid. l. 20. r. Mineral Queries. P. 532. l. 18 dele viz. P. 535. l. 2. r. impelled at the Nose. ibid. l. 15. r. Grand poisson.
In № 29. P. 541. l. 18. r. An intimation. P. 544. l. 5. r. from the Indexes. ibid. l. 22. dele and as. P. 545. l. 21. r. breath out. P. 548. l. 18. r. with wind or.
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, 1667.