A DISSERTATION UPON THE Beginning of the next CENTURY: AND THE Solution of the Problem; To Know Which of the two Years 1700 or 1701 is the first of the next Century?  
With some Considerations about the Observation of the Year of Jubilee.  
Translated out of French.  
LONDON, Printed, and are to be Sold by J. Nutt, near Stationers-Hall, MDCXCIX.   

A DISSERTATION Upon the Beginning of the Next CENTURY, etc.  
THE approach of the next Century has occasioned several Disputes upon the Question, Whether it will begin in the Year 1700, or 1701? Some are of Opinion, that 1700 still belongs to this present Century; and others affirm, that it will end with this present Year, 1699. Several Wagers have been laid about it, which are as yet undecided; both sides being very positive, either out of Obstinacy, or for want of a true Notion of the matter. Besides that, in these Cases, the desire of Winning, or the fear of Losing, often hinders us from seeing the Truth as we would do, were we not blinded by Prejudice or Interest. The main Reasons urged on both sides are these.  
Those who affirm that 1700 is the first Year of the next Century, Argue thus. A Year is never reckoned until it is ended, nor a hundred Years until they are completed. We never say that a Child is a Year old until the twelve Months from his Birth are actually accomplished. Neither did the World begin to reckon one Year until the expiration of the twelve Months from the Nativity of Jesus Christ, and consequently the first hundred Years were not reckoned so, till after the expiration of the said hundred Years. The same Rule stands good for all the succeeding Ages: And therefore, say they, we do conclude, that as as soon as 1700 will be reckoned, the 17th Century will be ended, and that the Year 1700 does entirely belong to the next Century; at the end of which, we will begin to reckon 1, or 1701, which will denote one Year already elapsed.  
The others, on the contrary, say, That it was not necessary to tarry for the conclusion of the first Year of the Epact to reckon one, the Unite having been applied from the beginning of the Year to the end, as it appears by custom: For Instance, do we not reckon 1699, from the Month of January unto the Month of December? Consequently 1699 will not be ended until we cease to reckon it. So likewise the Month of January of the Year 1700, will only be the Introduction of the last Year of this Century, which will end exactly when we cease to reckon 1700, and therefore the next Century will only begin when we reckon 1701.  
Some Persons fancy they decide the Question, in saying, That the first eight Days from the Nativity of Jesus Christ to his Circumcision, have passed for a Year, and that one was reckoned from the first of January, on which Day our Saviour was Circumcised. But, in my Opinion, none of them have stated the Question right.  

The Solution of the Problem; to how wh●ch of the Years 1700, or 1701, is the first of the next Century?  
Before we resolve this Question, it will be fit to Note,  
First, That a Number is only to be considered in relation to the Sum of the Unites which it contains, and then we use these Words, Two, Three, Four, etc. which denote that the Number is completed, and that Number is called the Cardinal Number.  
Secondly, When we consider a Number as expressing the Quotus of several Units, we use one of these Words, First, Second, Third, Fourth, etc. which barely express the order of things, and we call that Number, the Ordinal Number.  
EXAMPLE.  
Be the Line A, B. which represents four Spaces of time, or of Extent. In Order to express the Sum of all the Spaces from A to E, we use the Cardinal Number. Three or 3. But if we have only a mind to know which Quotus of these Spaces is the Line D E we use the Ordinal Number, Third, or 3d. and all the Points from D to E belong to the 3d. Space.  
Thirdly, You must also Note, that the Cardinal Number is used in answer to the Question, how many? or how much time? in Latin Quot? or Quandiu? For instance, if any one should ask how many Foot a Lineal Fathom does contain? It would be answered, Six. How much time does the Sun employ in surrounding the Circle of the Equator? 24 Hours. But the Ordinal Number is used in answering the Question, When, (Quando?)  
Example, When, or what time was St. John inspired by God, to come out of the Desert to Preach the Baptism of Repentance? The answer is, in the 15th Year of the Reign of Tiberius, Anno quinto decimo Imperii Tiberii Caesaris. The Ordinal Number is also used in answer to the Question, what, when, or what time, or on what, Quotus? For instance, on what Day of the Month of December was Jesus Christ Born? on the 25th, etc.  
Fourthly, It is true that the Cardinal Number can only be applied to the Spaces of time, after they are expired; but the Ordinal Number may be always applied to all manner of Spaces from the Beginning to the End. For instance, we cannot say that a Man is 30 Years Old until they are completed: But we may say that he is in his 30th Year, when the 30th is actually running on.  

The SOLUTION.  
This being premised, I say the next Century will not begin until 1701; and that the whole Year, from 1700 to 1701 still belongs to this Century. The reason of it is, that the Ordinal Number is used to express the time in which an Action was performed. For instance, we say the City and Fort of Barselona were Surrender'd to his Majesty on the 10th of August, 1697. In Latin, Die decima Augusti anno Millesimo Sexcentesimo Nonagesimo Septimo. For when we ask in what Year any thing was Transacted, we do not look for the precise Number of the Years that are expired, from the beginning of the Christian Era, to the time of the said Transaction; but we look for the Quotus of those Years in which the said case was transacted, and we impute to that Year whatever was transacted in the interval of the 12 Months that compose the said Year. So that when we say that we are in the Year 1699, it does not imply that the Number of 1699 Years is completed from the beginning of the Christian Era to this time, but that the, 1699th Year is actually running on: and whatever may be Transacted from this Moment to the very last of the Month of December next coming, will belong to this Year 1699. For this Reason, when ever we shall begin to reckon 1700, we will only be at the beginning of the 1700th Year. Now the 1700th Year does still belong to the present Century, by reason that a Century containing a Hundred Years inclusively, it cannot end before the Conclusion of the 100th Year, and Consequently 1700 is the last Year of the present Century, and 1701 the first of the next.  
Finally, It is not material in order to resolve the Question, to know precisely in what Year Jesus Christ came into the World, seeing that this present 1699th Year having 9 for its Golden Number, the first of the Years of the Christian Era, according to which we reckon, had 2 for its Golden Number, which answered the 46th Julian Year, whether it were that the said first Year was that which was consecrated by the Incarnation and Nativity of the Son of God, or whether it were the first of those that followed that Blessed Nativity: For though Chronologers do not agree about the time in which Jesus Christ came into the World, they agree nevertheless, that the first Year of the Christian Era, according to which we usually reckon, had 2 for its Golden Number, and answered the 46th Julian Year.   

OBJECTION.  
The Ordinal Number is used to reckon the order of the Hours of the Day; and yet we never reckon the first Hour until it is expired, etc. Years are like Days in this case, and therefore when we reckon the 100th Year, it is already ended, etc.  
To this, I answer, That there is a great disparity in the case, and that when Men first undertook to reckon the Hours of the Day, they observed, in the first place, that the Sun daily traced a Circle about the Earth, from which they inferred, that dividing the said Circle into 24 equal parts, and the time which the Sun employs in surrounding the said Circle also into 24 parts, they would have 24 Times answering the 24 Spaces of the circumference of the Diurnal Circle. In the next place, to fix those Spaces, and to make them sensible, by the help of some Machine; the nature of the movement of the Sun did direct them to describe a Circle to represent the diurnal Circle of the Sun, which they divided into 24 equal parts, by 24 Lines drawn from the Centre to the Circumference; and determining one of those Lines to represent the middle of the Day, which they called Noon, they accustomed themselves to reckon the Hours upon different Lines. So that having placed this Circle, thus prepared with a perpendicular side, into the Centre in the Plan of the Equator, in such a manner, that one of those Lines was in the Plan of the Meredian Circle, they found a very plain and very natural Machine to determine the different Times of the Day. This they called an Equinoxial, or Astronomical Dyal, and the Moment on which the shadow of the Sun was upon the Meridian Line, they called the Hour of Noon, and so on, reckoning the Hours upon the different Lines. In so much that those Hours are not so much Spaces of Time, as the Moment's that divide those Spaces. For the Hour of Noon (for Instance) is nothing but the Moment which divides the Day into two equal parts. The other Hours are answerable to this, and may be called. Lineal Hours, as Isaiah has it, Chap. 38. v. 8. where he says, that the shadow of the Sun turned back ten Lines upon the Dyal of Achaz, that is ten Hours, Et reversus est Sol decem Lineis per gradus quos descenderat.  
But when they had a mind 〈◊〉 six their Actions on more considerable Spaces of Time, they reckoned quite otherwise. For Instance, the Jews, besides the common Hours which they traced upon their Dial's by Lines, of which 12 served for the Day, and the rest for the Night, did divide the Day into four parts, which they called Stationary Hours, and the Night likewise into four parts, which they called Watches. The first Stationary Hour began with the rising of the Sun, and did end at the third Lineal Hour of the Day, and whatever was transacted in that Interval of time, was said to be done in the first Hour. The second Stationary Hour began at the third Line, and did end at the sixth, which did answer to Noon. And the third Stationary Hour began at the sixth Line and did end at the 9th. So that when St. John says, that Jesus Christ was Condemned by Pilate about the 6th Hour, he reckoned by the Lineal Hours, according to the first manner, that is, that it was about Noon: And when St. Mark says, that he was Crucified at the third Hour, he reckoned by the Stationary Hours, that is, at the beginning of the third Space, from the sixth Line to the ninth.  
But the order of Years is not calculated by the Moment's that divide them the one from the other; but by very considerable spaces of time to which Men fix their Actions. And as all the Moment's that slide away from the beginning of the first Month of a Year do belong to that first Month; so likewise all the Moment's that slide away, or run on from the beginning of a Year unto the end thereof, do belong to that Year, and whatever is transacted in one of those Moment's, is ever fixed to that Year, whether done towards the beginning, middle, or end. This Method is practised by all Chronological Historians, who fix to the first Year of a Century, whatever remarkable Events have fallen out from the first Moment of that Century, until the twelve Months that compose that first Year are absolutely completed; and in the same manner to the first Century, what ever was done in the whole space of the hundred Years of which it is composed. And they follow the same Method, in fixing to the first Year of a King's Reign what ever has been transacted from the Moment of his Being Crowned or Proclaimed King, until the space of the first twelve Months is absolutely accomplished.  
Those who are desirous to know the time on which the holy Year, or the Year of the universal Jubilee is to begin, are to observe that Boniface the 8th did institute the Jubilee, in imitation of the Israelites, in the Year 1300. Ordaining at the same time that the Indulgences of the Jubilee should be renewed every hundred Year; for which Reason every 100th Year has been termed a holy Year, ever since the said Institution. After him Clement the VIth decreed that the said Indulgences should be renewed every fifty Years; thus making the 100th, and 50th Years Jubilary. Lastly, Xistus the iv fixed it on the 25th Year; so that we have an universal Jubilee every 25 Years.     

A CRITICAL LETTER, From M— Bachelor in Divinity, to the Author of the Dissertation upon the beginning of the next Century. With an Answer to the said Letter.  
SIR  
I Was not deceived in the hopes I conceived, at the sight of the Title of the Dissertation upon the next Century, of meeting something therein both surprising and new. I must confess, that it never entered into my thoughts, that any Man could imagine, that the Year 1700 should be the first of the next Century; and yet I find that you do not only suppose, but also endeavour to refute that Error by solid Reasons, and to establish your Opinion, which is every Bodies. But as it often happens, that in endeavouring to defend Truth, we expose it by a weak defence, preferring weak Proofs before solid convincing Reasons, by which means we lose sight of it, or at most retain but a slight glance thereof, as it were through a Mist: or finally, in combating the Enemies of it, with Arguments that produce Effects directly opposite to those they should naturally produce. I fear we are fallen into this misfortune in the Problem, viz. Which of the two Years 1700, or 1701, gins the next Century. You promise to destroy the Opinion of those who say, that 1700 gins the next Century, by Reasons that are to prove, that it will only begin with the Year 1701. You are not ignorant that it is impossible to destroy an Opinion by the same Argument that is used to prove it. Let us examine in few words, whether this be true? Those who affirm, say you, that 1700 is the first Year of the next Century, argue thus. A Year is only reckoned after it is ended, and a hundred Years after they are past and completed. We never say, that a Child is a Year old until the 12 Months from his Birth are expired. Neither did the World bein to reckon one Year until the expiration of the twelve Months from the Nativity of Jesus Christ; and consequently the first hundred Years were not reckoned so, till after the expiration of the said hundred Years: And therefore, say they, we do conclude, that as soon as the World will begin to reckon 1700, the 17th Century will be ended. This is the first Argument you put into the Mouth of those you fancy you are combating with. If they are persons of Merit, you injure them in making them argue so ill: If they are Fools, you are to blame to lose your time in refuting their Follies: Such Fooleries are beneath a Man of your Character. I am surprised at your not having shown the Weakness of their Argument, you would have found that it concludes demonstrativety against them, in this manner. If Men only begin to reckon a hundred Years after they are expired, it follows of necessity, that when we begin to reckon 1700, the 17th Century will be begun; and if the 17th Century does begin at that time, it cannot be ended. To deal plainly with you, I am afraid you have only raised a Phantasm to have the pleasure of encountering it, being persuaded that there never was any Man so destitute of Sense, as to imagine that the 17th Century is the beginning of the 18th. For my part, I am not liable to that censure, since you give me cause to remove the difficulties, which your Dissertation might raise in some Men's minds concerning the next Century. There is no need of knowing what the Christian Era is, nor when the World first began to reckon the Years after the Nativity of Jesus Christ. It is sufficient to know, that Men commonly reckon from the Nativity of Jesus Christ to this Day 1699 Years begun. And tho' it is undeniable, that Dennis the Little, who made the Calendar to reckon by the Years of Jesus Christ instead of those of the Consuls, has placed the Nativity of Christ four Years later than he should have done; the Question is still the same. This being premised, I say that by the Epact of the said Dennis, which we follow, the Year 1700 is the last of the Century, and 1701 the beginning of the next. I do demonstrate it thus, 1700 Years completed make up 17 entire Centuries: Now in 17 entire Centuries there can be nothing of the 18th. Consequently, the Year 1700 ended, is not the beginning of the next Century. The number of completed Years (for instance) is like the number of Sheep, of Oxen, of Pounds, etc. Now as it would be ridiculous to say that a hundred Sheep, Oxen, or Pounds, etc. are the beginning of a second hundred, so it would be absurd to think that 17 complete Centuries can have any thing of the 18th in them; and therefore 1700 cannot be the beginning of 1701. Unites are the beginnings of all Numbers whatever, from whence it follows that the first Year after 1700 completed gins the next Century. Moreover if 1700 was the beginning of the next Century, the Year 1699 would end the 17th; which would be as ridiculous, as to say that 99 Pounds are a hundred. This, Sir, in my Opinion, was the way to silence those who are foolish enough to imagine that 1700 can be the beginning of the 18th Century: for I look upon all your terms of Sums, Units, Cardinal and Ordinal Numbers, your Questions by how many? or how much time? in what Place, or at what time? to be much fit for the Schools, than to determine such ridiculous Questions as these. We should contemn them, according to the direction of the Holy Ghost, nor answer a Fool for fear of catching his disease. Ne respondeas Stulto juxta stultitiam suam, ne efficiaris ei similes. I am sensible, and so are you, that the number of Fools is very considerable: Let us never give ear to their discourses, which have no solidity, and can never edify nor satisfy the Mind. Doctrina Stultorum fatuitas. It is the best way not to increase their Number. I am, etc.  
An Answer to the Letter of M—  
SIR  
JUST now I received an Anonimous Letter, written with your own Hand, in which you are pleased to censure some Passages of the Dissertation upon the Beginning of the next Century. You accuse me of being guilty of a Paralogism in the Argument I put into the Mouth of those who affirm that 1700 is the beginning of the next Century. Had you minded the matter attentively, you would have found, that since they pretend that we ought not to begin to reckon 100 until the 100 Years are completed; it was absolutely necessary to draw the Consequence I have drawn from thence, which is, that according to that Argument, as soon as we begin to reckon 1700, 1700 Years will be completed, which is as much as to say, that the 17th Century will be ended. You say, on the contrary, that I should have said, the 17th will be begun. The truth is, it will be so far begun, that it will want but one Year of being ended. I find that the word begun has dazzled your Eyes: and yet, methinks, that word should not have startled you so much, seeing that according to your way of arguing about Oxen and Sheep, Men never reckon 100 Bullocks until they have them, and as soon as they begin to reckon 100, the number of the said 100 Bullocks is completed. For that very reason it was necessary, in order to discover the knot of the Question, to how the difference there is between two ways of reckoning the Spaces of Time.  
You add, that I am to blame in losing my time in refuting such Fooleries. You might have censured me with more justice, for not having taken more care, after having made them argue thus, to show the defect of their Argument: For after having nakedly exposed two different Arguments upon one and the same Subject; I barely made some Remarks upon the nature of the Question, showing two different manners of reckoning Years, the one by the Cardinal, and the other by the Ordinal Number. You say moreover, That such Trifles are below a Man of my Character. This Reproach is very different from other Censures that have been made upon the said Dissertation. Be pleased to mind them a little.  
Several Gentlemen, that are reputed Men of Sense, have found fault with my boldness in deciding a Question which the Court of Rome has not determined, and which several Doctors in Divinity have looked upon to be so nice and full of difficulties, that they would not presume to affirm any thing, pro or con, in the matter. To this I answered, That if the Court of Rome and the said Doctors in Divinity have said nothing about it, it was because they did not foresee that such a Question should ever have been proposed, or did not think that it had any relation to Divinity; it belonging purely to human Sciences.  
Others have found fault with my using Mathematical Arguments to prove my Opinion, without so much as quoting the least Authorities for it. To these I could answer, That the knowledge of Times properly belongs to that Science; and that the reason of my not giving Authorities was, that I thought them needless, to confirm things that are evidently demonstrated by the bare light of Reason. Nevertheless, since they desire Authorities, I refer them to a very authentic one in the Dictionary of the French Academy, which says, speaking of the Year 1601, That it was the first of the Century: as also to the Astronomical Tables of M. de la Hire, of the Royal Academy of Sciences, in which they will not only find the Authority of a Man of his Learning; but also Calculations that will discover the truth of the matter to them. I also give them the Opinion of Monsieur Varignon, a Member of the same Royal Academy of Sciences, who is so clear sighted, and so methodical, that he cannot possibly fall into an Error out of prejudice. I believe farther, that I may presume to affirm, that the whole Body of that famous Academy is of my Opinion.  
Others have objected, that Pope Gregory the XIII. has decided the contrary, in ordaining that during the space of 400 Years, 3 Bissextile should be omitted in the 3 first Years of the hundreds; for, say they, the Calculations that are made to find the Dominical Letters, and the Epacts, are made for the Years of this Century to 1700 exclusively: Therefore say they again 1700 is excluded out of this Century, and consequently belongs to the next. To this I answer, that the Consequence is not good, the omission of the Bissextiles in the 100th Years being Arbitrary, in so much that it might as well have been made in the 96th Year; and then the Calculations for the Dominical Letters and the Epacts would have been made for the Years until the 96th Year of the Century exclusively, and yet it would have been ridiculous to say that the Year 1696 did belong to the next Century, on the account of that exclusion.  
Others say, that I have not said enough to convince the Obstinate. Had I expected the Objection, I should have added what follows in the Solution of the Problem, P. 7. of the Dissertation. Note that this Expression Die 10 Augusti anni 1697, is very different from this, Die 10 Augusti post annum 1697; for the first signifies that 1697 is the running Year, and the other shows that it is past. All Historians reckon according to this first way, placing every Event in the running Year; and when they place it after the Year is completed, they express themselves the other way.  
Moreover, the Quotus Years of the Centuries are reckoned like the Quotus Days of the Months. When a Deed is dated at a Notaries on the 21st of March, it does not signify, that the said 21st Day is past or completed, but that it is actually running on: So when a Deed is dated of a certain Year; for Instance, the 15th of March 1699, it is understood, to be the 15th running Day of the 1699th running Year, and not the running Day after the 15th compleatted, or the running Year after the 1699th Year completed: For it would be ridiculous to date a Deed in the present Year 1699, supposing the said 1699 to be actually revolved and completed; in which case one should be obliged to add the time Elapsed since the Completion of the said 1699. which is never done.  
In order to be evidently convinced that the Civil Year, for instance, 1699, is the 1699th running Year of the Christian Era, it will be sufficient to observe the Calculation of the Astronomers, who make use of revolved completed spaces of Time: When they go about to find the true place of the Sun in the Ecliptic, they first of all reduce the Civil Time into an Astronomical Time, taking whatever is completed, solid, and revolved in the running time. For instance, having a mind to find the true place of the Sun in the Ecliptic, on the 25th of January in the Year 1699, at 4 in the Morning, I must take in order thereunto the whole completed Time, that is, 1698 completed, 23 Days, 16 Hours, after which the remainder of the Calculation is to be made, according to Astronomical Rules. In the like manner this Civil Time, the 4th of January at Noon of the Year 1700, being reduced to an Astronomical Time, it will make 1699 completed, and 3 Days into the Month of January, and consequently, when we do begin to reckon 1700, there will only be 1699 Years revolved and completed. Therefore the Year from 1700 to 1701, is the last of this Century.  
But after this Digression, let us return to your Letter. You say that it is not necessary to know what the Christian Era is, nor when Years were first reckoned. Which way then will you know what Year you are in, if you do not know that the first Year of the Christian Era had 2 for its Golden Number, and B for the Dominical Letter, and that it is of necessity affixed to the 46th Julian Year. One would be apt to think by your words, that you make a difference between the Christian and the common Era, and yet, I must tell you by the by, that it is one and the same thing. You add, That it is sufficient to know that it is usual to reckon from the Nativity of Jesus Christ to this present time 1699 Years begun. You would have spoken more justly, had you said from the Moment in which Dennis the Little has supposed the Nativity of Jesus Christ.  
You pretend, in the first place, to give a convincing Demonstration, that 1701 is the first of the Century, and thereby to close the Mouths of those, who, in your Opinion, are so destitute of Sense as to say, that 1700 is not the last of this Century. You demonstrate it thus, 1700 completed Years make up 17 completed Centuries; Ergo, the Year 1700 ended, is not the beginning of the next Century In my Opinion, you do not close the Mouths of such as might retort your Argument upon you, saying, Therefore the Year 1700 being ended, the first Year of the next Century will begin: For their difficulty only consists in saying, that the Years are only reckoned such at the end thereof. Wherefore, say they, as soon as 1700 will be reckoned, 1700 will be completed; and when 1701 will be reckoned, the Year 1701 will be completed.  
Let us now, I beseech you, return to your Oxen and Sheep. The Number of Years, say you, is (for Instance) like the number of Sheep, of Oxen, of Pounds, etc. It cannot be said justly, that 100 of Sheep, Oxen, Pounds, etc. are the beginning of a second 100, that is true. Therefore 17 completed Centuries have nothing of the 18. This is true still. But if 17 Centuries are completed as soon as we begin to reckon 1700, the whole Year from the time we begin to reckon 1700, until we begin to say 1701, will be the first of the 18th Century. Just as when you begin to reckon 100 Oxen, the next Ox after you have begun to reckon 100, until you begin to reckon 101, is the first of the second 100 Therefore if you will avoid falling into this Inconveniency, you must reckon the Spaces of Time otherwise than you reckon Oxen and Sheep, and observe that the Cardinal Number is only applied at the end of those Spaces; but that the Ordinal Number may always be applied from the beginning of every Space unto the end: As we say that a Man is 30 Years old when they are completed; but that he is in his 30th Year, when the 30th Year is begun. You add, All these Terms are fit for the Schools, than to resolve such ridiculous Questions. As if it were unlawful, out of the Schools, to mend Latin and French Expressions, to discover the nature of the Ideas they are to excite. 'Tis in that place you inform me, that the Holy Ghost inspires you to call all those Fools and Idiots who make Questions of this nature. I am not offended at those Words taken out of the Proverbs of Solomon, which are very edifying in the holy Bible; but ill applied by you: For if you mean them to me, your Neighbour will not be much edified at your treating a Minister of J. C. thus; and one who has always been your Friend. If you apply 'em to others who have proposed the same Question, you are uncharitable; seeing that Persons of great Wisdom, whom you ought to reverence, have made 'em before me. And among the rest, a very worthy Doctor in Divinity, who proposed the same Question in a Journal to the Learned; and affirms, that 1700 is the first Year of the next Century. I am,  
SIR, Your most affectionate Servant, De L'Aisement, Academical Professor.  
FINIS.