ΣΤΙΓΜΑΙ {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} OR marks Of the 

Absurd Geometry  
Rural Language  
Scottish church-politics  
And barbarisms   OF JOHN WALLIS Professor of Geometry and Doctor of Divinity. By THOMAS HOBBES of MALMESBURY.  
LONDON, Printed for Andrew crock, at the Green Dragon in Paul's churchyard, 1657.   

To the Right honourable Henry Lord Pierrepont Viscount Newarke, Earl of Kingston, and Marquis of Dorchester.  
My most Noble Lord,  
I Did not intend to trouble your Lordship twice with this Contention between me and Doctor Wallis. But your Lordship sees how I am constrained to it; which (whatsoever reply the Doctor makes) I shall be constrained to no more. That which I have now said of his Geometry, Manners, Divinity, and G●ammar all together is not much, though enough. As for that which I here have written concerning his Geometry, which you will look for first, is so clear, that not only your Lordship and such as have proceeded far in that Sicence, but also any man else that doth but know how to add and subtract Proportions (which is taught at the twentieth third Proposition of ●the sixth of Euclid) may see the Doctor is in the wrong. That which I say of his ill Language and politics is yet shorter. The rest (which concerneth Grammar) is almost all another man's, but so full of Learning of that kind, as no man that taketh delight in knowing the proprieties of the Greek and Latin Tongues, will think his time ill bestowed in the reading it. I give the Doctor no more ill words; but am returned from his manners to my own. Your Lordship may perhaps say my compliment in my Tittle page is somewhat course; And 'tis true. But, my Lord, it is since the writing of the Title page, that I am returned from the doctor's manners to my own; which are such as I hope you will not be ashamed to own me, my Lord, for one of  
Your lordship's most humble and obedient Servants Thomas Hobbes.   

TO DOCTOR WALLIS In answer to his school DISCIPLINE.  
SIR,  
WHen ●nprovok'd you addressed unto me in your Elenchus your ha●sh compliment with great security, wantonly to show your wit, I confess you made me angry, and willing to put you into a better way of considering your own forces, and to move you a little as you had ●moved me; which I perceive my Lessons to you have in some measure done; But here you shall see how easily I can bear your reproaches, now they proceed from anger, and how calmly I can argue with you about your Geometry, and other parts of Learning.  
I shall in the first part confer with you about your Arit●metica Infinitorum, and afterwards compare our manner of Elocution; then your politics; and last of all your Grammar and critics. Your spiral line is condemned by him whose Authority you use to prove me a Plagiary, (that is, a man that st●aleth other men's inventions, and arrogates them to himself) whether it be Roberval or not that w●it that paper, I am not certain. But I think I shall be shortly, but whosoever it be, his authority will serve no less to show that your Doctrine of the sp●rall line from the fi●th to the eighteenth proposition of your Arithmetica Infinitorum, is all false; and that the principal fault therein (if all faults be not principal in Geometry, when they proceed from ignorance of the Science) is the same that I objected to you in my Lessons. And for the Author of that paper, when I am certain who it is, it will be then time enough to vindicate myself concerning that name of Plagiary; And whereas he challenges the invention of your Method delivered in your Arithmetica Infinitorum to have been his before it was yours, I shall (I think) by and by say that which shall make him a shamed to own it; and those that writ those encomiastic Epistles to you ashamed of the Honour they meant to you: I pass therefore to the nineteenth proposition, which in L●tine is this.  

Your Geometry.  
Si proponatur series Quantitatum in duplicata ratione Arithmetice. proportionalium (sive juxta seriem numerorum Quadraticorum) continu● crescentium, à puncto vel o inchoa●arum, (puta ut 0. 1. 4. 9 16. &c.) propositum sit, inquirere quam habeat illa rat●onem ad seriem totid●m maximae aequalium.  
Fiat Investigatio per modum inductioni● ut (in prop. 1.)  
Eritque 

 
 
& sic dein●eps.    
Ratio proveniens est ubique major quam subtripla seu ⅓▪; Excessus autem perpetuo decresci● prout▪ numerus terminorum augetur (puta 1/6 1/12 1/18 1/30 &c.) aucto nimirum fractionis denominatore sive consequente rationis in singulis locis numero senario (ut pa●et) ut ●it rationis provenientis excessus supra subtriplam, Ea quam habet unitas ad sextuplum numeri terminorum posto; adeoque.   
That is, if there be propounded a row of quantities in duplicate proportion of the quantities Arithmetically proportional (or proceeding in the order of the square numbers) continually increasing; and beginning at a point or 0; let it be propounded to find what proportion the row hath; to as many quantities equal to the greatest;  
Let it be sought by induction (as in the first proposition)  
The proportion arising is everywhere greater than subtriple, or ⅓, And the excess perpetually decreaseth as the number of terms is augmented, as here, 1/6 1/12 1/18 1/24 1/30 &c. the denominator of the fraction being in every place augmented by the number six (as is manifest) so that the excess of the rising proportion above subtriple is the same which unity hath to six times the number of terms after 0; and so.  
Sir, In these your Characters I understand by the cross+ that the quantities on each side of it are to be added together and make one Aggregate; and I understand by the two parallel lines= that the quantities between which they are placed are one to another equal; This is your meaning, or you should have told us what you meant else: I understand also, that in the first row 0+ 1 is equal to 1, and 1+ 1 equal to 2; And that in the second row 0+ 1+ 4 is equal to 5; and 4+ 4+ 4 equal to 12; But (which you are too apt to grant) I understand your symbols no further; but must confer with yourself about the rest.  
And first I ask you (because fractions are commonly written in that manner) whether in the uppermost row (which is ) 0/1 be a fraction, 1/1 be a fraction, ½ be a fraction, that is to say, a part of an unite, and if you will (for the cyphers sake) whether 0/1, be an infinitely little part of 1; and whether 1/1, or 1 divided by 1 signify an unity; if that be your meaning, than the fractio● 0/1 added to the fraction 1/1 is equal to the fraction ½: But the fraction 0/1 is equal to 0; therefore the fraction 0/1+ 1/1 is equal to the fraction 1/1; and 1/1 equal to ½ which you will▪ confess to be an absurd conclusion, and cannot own that meaning.  
I ask you therefore again if by 0/1 you mean the proportion of 0 to 1; and consequently by 1/1 the proportion of 1 to 1, and by ½ the proportion of 1 to 2: if so, than it will follow, that if the proportions of 0 to 1 and of 1 to 1 ●e compounded by addition, the proportion arising will be the proportion of 1 to 2. But the proportion of 0 to 1 is infinitely little, that is, none. Therefore the proportion arising by composition will be that of 1, to 1, and equal (because of the symbol=) to the proportion of 1 to 2 and so 1= 2: This also is so absurd that I dare say that you will not own it.  
There may be another meaning yet: perhaps you mean that the uppermost quantity 0+ 1 is equal to the uppermost q●antity 1; and the lowermost quantity 1+ 1 equal to the lowermost quantity 2: Which is true: but how then in this equation ½= ⅓+ ⅙ is the uppermost quantity 1 equal to the uppermost quantity 1+ 1; or the lower most quantity 〈◊〉 equal to the lowermost quantity 3+ 6? Therefore neither can this be your meaning; unless you make your symbols more significant, you must not blame me for want of understanding them.  
Let us now try what better success we s●all have where the places are three, as here : If your Symbols be fractions, the compound of them by addition is 5/4; For 0, ¼ and 4/4 make 5/4; and consequently (because of the symbol=) 5/4 equal to 5/12 which is not to be allowed, and therefore that was not your meaning. If you meant that the proportions of 0 to 4 & of 1 to 4 & of 4 to 4 compounded is equal to the proportion of 5. to 12. you will fall again into no less an inconvenience. For the proportion arising out of that Composition will be the proportion of 1. to 4. For the proportion of 0. to 4. is infinitely little. Then to compound the other two, set them in this order 1. 4. 4. and you have a proportion compounded of 1. to 4. and of 4. to 4. namely, the proportion of the first to the last, which is of 1. to 4. which must be equal (by this your meaning) to the proportion of 5. to 12. and consequently as 5. to 12. so is 1. to 4. which you must not own. Lastly, if you mean that the uppermost quantities to the uppermost, and the lowermost to the lowermost in the first Equation are equal, 'tis granted, but then again in the second Equation it is false. It concerns your fame in the mathematics to look about how to justify these Equations which are the premises to your conclusion following, namely, that the proportion arising is everywhere greater than subtriple, or a third; and that the excess (that is, the excess above subtriple) perpetually decreaseth as the number of terms is augmented, as here 1/6 1/12 1/18 1/24 1/30 &c. which I will show you plainly is false.  
But first I wonder why you were so angry with me for saying you made proportion to consist in the Quotient, as to tell me it was abominably false, and to justify it, cite your own words Penes Quotientem, do not you say here, the proportion is everywhere greater than subtriple, or ⅓? And is not ⅓ the quotient of 1. divided by 3? You cannot say in this place that Penes is understood; for if it were expressed you would ●ot be able to proceed.  
But I return to your conclusion, that the ex●ess of the proportion of the increasing quantities above the third part of so many t●mes the greatest, decreaseth as 1/6 1/12 1/18 1/24 1/30 &c. For by this account in this row where the quantity above exceeds the third part of the quantities below by ⅓' you make ⅓ equal to ⅙' which you do not mean. It may be said your meaning is that the proportion of 〈◊〉. to the subtriple of 2. which is ⅔ exceedeth what? I cannot imagine what, nor proceed further where the ter●s be but two. Let us therefore take the second row, that is, The sum above is 5. the sum below is 12. the third part whereof is 4. if you mean, that the proportion of 5. to 4. exceeds the proportion of 4▪ to 12. (which is subtriple) by 1/12' you are out again. For 5. exceeds 4. by unity, which is 12/12 I do not think you will own such an equation as . Therefore I believe you mean (and your next proposition assures me of it) that the proportion of 5. to 4. exceeds subtriple proportion by the proportion of 1. to 12. if you do so, you are yet deceived.  
For if the proportion of 5. to 4. exceeds subtriple proportion by the proportion of 1. to 12. then subtriple proportion, that is, of 4. to 12. added to the proportion of 1. to 12. must make the proportion of 5. to 4. But if you look on these quantities 4. 12. 144. you will ●ee and must not dissemble that the proportion of 4. to 12. is subtriple, and the proportion of 12. to 144. is the same with that of 1▪ to 12. Therefore by your assertion it must be as 5. to 4. so 4. to 144. which you must not own.  
And yet this is manifestly your meaning as appeareth in th●se words; u● 〈◊〉 rationis pr●venien●is excessus supra subtriplam ●a quam ●abet unitas ad sextuplum numeri terminorum post 0, adeoque, which cannot be rendered in English, nor need to be. For you express yourself in the 20th. pr●position very clearly; I noted it only that you may be more merciful hereafter to the stumblings of a hasty Pen. For excessus ea quam does not well, nor is to be well excused by subauditur ratio. Your 20th. proposition is this▪  
Siprop●natur serie● quantitatum in duplicata ratione Arithmeticè proportionalium (sive jux●a seriem Numerorum Quadraticorum) continuè crescentium, a puncto vel O in choatarum, ratio quam habet illa ad seriem to●idem maximae aequalium subtriplam superabit; eritque excessus ea ratio qua● habet unitas ad sex●uplum n●meri terminorum post 0, sive quam habet radix Quadraticae termini primi post 0 ad sextuplum radicis Quadraticae termini maximi.  
That is, if there be propounded a row of quantities in duplicate proportion of Arithmetically-proportionals (or according to the row of square numbers) continually increasing, and beginnin gwith a point or 0. The proportion of that row to a row of so many equals to the greatest, shall be greater than subtriple proportion, and the excess s●all be that proportion which unity hath to the sextuple of the number of terms after 0, or the same which the square roo● of the first number after 0, hath to the sextuple of the square root of the greatest.  
For proof whereof you have no more here, then pa●e● ex praeceden●●bus; and no more before but adeoque. You do not we●l to pass over such curious propositions so slightly; none of the ancients did so; nor, that I remember, any man before yourself. The proposition is false, as you shall presently see.  
Take for example any one of your rows; as . By this proportion of yours 1+ 4 which makes 5 is to 12 in more than subtriple proportion; by the proportion of 1 to the sextuple of 2 which is 12. Put in order these three quantities 5. 4. 12. And you must see that the proportion of 5 to 12 is greater than the proportion of 4 to 12, that is, subtriple proportion, by the proprtion of 5 to 4. But by your account the proportion of 5 to 4 is greater than that of 4 to 12 by the proportion of 1 to 12. Therefore as 5 to 4 so is 1 to 1●. which is a very strange Parodox.  
After this you bring in this Consectary.  
Cum autem cresente numero terminorum excessus ille supra rationem sub●riplam conninuò minuatur, ut tandem quovis assignabili minor eva●●t (un p●tet) si in in●ini●um producatur prorsus evaniturus est. Adeoque.  
That is, seeing as the number of terms increaseth, that excess above subtriple proportion continually decre●seth, so as at length it be●omes less than any assignable (as is manifes●) if it be produced infinitely, it shall utterly vanish, and so. And so what?  
Sir, This consequence of yours is false. For two quantities being given, and the excess of the greater above the less, that excess may continually be decreased, and ye● never quite vanish. Suppose any two unequal quantities differing by more than an unite, as 3 and 6, the excess 3, let three be diminished, fi●st by an unite, and the excess will be 2 and the quantities will be 3 and 5. 5 is greater than 4; the excess 1. Again, let 1 be diminished and made ½. the excess ½ and the quantities 3 and 4½. 4½ is yet greater than 4. Again diminish the excess to ¼, the quantities will be 3 and 4¼ yet still 4¼ is greater than 4. In the same manner you may proceed to ⅛, 1/16, 1/32, &c. Infinitely; and yet you shall never come within an unite (though your unite stand for 100 mile) of the lesser quantity propounded 3, if that 3 stand for 300 Mile. The exce●ses above subtriple proportion do not d●creas● in the manner you say it does, but in the manner which I shall now show you.  
In this first row a third of the quantities below is ⅔. set in order these thre3 quantities 1. 2/ 9 ⅔. The first is 1 equal to the sum above, the last is ⅔ equal to the subtriple of the sum below. The middlemost is 2/9 subtriple to the last quantity ⅔. The excess of the proportion of 1 to ⅔ above the subtriple proportion of2/9 to ⅔ is the proportion of 1 to 2/9, that is, of 9 to 2, that is of 18 to 4.  
Secondly in the second row which is a third of the sum below is 4 the sum above is 5. Set in order these quantities 15. 4. 12. There the proportion of 15 to 12 is the proportion of 5 to 4. The proportion of 4 to 12 is subtriple; the excess is the proportion of 15 to 4, which is less than the proportion of 18 to 4. as it ought to be; b●t not less by the proportion of ⅙ to 1/12, as you would have it.  
Thirdly, in the third row, which is . A third of the sum below is 12, the su● above is 14. Set in order these quantities 4 〈◊〉. 4. 12. There the proportion of 42 to 12. is the same, with that of 14 to 4. And the p●oportion of 4 to 12 subtriple, less than the former excess of 15 to 4. And so it goes on deceasing all the way in this manner, 18 to 4. 15 to 4. 14 to 4 &c. which differs very much from your 1 to 6. 1 to 12. 1 to 18 &c. and the cause of your mistake is this; you call the twelfth part of twelve 1/12, and the eighteenth part of thirty ●ix, you call 1/18, and so of the rest. But what need all those equations in Symbols, to show that the proportion decreases; is there any man can doubt, but th●t the propartion of 1 to 2 is greater than that of 5 to 12, or that of 5 to 12 greater than that of 14 to 36, and so continually forwards; or could you have fallen into this error, unless you had taken, as you have done in very many places of your Elenchus, the Fra▪ ctions ⅙ and 1/12, &c. which are the quotients of 1 divided by 6 and 12. for the very proportions of 1 to 6, and 1 to 12. But notwithstanding the excess of the proportions of the increasing quanti●ies, to subtriple proportion decrease still, as the number of terms increaseth, and that what proportions soever I shall assign, the decrement will in time (in time I say without proceeding in in●initum) produce a less, yet it does not follow that the row of the increasing qu●ntities shall ever be equal to the third part of the row of so many equals to the last or greatest. For it is not, I hope, a Paradox to you, that in two rows of quantities the proportion of the excesses may decrease, and yet the excesses themselves increase, and do perpetually.  
For in the second and third rows, which are and 5 exceeds the third part of 12, by a quarter of the square of fo●r, and 14 exceeds the third part of 36 by 2 quarters of the square of 4, and proceeding on, the sum of the increasing quantities where the terms are 5 (which sum is 30) exceedeth the third part of those below (those below are 80 and their third part 26⅔ by 3 quarters and ½ a quarter of the square of 4. and when the terms are 6 the quantities above will exceed the third part of them below by 5 quarte●s of the square of four. Would you have ●en believe, that the further you go, the excess of the increasing quantities above the third p●r● of those below shall be so much the less? And yet the proportions of those above, to the the thirds of those below, shall decrease eternally; and therefore your 〈◊〉 proposit●on is ●alse, namely this.  
Siproponatur series Infinita quantitatum in duplic●t● ratione Arithmeticè proportionalium (sive juxta seriem numerorum quadraticorum) continué crescentium 〈◊〉 puncto ●ive O inchoata●um; eri● illa ad seriem to●idem maximae aequalium, ut 1 ad 3.  
That i●, if an infinite row of quantities be propounded in duplicate proportion of Arithmetically proportio●alls (or ●ccording to the row of quadratick numbers) continually increasing and beginning from a point or 0; that row shall be to the row of as many equals to the greatest, as 1 to 3. This is false, ut patet ex praecedentibus, and consequently all that yo● say in proof ●f the proportion of your Parabola to a parallelogram, or of the spiral (he true spiral) to a circle is in vain.  
But your spiral puts me in mind of what you h●ve underwritten to the diagramme of your prop 5. The spiral in both f●gures was to be continued whole to the middle, but by the carelessness of the Graver it is in one figure manca, in the other intercis●.  
T●uly Sir, you will hardly make your Reader believe that a Graver could ●ommit those faults without the help of your own copy, nor that it had been in your copy, if you had known how to describe a spiral line then as now. This I had not said, though truth, but that you are pleased to say, though not truth, that I attributed to the Printer some f●ults of mine;  
I come now to the thirty ninth proposition which is this  
Si proponatur series quantitatum in triplicata ratione Arithmeticè proportionalium (sive juxta seriem numerorum cubicorum) continuè cresentium a puncto sive O inc●oata●um, (puta ut O. 1. 8. 27. &c.) propositum sit inquirere quam habeat series illa rationem ad seriem totidem maximae ●qualium.  
Fiat investigatio per modum Inductionis (ut in prop. 1 & prop 19)  
Eritque 

 
 
Et sic d●inceps    
Ratio proveniens est ubique major quam subquadrupla, sive ¼. Excessus autem perp●●uo decrescit, p●o ut numerus terminor●m augetur, puta ¼. ⅛. 1/12. 1/16 &c. Aucto nimirum fractionis denominator●●ive cansequente rationis in ●ingulis locis numero quaternatio (ut patet) ut sit rati●nis provenie●…●xcess●… supra subquadruplam e● quam habet unitas ad Quadruplum numeri terminorum post 0. Adeoque.  
That is, if a row of quantities be propounded in triplicate proportion of Arithmetically proportionals (or according the row of cubiqune numbers) continually increasing, and beginning from a point or o (as 0. 1. 8. 27. 64. &c.) let it be propounded to inquire what proportion that row hath to a row of as many equals to the greatest●  
Be it sought by way of induction, (as in prop. 1. 19).  
The proportion arising is everywhere greater than subquadruple, or ¼, and the excess perpetually decreaseth as the number of terms increaseth as ¼, ⅛, 1/12, 1/16, 1/20, &c. The denominator of the fraction, or consequent of the proportion being in every place augmented by the number 4 (as is manifest) so that the excess of the arising proportion above subquadruple is the same with that which an unite hath to the quadruple of the number of the terms after 0. And so. Here are just the same faults which are in prop. 19  
For if 0/1 be a fraction, and 1/1 be a fraction and ½ be another fraction, than this equation is false. For this fraction 0/1 is equal, to 0▪ and therefore we have 1/1= ½, that is the whole equal to half. But perhaps you do not mean them fractions, but proportions; and consequently that the proportion of 0 to 1, and of 1 to 1 compounded by addition (I say by addition; not that I, but that you think there is a composition of proportions by multiplication, which I shall show you anon is f●lse) must be equal to the proportion of 1 to 2. which cannot be, For the proportion of 0 to 1 is infinitely little, that is, none at all; and consequently the proportion of 1 to 1 is equal to the proportion of 1 to 2▪ which is again absurd, There is no doubt, but the whole number of 0+ 1 is equal to 1, and the whole number 1+ 1 equal to 2. But reckoning them as you do, not for whole numbers, but for fractions, or proportions, the equations are false.  
Again your second equation 2/4= ¼+ ¼ though meant of fractions, that is of quotients it be true, and serve nothing to your purpose, yet if it be meant of proportions, it is false. For the proportion of 1 to 4 and of 1 to 4 being compounded are equal to the proportion of 1 to 16, and so you make the proportion of 2 to 4 equal to the proportion of 1 to 16, where as it is but subquaduplicate, as you call it, or the quarter of it as I call it. And in the same manner you may demonstrate to yourself, the same fault in all the other rows of how many terms soever they consist, Therefore you may give for lost this 39 prop. as well as all the other 38 that went before. As for the conclusion of it, which is, that the excess of the arising proportion &c. They are the words of your 40▪ proposition, where you▪ e●presse yourself better, and make your error more easy to be detected.  
The proposition is this.  
Si proponatur series quantitatum in triplicata ratione Arithmeticè proportionalium (sive juxta seriem numerorum cubicorum) continue crescentium à puncto velo inchoa●arum, ratio quam habet illa ad seriem totidem maximae aqualiùm subquadruplam superabit; eritque excessus ea ratio quam habet unitas ad quadruplum numeri terminorum post 0; sive quam habet radix cubica termini primi post 0 ad quadruplum radicis cubicae te●mini maximi. Pat●● ex praecedente.  
x autem crescente numero terminorum excessus ille supra rationem subquadruplam i●a continuo minuatur, ut tandem qu●libet assignabili minor evadat, (u● pa●et) si in Infinitum procedatur, prorsus evaniturus est. Ade●que.  
Paret ex prop. praecedent.  
That is; If a row of quantlties be propounded in triplicate proportion of Arithmetically proportionals (or according to the row of cubick numbers) continually increasing; and beginning at a point or 0; The proportion which that row hath to a row of as many equals to the greatest is greater than subquadruple proportion; and the excess is that proportion which one unite hath to the Quadruple of the number of terms after 0. Or which the cubick root of the first term after 0 hath to the quadruple of the root of the greatest term.  
It is manifest by the precedent propositions.  
And seeing, the number of terms increasing, that excess above quadruple proportion doth so continually decrease, as that at length it becomes less than any proportion that can be assigned (as is manifest) if the proceeding be infinite, it shall quite vanish; And so.  
This conclusion was annexed to the end of your 39 proposition; as there proved. What cause you had to make a new proposition of it, without other proof than pate● ex praecedente, I cannot imagine. But howsoever the proposition is false.  
For example, set forth any of your rows, as this of four terms.  
The row above is 36▪ the fourth part of the row below is 27. The quadruple of the number of terms after 0 is 12▪ then by your account, the proportion of 36 to 108 is greater than subquadruple proportion by the proportion of 1 to 12. For trial whereof set in order these three quantities 36. 27. 108. The proportion of 36 (the uppermost row) to 108 (the lowermost row) is compounded by addition of the proportion● 36 to 27, and 27 to 108. And the proportion of 36 to 108 exceedeth the proportion of 27 to 108 by the proportion of 36 to 27. But the proportion of 27 to 108 is subquadruple proportion. Therefore the proportion of 36 to 108 exceedeth subquadruple proportion, by the proportion of 36 to 27. And by your account by the proportion of 1 to 12; and consequently as 36 to 27 so is 1 to 12. Did you think such demonstrations as these, should always pass?  
Then for your inference from the decrease of the proportions of the excess to the vanishing of the excess itself, I have already showed it to be false; and by consequence that your next Proposition, namely, the 40 is also false.  
The proposition is this.  
Si pr●ponatur series infinita quantitatum in triplicata ratione Arithmeticé proportionalium (sive juxta seriem numerorum cubicorum) continuè crescentium à puncto sive 0 inchoatarum, erit illa ad seriem totidem maximae aequalium, ut 1 ad 4. pa●et ex praecedente.  
That is, If there be propounded an infinite row of quantities in triplicate proportion of Arithmetically proportionals (or according to the row of cubick numbers) continually increasing, and beginning at a point or 0; it shall be to the row of as many equals to the greatest as 1 to 4. Manifest out of the precedent proposition.  
Even as manifest as that 36. 27. 1. 12. Are proportionals: seeing therefore your Doctrine of the spiral lines and spaces is given by yourself for lost, and a vain attempt, your first 41 propositions are undemonstrated, and the grounds of your demonstrations all false. The cause whereof is partly your taking quotient for proportion, and a point for 0, as you do in the 1. 16 and 40. propositions and in other places where you say beginning at a point or 0; though now you deny you ever said either. There be very manay places in your Elenchus, where you say both; and have no excuse for it, but that in one of the places, you say the proportion is p●nes quotientem, which is to the same or no sense.  
Your 42 proportion is grounded on the 40; and therefore though true, and demonstrated by others, is not demonstrated by you.  
Your 43 is this.  
Pari methodo invenietur ratio seriei infinitae quantitatum Arithmeticè proportionalium in ratione quadruplicata, quintuplicata, sextuplicata, etc Arithmeticè proportionalium à puncto seu 0 in choatarum, ad seriem totidem maximae aequalium. Nempe in quadruplicata ●●it, ut 1 ad 5; in quintuplicata ut 1 ad 6; in sextuplicata ut 1 ad 7.  
Et sic d●inceps.  
That is, By the same method will be found the proportion of an infinite row of Arithmetically proportionals in proportion quadruplicate, quintuplicate, sextuplicate &c. of Arithmetically proportionals beginning at a point or 0, to the row of as many equals to the greatest; Namely, in quadruplicate, it shall be as 1 to 5, in quintuplicate as 1 to 6; in sextuplicat● as 1 to 7; and so forth.  
But by the same method that I have demonstrated that the 19 20. 21. 39 40. 41. Propositions are false, any man else that will examine the 43 may find it false also. And because all the rest of the propositions of your Arithmetica infinitorum depend on these, they may safely conclude that there is nothing demonstrated in all that Book, though it consist of 194 propositions. The proportions of your Parabolo●ides to their Parallellogrammes are true, but the demonstrations false, and infer the contrary. Nor were they ever demonstrated (at least the demonstrations are not extant) but by me; nor can they be demonstrated, but upon the same grounds concerning the nature of proportion, which I have clearly laid, and you not understood. For if you had, you could never have fallen into so gross an error as is this your Book of Arithmetica Infinitorum, or that of the Angle of Contact. You may see by this that your symbolic Method is not only, not at all inventive of new Theormes, but also dangerous in expressing the old. If the best Masters of Symbolicks think for all this you are in the right, let them declare it. I know how far the Analysis by the powers of the lines extendeth, as well as the best of your half-learned Epistlers, that approve so easily of such An●logismes as those. 5. 4. 1 12, and 36. 27▪ 1. 12▪ &c.  
It is well for you that they who have the disposing of the professors places take not upon them to be Judges of Geometry, For if they did, seeing you confess you have read these Doctrines in your School● you had been in danger of being put out of your place.  
When the Author of the paper wherein I am called Plagiary, and wherein the honour is taken from you of being the first inventor of these fine theorems, shall read this that I have here written, he will look to get no credit by it; especially if it be Roberval, which me thinks it should not be. For he understands what proportion is, better than to make 5 to 4 the same with 1 to 12. Or to make again, the proportion of 36 to 27 the same with that of 1 to 12; and innumerable disproportionalites that may be inferred from the grounds you go on. But if it be Robeval indeed, that snatches this invention from you, when he shall see this burning coal hanging at it, he will let it fall again, for fear of spoiling his reputation.  
But what shall I answer to the Authority of the three great Mathemiticians that sent you those encomiastic letters. For the first, whom you say I use to praise, I shall take better ●eed hereafter of praising any man for his Learning whilst he is young, further than that he is in a good way. But it seems he was in too ready a way of thinking very well of himself, as you do of yourself. For the muddiness of my brain, I must confess it. But ●r, Ought not you to confess the same of yours? No, men of your tenets use not to do so. He wonders, (say you) you thought it worth the while to ●o●●l your fingers about such a piece. 'tis well; Every man abounds in his own sense. If you and I were to be compared by the compliments that are given us in p●ivate letters, both you and your Complementors would be out of Countenance; which ●omplements, besides that which has been printed and published in the Commendations of my writings, if it were put together would make a greater volume then either of your Libels. And truly Sir, I had never answered your Elenchus as proceeding from Dr. Walli●▪ if I had not considered you also as the Minister to execute the malice of that sort of people that are offended with my L●viathan.  
As for the judgement of that public Professor that makes himself a witness of the goodness of your Geometry, a man may easily see by the letter itself that he is a dun●. And for the English person of quality whom I know not, I can say no more yet, than I can say of all three, that he is so ill a Geometrician, as not to detect those gross paralogisms as in●er that 5 to 4 and 1 to 12 are the same proportion. He came into the cry of those whom your title had deceived.  
And now I shall let you see that the composition of proportion by multiplication as it is in the 5 d●f. of the 6 Element, is but another way of adding proportions one to another. Let the proportions be of 2 to 3, and of 4 to 5. Multiply 2 into 4 and 3 into 5 the proportion arising is of 8 to 15. Put in order these three quantities 8. 12. 15. The proportion therefore of 8 to 15 compounded of the proportions of 8 to 12 (that is, of 2 to 3) and of 12 to 15. that is, of 4 to 5 by addition. Again, let the proportion be of 2 to 3 and & 4 to 5 multiply 2 into 5 and 3 into 4 the proportion arising is of 10 to 12. Put in order these 3 numbers 10▪ 8. 12. The proportion 10 to 12 is compounded of the proportions of 10 to 8 that is of 5 to 4, and of 8 to 12, that is of 2 to 3 by addition▪ I wonder you know not this.  
I find not any more clamour against me for saying the proportion of 1 to 2 is double to that of 1 to 4.  
Your Book you speak of concerning proportion against Maybonius is like to be very useful when neither of you both do understand what proportion is.  
You take e●ceptions at that I say, that Eucilde has but one word for double and duplicate; which nevertheless was said very truly, and that word is sometimes {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} and sometimes {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}▪ And you think you come of handsomely with asking me whether {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} and {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} be one word.  
Nor are you now of the mind you were, that a point is not quantity unconsidered; but that in an infinite series it may be safely neglected. What is neglected but unconsidered?  
Nor do you any more stand to it, that the quotient is the proportion. And yet were these the main grounds of your Elenchus.  
But you will say perhaps I do not answer to the defence you have now made in this your School Discipline, 'tis true. But 'tis not because you answer never a word to my former objection against these prop. 19▪ 39 But because you do so shift and wriggle and throw out ink, that I cannot perceive which way you go; nor need I, especially in your vindication of your Arithmetica Infinitorum. only I must take notice that in the end of it, you have these words, well, Arithmetica Infinitorum is come off clear. You see the contrary. For sprawling is no defence.  
It is enough to me, that I have clearly demonstrated both, before sufficiently, and now again abundantly, that your Book of Arithmetica In●●ni●orum is all nought from the beginning to the end, and that thereby I have effected that your Authority shall never hereafter be taken for a prejudice. And therefore they that have a desire to know the truth in the questions between us, will henceforth, if they be wise, examine my Geometry by attentive reading me in my own writings, and then examine, whether this writing of yours confute or enervate mine.  
There is in my 5 lesson a proposition, with a diagramme to it to make good, (I dare say,) at least against you, my 20. Chapter concerning the dimension of a Circle. If that demonstration be not shown to be false, your objections to that Chapter (though by me rejected) come to nothing. I wonder why you pass it over in silence. But you are not, you say, bound to answer it. True, nor yet to defend what your have written against me.  
Before I give over the examination of your Geometry, I must tell you that your words (pag. 〈◊〉 of this your school Discipline) again the first Corollary are untrue.  
Your words are these, you aff●…n that the proportion of the parabola A B I to the parabola A F K is triplicate to the proportion of the time A B to A F, as it is in the English. This is not so. Let the Reader turn to the place and judge. And going on you say, or of the imp●… B I to F K, as it is in the Latin. Nay, as it is in the English, and the other in the Latin. 'tis but your mistake; but a mistake is not easily excused in a false accusation.  
Your exception to my saying, That the differences of two quantities is their proportion (when they differ, as the no difference, when they be equal) might have been put in amongst other marks of your not sufficiently understanding the Latin tongue. Differre and Differentia differ no more than vivere and vita, which is nothing at all, but as the other words require that go with them, which other words you do not much use to consider. But differre and the quantity by which they differ, are quite of another kind. Di●ferre ({non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}) differing, exceeding, is not quantity, but relation. But the quantity by which they differ is always a certain and determined quantity, yet the word differrentia serves for both, and is to be understood by the coherence with that which went before. But I had said before, and expressly to prevent cavil, that relation is nothing but a comparison, and that proportion is nothing but relation of quantities and so defined them, and therefore▪ I did there use the word differentia for differing, and not for the quantity which was le●t by substraction. For a quantity is not a differing. This I thought the intelligent Reader would of himself understand without putting me, instead of differentia to use (as ●ome do, and I shall never do) the mongrel word {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} differre. And whereas in one only place for differre ternario I have writ ternarius, If you had understood what was clearly expressed before, you● might have been sure, it was not my meaning, and therefore the excepting against it, was either want of understanding, or want of Candou●; choose which you will.  
You do not yet clear your Doctrine of Condensation and Rarefa●lion. But I beleev● you will be degrees become satisfied that they who say the same Numerical Body may ●e sometimes greater, sometimes less, speak absurdly, and that Condensation and Rarefaction here, and definitive and ci●cumscriptive and some other of your distinctions elsewhere are but ●nares, such as School-Divines have invented 
— {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman},  
{non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}  to entangle shallow wits.  
And that that distinction which you bring here, that it is of the same quantity, while it is in the same place, but it may be of a different quantity, when it goes out of its place, (as if the place added to, or took any quantity from the body placed) is nothing but mee● words. 'tis true that the Body which swells changeth place; but it is not by becoming itself a greater body, but by admixtion of air or other body; as when water riseth up in boiling, it taketh in some parts of air. But seeing the first place of the body is to the body equal, and the second place equal to the same body, the places must also be equal to one another, and consequently the dimensions of the body remain equal in both places.  
Sir, When I said that such Doctrine was taught in the Universities, I did not speak against the Universities, but against such as you. I have done with your Geometry, which is one {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}.   

As for your El●quence let the Reader judge, whether your● or mine be the more muddy, though I in plain s●olding should have out done you, yet I have this excuse which you have not, that I did but answer your challenge at that weapon which you thou●ht fit to choose. The Catalogue of the hard language which you put in at the 3. and 4. pages of your School-discipline, I acknowledge to be mine, and would have been content you had put in all. The titles you say I give you of fools, Beasts, and Asses I do not give you, but drive back upon you; which is no more than not to own them; ●or the rest of the Catalogue I like it so well as you could not have pleased me better, then by setting those passages together to make them more conspicuous, that's all the de●ence I will make to your accusations of that kind.  
And now I would have you to consider whether you will make the like de●ence against the ●aults that I shall ●inde in the Language of your School-Discipline.  
I observe first the facetiousness of your Title page. Due Correction for Mr. H●●bs, or school Discipline, for not saying his lessons right, what a quibble is this upon the word Lesson; Besides, you know it has taken wind; for you vented it amongst your ac acquaintance at Oxford then when my Lessons were but upon the press. Do you think if you had pretermitted that piece of wit, the opinion of your judgement would have been ●re the less. But you were ●ot content with this but must make this Metaphor from the rod, to take up a considerable part of your book; in which there is scarce any thing that yourself can think wittily said besides it. Consider also these words of yours; It is to be hoped that in time you may come to learn the Language, for you be come to great A already. And presently after, were I great A before I would be willing to be so used, I should wish myself little a, a hundred times. Sir, you are a Doctor of Divinity, and a professor of Geometry, but do not deceive yourself; this does not pass for wit in these parts; no nor generally at Oxford. I have acquaintance there that will blush at the reading it.  
Again, in another place you have these words, than you catechise ut, what's your name. Are you Geometricians? who gave you that name &c. Besides in other places such abundance of the like insipid conc●ipts as would make men think, if they were no otherwis● acquainted with the Universitv but by reading your Books, that the dearth there of salt were very great. If you have any passage more like to salt then these are (excepting now and anon) you may do well to show it your acquaintance, lest they despise you; For (since the detection of your Geometry) you have nothing left you else to defend you from contempt. But I pass over this kind of eloquence; and come to somewhat yet more rural.  
Page 27. line 1. You say I have given Euclid his Lurry. And again pag. 129. l. 11. A●d And now he is lest to learn his Lurry. I understand not the word Lurry. I never read it before, nor heard it, as I remember, but once, and that was when a Clown threatening another Clown said he would give him such a Lurry come poop &c. Such words as these do not become a learned mouth, much less are fit to be registered in the public writings of a Doctor of Divinity. In another place you have these words, just the same to a cow's thumb, a pretty Adage.  
Page 2. But prithee tell me. And again page 95. prithee tell me, why dost thou ask me such a question, and the like in many other places. You cannot but know how casy it is and was for me; to have spoken to you in the same language. Why did I not? Because I thought that amongst men that were civilly bred it would have redounded to my shame, as you have cause to fear that this will redound to yours. But what moved you to speak in that manner? were you angry? If I thought that the cause, I could pardon it the sooner, but it must be very great anger that can put a man that pro●esseth to teach good manners, so much out of his wits as to ●all into such a language as this of yours; It was perhaps an imagination that you were talking to your inferior, which I will not gran● you, nor will the Heralds I believe trouble themselves to decide the question. But howsoever I do not find that civil men use to speak so to their inferiors. If you grant my learning but to be equal to yours (which you may certainly do without very much disparaging of yourself abroad in the world) you may think it less insolence in me to speak so to you in respect of my age, then for you to speak so to me In respect of your young doctorship. You will find that for all your doctorship, your elders, if otherwise of as go●d repute as yo●, will be respected before you. But I am not sure that this language of yours proceeded from th●t cause; I am rather inclined to think you have not been enough in good company, and that there is still somewhat le●t in your manners for which the honest youths ●of Hedington and Nincsey may compare with you ●or good Language as great a Doctor as you ar●.  
For my verses of the Peak, though they be as ill in my opinion as I bel●eve they are in yours, and made long since, yet are they not so obscene, as that they ought to be blamed by Dr. Wallis. I pray you Sir, whereas you have these words in your school-discipline page 96. unless you will say that one and the same motion may be now, and anon too; what was the reason you put these words now and anon too in a different Character, that makes them to be the more taken notice of; Do you think that the story of the Minister that uttered his affection (if it be not a sl●nder) not unlawfully but unseasonably, is not known to others as well as to you? what needed you then (when there was nothing that I had said could give the occasion) to use those words; there is nothing in my verses that do olerehircum, so much a● this of yours, I know what good you can receive by ruminating on such Ideas, or cherishing of such thoughts. But I go on to other words of 〈◊〉 by you reproached, you may as well se●k the Focu● of the Parabola of Dives and Lazarus, which you say is mocking of the Scripture. To which I answer only, that I intended not to mock the Scripture, but you; and that which was not meant for mocking was none. And thus you have a second {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}.   

Grammar and critics.  
I come now to the comparison of our Grammar and critics. You object first against the signification I give of {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, & say thus, what should come into your cap (that if you market in a man that wears a square cap, to one that wears a hat is very witty) To make you think that {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} signifies a mark or brand with a hot iron, I perceive where the business lies. 'twas {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} run in your mind when you talked of {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}; and because the words are somewhat alike you jumble them both together. Sir, I told you once before, you presume too much upon your first cogitations. Aristophanes, in R●nis. Act. 5. Scen. 5. {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} &c. The old Commentator upon the word {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} saith thus {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. That is, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} for {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} for he (Adimantus) was not a Citizen. I hope the Commentator does not here mock Aristophanes for jumbling {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} and {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} together for want of understanding Greek. No, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} and {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} signify the same, save that for branding I seldom read {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} but {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. For {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} does no more signify a brand with a hot iron then {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} a point made also with a hot iron. They have both one common theme {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, which does not signify pungo, nor interpungo nor inuro (for all you Lexicon) but notam inprimere, or pungendo notare, without any restriction to burning or punching. It is therefore no less proper to say that {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} is a mark with a hot iron, then to say the same of {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. The difference is only this, that when they marked a slave, or a rascal as you are not ignorant is usually done here at the Assizes in the hand or shoulder with a hot iron they called that {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, not for the burning but for the mark. And as it would have been called {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} that was imprinted on a slave, though made by st●yning or incision, so it is {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} though done with a hot iron▪ And therefore there was no jumbling of those two words together as for want of reading Greek Authors, and by trusting too much to your Dictionaries (which you say are proofs good enough for such a business) you were made to imagine. The use I have made thereof was to show that a point (both by the word {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} in Euclid, and by the word {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} in some others) was not nothing, but a visible mark; the ignorance where of hath thrown you into so many paralogisms in Geometry.  
But do you think you can defend your Adducis Malleum as welll as I have now defended my {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}? You have brought, I confess, above a hundred places of Authors where there is the word Duco, or some of its compounds; but none of them will justify Adducis Malleum and (excepting two of those places) you yourself seem to condemn them all, comparing yours, with none of the rest but with these two only; both out of Plautus, by you, not well understood. The first is in Casina Act. 5. Scen. 2. ubi intro hanc Novam Nuptam deduxi, via recta, Clavem abduxi. Which you presently presuming of your first thoughts (a peculiar fault to men of your principles) assure yourself is right. But if you look on the place as Scaliger reads it cited by the commentator, you will find it should be obduxi, and that Clavis is there used for the bolt of the lock. Besides he bolted it within. Whither then could he carry away the key? The place is to be rendered thus, when I had brought in this new bride I presently locked the door, and is this as bad every whit as Adducis Malleum. The second place is it Amphytryo Act. 1. Scen. 1. Eam (Cirneam) ut à matre ●uerat natum plenum vini Eduxi me●i. Which you interpret I brought out a flag●n of Wine. Unlearnedly. They are the words of Mercury transformed into Sofia. And to try whether Mercury were So●ia or not, So●ia asked him where he was and what he did during the Battle; to which Mercury answered, (who knew where Sofia then was and what he did) I was in the Cellar where I filled a Cirnea, and brought it up full of Wine, pure as it came from its mother. By the mother of the Wine meaning the Vine, and alluding to the Education of Children, for Ebibi said Eduxi, and with an Emphasis in meri, because Cirnea (from {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, Misceo) was a vessel wherein they put water to temper to their Wine. Intimating that th●ugh the vessel were Cirnea, yet the Wine was meru●…. This is the true sense of the place; but you will have Eduxi to be I brought out, though he came not out himself. You see Sir, that nei●her this is so ●ad as Addu●●s Malleum.  
But suppose out of some one place in some one blind Author you ●ad pa●ralled your Addu●is M●ll●um, do you think it must therefore presently be held for good Latin, why more than learn his lurry must be therefore thought good English a thousand years hence, because it will be read in Dr. Wallis long▪ lived works. But how do you construe this passage of the Greek Testament {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. You construeit thus: she shall be saved notwithstanding Child bearing, if (the w●men) remain in the faith. Is childbearing any obstacle to the salvation of women? You might as welll have translated the first verse of Rom. 5. in this manner, Being then justified by fait●, ●e have pea●e with God notwithstanding our Lord Jesus Christ. I let pass your n●t ●●nding in {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}▪ as good a Gra●arian as you are, a Nominative case to {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. If you had remembered the place. 1. Pet. Chap. 3. verse 20. {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, that is, They were saved in the wars, you would have thought your construction justified then very well; but you h●d been deceived, for {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} does not there signify causam, nor ablationem impedimenti but tran●…m; not cause or removing an impediment but passage. Being come thu●●●r I found a friend that hath eased me of this dispute; for he showed me a letter written to himself from a learned man, that hath out of very good Authors collected enough to decide all the Grammatical questions between you and me both Greek and Latin. He would not let me know his na●e, nor any thing of him but only this, that he had better ornaments then to be willing to go clad abroad in the habit of a Grammarian. But he gave me leave to make use of so much of the letter as I thought fit in this dispute. Which I have done and have added it to the end of this writing. But before I come to that, you must not take it ill (though I have done with your School Discipline) if I ex●mine a little some other of your printed writings as you have examined mine; for neither you in Geometry nor such as you in Church politics can not expect to publish any unwholesome doctrine without some Antidotes from me, as long as I can hold a pen. But why did you answer nothing to my sixth Lesson? because (you say) it concerned your Colle●gue only; No Sir, It concerned you also, and chiefly. For I have not heard that your Colleague holdeth those dangerous principles which I take notice of in you. In my sixth Lesson page 62. upon the occasion of these words, not his but yours. Perhaps you t●ke the whol● History of the fall of Adam for a fable, which is no wonder, seeing you say the rules of honouring and worshipping of God are to be taken form the laws. In answer to which I said thus. You that take so heinously, tha● I would have the rule of God's worship in a Christian commonwealth to be taken from the Laws, tell me from whom you would have th●m taken. From yourself? Why so, more than from me? From the Bishops? Right, if the Supreme power of the commonwealth will have it so; if not, why from them rather than from me? From a Consistory of presbyters▪ themselves or joined with Lay-Elders, whom they may sway as they please? Good, If the supreme governor of the commonwealth will have it so. If not, why fr●m them rather then from me, or from any man else? They are wiser and learneder than I▪ It may be so; but it ha● n●t yet appeared. Howsoever, let that be granted. Is ●h●re any man so very a fool a● to subje●● himself to the rules of other men in those things which do so nearly concern himself, for the title they assume of being wise and learne●, unless they also have the sword which must portect them. But it seems you understand the sword as comprehended. If so, Do not you then r●ceive the rules of God's worship from the Civil Power? Yes doubtless; and you would expect, if your Consistory had that sword, that no man should dare to ex●rcise or teach any rules concerning God's worship which were not by you allowed.  
This will be thought strong arguing, if you do not answer it. But the truth is, you could say nothing against it without too plainly discove●ing your disaffection to the Goverme●t. And yet you have discovered it pretty well in your second Thesis maintained in the Act at Oxford 1654., and since by yourself published. This Thesis I shall speak briefly to.   

Scotch-Church politics.  
You define Ministers of the Gospel to be those to whom the preaching of the Gospel by their o●fice is enjoined by Christ. Pray you, first, what do you mean by saying preaching ex Offici● is enjoined by Christ. Are they Preachers ●x Officio, and afterwards enjoined to Preach? Ex Officio adds nothing to the definition; but a man may ●asily see your purpose to disjoin yourself from the State by inserting i●.  
Secondly, I desire to know in what manner you will be able out of this d●●inition to prove yourself a Minister? Did Christ hi●self immediately enjoin you to preach, or give you orders? No. Who then, some Bishop, or Minister or Ministers? Yes; by what Authority? Are you sure they had Authority immediately from Christ? no. How then ar● you sure but that they might have none? At least, some of them through whom your Authority is derived might have none. And therefore if you run b●ck for your Authority towards the Apostles times but a matter of sixscore years, you will ●inde your Authority derived from the Pope; which words have a sound very unlike to the voice of the Laws of England. And yet the Pope will not own you. There's no man doubts but that you hold that your Office comes to you by successive impo●ition o● hands ●rom the time of the Apostles. Which opinion in those gentle terms passeth well enough; But to say you derive your Authority from thence, not through the Authority of the sovereign power civil, is too rude to be endured in a state that would live in peace. In a word you can never prove you are a Minister, but by the supreme Autho●ity of the commonwealth. Why then do you not put some such clause into your definition? As thus, Ministers of the Gospel are those to whom the preaching of the Gospel is enjoined by the sovereign power in the name of Christ. What harm is there in this definition, saving only it crosses the ambition of many men that hold your p●inciples? Then you d●●ine the power of a Minister thus; The power of a Minister is that which belongeth to a Minister of the Gospel in virtue of the Office he holds; in as much as he holds a public Station, and is distinguished from private Christians. Such as is the power of preaching the Gospel; administering the Sacrament; the use of Eccles●astical censure●; and Ord●ining of Ministers &c.  
Again; how will you prove out of this definition that you or any man ●lse hath the power of a Minister, i● it be not given him, by him that is the sovereign o● the commonwealth▪ For seeing (as I have now proved) it is from him that you must d●rive your ministry, you can have no oth●r power then that which is limited in y●ur Orders, ●or ●ha● neithe● longer then he thinks fit. For if he give it you for the instruction of his subjects in their duty, he may take it from you again whensoever he shall see you instruct them wi●h undutiful and seditious principles. And if the Sogeraign power give me command (though without the ceremony of imposition of hands) to teach the Doctrine of my Leviathan in the Pulpit, why am not I if my Doctrine and life be as good as yours, a Minister as well as you, and as public a person as you are? For public person primarily is none but the civil sovereign, and so seconda●ily all that are employed in the execution of any part of the public Charge. For all are his Ministers, and therefore also Christ's Ministers because he is ●o; and other Ministers are but his Vicars, and ought not to do or say any thing to his people contrary to the intention of the sovereign in giving them their Commission,  
Again, if you have in your Commission a power to Ex●ommunicate, how can you think that your Soveraig● who gave you that Commission intended it for a commission to Excommunicate himself, that is, (as long as he stands Excommunicate; to deprive him of his Kingdom) If all Subjects were of your mind, as I hope▪ they will never be, they will have a very unquiet life. And yet this has (as I have often heard) been practised in Scotland, when Ministers holding your principles had power enough (though no right) to do it.  
And for Administration of the Sacraments, if by the supreme power of the commonwealth it were committed to such of the Laity as know how it ought to be done as well as you, they would ips● facto be Ministers as good as you. Likewise the right of Ordination of Ministers depends not now on the Imposition of hands of a Minister or Presbytery, but on the authority of the Christian sovereign Christ's immedi●t Vicar and supreme governor of all Persons and Judge of all causes both spiritual and temporal in his own Dominions, which I believe you will not deny.  
This being evident, what Acts are those of yours which you call Authoritative, and receive not from the Authority of the civil power? A Constable does the acts of a Constable authoritatively in that sense. There●ore you can no otherways claim your power then a Constable claimeth his, who does not exercise his Office in the Con●●ablery of another. But you ●orget that the Scribes and the Pharisees ●it no more in Moses chair.  
You would have every Minister to be a Minister of the Universal Church, and that it be lawful for you to preach your Doctrine at Rome; if you would be pleased to try, you would find the Contrary. You bring no argument for it that looks like reas●n. Examples prove nothing, where persons, times, and other circumstances differ; as they differ very much now when Kings are Christians, from what they were then when Kings per●ecuted Christians. It is ea●ie to perceive what you aim at.  
You will fain have Market-day Lectures set up by authority (not by the authority of the Civil power but by the authority of example of the Apostles in the Emission of Preachers to 〈◊〉 I●fidels) not knowing that any Christian may lawfully preach to the Infidels. that is to say, proclaim unto them that Jesus is the Mesiah without need of being other ways made a Minister; as the Deacons did in the Apostles time; nor that many teachers unless they can agree better, do any thing else but prepare men for faction, nay, rather you know it well enough; but it conduces to your end upon the market-days to dispose at once both Town and Country, under a false pretence of obedience to God, to a Neglecting of the Commandments of the Civil sovereign, and make the Subject to be wholly ruled by yourselves; wherein you have already found yourselves deceived. You know how to trouble and sometimes und●e a ●lack Government, and had need to be warily looked to, but are not fit to hold the rei●es. And how should you, being men of so little judgement as not to see the Necessity of unity in the governor, and of Absolute obedience in the Governed, as is manifest out of the place of your Elenchus above recited. The Doctrine of the duty of private men in a commonwealth is much more difficult, not only than the knowledge of your symbols, but also then the knowledge of G●ometry itself▪ How then do you think, when you err so grossly in a few Equations, and in the use of most common words, you should be fit to Govern so great Nations as England, Ireland, and Scotland, or so much as to teach them. For it is not reading but judgement that enables one man to teach another.  
I have one thing more to add, and that is the disaffection I am charged with all to the Universities. Concerning the Universities of Oxford and Cambridge, I ever held them for the greatest and Noblest means of advancing learning of all kinds, where they should be therein employed, as being ●urnished with large endowments, and other helps of Study, and frequent▪ with abundance of young Gentlemen of good families ●●d good breeding from their child hood. On the other side, in case the same means and the same wits should be employed in the advancing of the Doctrines that tend to the weakening of the public, and strengthening of the power of any private ambitious party, they would also be very effectual for that; And consequently that if any Doctri●e tending ●o the diminishing of the civil power were taught there, not that the Universities were to blame, but only those men that in the Universities either in Lectures, Sermons, printed Books, or Thesis did teach such Doctrine to their hearers or readers. Now yo● know very well that in the time of the Roman Religion, the power of the Pope in England was upheld principally by such teachers in the Universities. You k●ow also how much the Divines that held the ●ame princi●les in Church Government with you, have contributed to our late troubles. Can I therefore be justly taxed with disaffection to the Universities for wishing this to be reformed. And it hath pleased God of late to reform it in a great measure, and indeed as I thought totally, when out comes this your Thesis boldly maintained to show the contrary; Nor can I yet call this your Doctrine the Doctrine of the Vniver●ity, b●t surely it will not be unr●asonable to think so, if by public act of the university it be not disavowed, which done, and that as often as there shall be need, there can be no longer doubt but that the universities of England are not only the Noblest of all Christian universities, ●ut also absolutely, & of the greatest benefit to this Common wealth that can be imagined, except that benefit of the head itself that uniteth and ruleth all. I have not here perticularized at length all the ill consequences that may be deduced fromthis Thesis of yours, because I may, when further provoked, have somewhat to say that is new.  
So much for the 3. {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}.   

An extract of a Letter concerning the grammatical part of the controversy between Mr. HOBBES and Dr. WALLIS. Mr. Hobbes hath these words  
LOngi●udinem percu●sam motu uniformi, cum impetu ubique ipsi B D ●quali. Dr. Wallis saith come were better out, unless you would have impe●us to be only a companion, not a cause. Mr. Hobbes answered it was th●Abla●ive case of the manner. The truth is the Ablatives case of the manner, and cause both, may be used with the conjunction cum, as may be justified. Cicero in the 2. de Nat. Deor. moliri aliquid cum labore operoso ac molesto; and in his Oration for C●cinn●. De se autem hoc praedicat, Antiocho Ebul●j se●vo imperâsse ut in Caecinan advenien●em cum serro invaderet. Let us see than what Dr. Wallis objects against Tully; where a Causality is imported; Though we may use with in English, yet not cum in Latin, to kill with a sword (importing this to have an instrumental or causal in●luence, and not only that it h●ngs by the man's side whilst some other weapon is made ●se of) is not in Latin, occidere cum gladio, but gladio occidere. This shows that the Dr. hath not forgot his grammar, for the subsequent examples as well as this rule are borrowed thence. But yet he might have known that great Personages have never confined themselves to this Pedantry, but have chosen to walk in a greater latitude. Most of the Elegancies and Idioms of every Language are exceptions to his Grammar. But since Mr. Hobbes saith it is the Ablative case of the manner, there is no doubt it may be expressed with cum. The Doctor in the mean time knew no more than what Lilly had taught him; Alvarez would have taught him more. And Voss●us in his Book de constructione Cap. 47. expressly teacheth, Ablativ●s causae, instrument●, vel modi, non à verbo regised à praepositione omiss●, à vel ab, de, è, vel ex, prae, aut cum, ac praepositiones eas quandoque exprimi nisi quòd cum ablativis inst●umenti haud ●emerè inve●ias; and afterwards he saith non timerè imitandum. If this be so, then did Mr. Hobbes speak Grammatically, and with Tully, but not usually. And might not one retort ●pon the Doctor, that Vossius is as great a critic a●●ie.  
His next reflection is upon praetendi● scire, this he saith is an anglicism. If this be all his Accusation, upon this score, we shall lose ma●y expres●ions that are used by the best Authors, which I take to be good Lati●…smes, though they be also anglicisms, the latter being but an imitation of the former. The Do●tor therefore was too fierce to condemn upon so general an account, that which was not to have been censured for being an anglicism, unless also it had been no latinism. Mr. Hobbes replies, that the Printer had omitted se. He saith, this mends the matter a little It is very likely, for than it is just such another anglicism as that of Quintilian; Cùm loricatus in foro ambularet, praetendebat se id metu facere. The Doctor certanily was very negligent, or else he could not have missed this in Robert Stephen. Or h●ply he was resolved to condemn Quintilian for this and that other anglicism, Ignorantia p●●tendi non potest, as all those that have used praetendo, which are many and as good Authors as Doc●●r Wallis that makes his own Encomiasts (not an English ma●) amongst them to w●●te A●glicismes.  
Then ●e bl●mes Tractatus ●●jus partis t●rtiae, in q●â mo●us & magnitudo per se & abstract● consideravimus, te●minum hic statuo. Here I ●●st con●esse the exception is colonrable, yet I can parallel it with the like objection made by Erasm●s aga●●st Tully, out of whom Erasmus q●otes this passage; D●ut ùs comm●tans Athents; quo●●am ven●… negabant solvendi facultatem, e●at ani●us ad ●e scr●bere: and excuses it hu●, that Tully might have had at fir●t in his thoughts v●…bam or statuebam, which he afterwards relinquished for erat animus, and did not remember what he had antecedently w●itt●n, which did not vary fr●m his succeeding, though●●, but words. A●d this excuse may pass with any who knows that Mr. Hobbes values not the study of word●, but as it s●rves to express his thoughts, which were the same whe●her he wrot●; in quâ metus & m●g●i●udo per se a● abstractè considerati sunt, or consideravimus. And if the Dr▪ will make this so capital; he must prove it volunta●y, and show that it is greater than what is legible in the p●ny Letter of his Encomiast, whom he would have to be beyond except●●n.  
Now ●ollowes his r●diculous apol●gi● for adducis malleum, ut occidas muscam▪ The cause why he did use that prov●rb (of his own phrasing) was this. Mr. Hobbes had taken a great deal of pains to demonstrate what Dr. Wallis thought he could have proved in shor●; upon this occasion he objects, ad ducis malleum ut occidas muscam, which I shall suppose he intended to English thus, you bring a beetle to kill a ●●y. Mr. Hobbes retor●ed that adduco was not used in that sense. The Dr. vindicates himself thu●; duco, dedu●●, reduco, perduco, produco, &c. signify s●range things, ergo, adduco may be used in that sense; whi●h is 〈◊〉 most ridic●lo●● kind of arguing, where we are but to take up our Language from others, and not to coyve new phr●ses. It is not the Grammar that shall secure the Dr. nor weak Analogies, where Elegance comes in contest. To jus●i●ie his expression he must have showed it usu tritum, or alleged the Authori●y of some Author of great note for i●. I have not the leisure to exam●…e his impertinent citations about those other compounds, nor yet of that simple verb duco; nay, to justify his saying he hath not brought one parallel example. He talks indeed very high, that duco (●ith its compounds) i● a word of a large signification, & amongst the rest to Bring, fetch, carry &c. i● so exceeding frequent ●n all Authors (Plautus, Terence, Tully Ca●ar, Tacitus, Pliny, Seneca, Virgil, Horace, Ovid, Claudian, etc that he must needs be either maliciously blind, or a very stranger to the Latin tongue that doth not know it, or c●n have the face to deny it. 〈◊〉 ●ead what will ●e my doom for not allowing his Latin; yet 〈◊〉 must profess I dare secure the Dr, for having read all Authors, notwithstanding his assertion, and I hope he will do the like for me. And for those which he hath read, had he brought no better proofs than these, he had, I am sure, been whipped soundly in Westminster-School, for hi● impudence as well as ig●or●nce, by the learned M●ster thereof a● present. But I da●e f●●ther a●…m, the Dr. hath no● read in this point any,▪ but only consulted with Robe●t S●ephen's Thesaurus Li●guae La●inae, whence he hath borrowed his allegations in adduco; and for the other I had not so much Idle ●ime as to compare them. And lest the fact might be discovered he hath sophi●●icated those Authors whence Stephen citys the expressions, and imposed upon th●m others. If it be not so, o● that the Dr. could not write it right wh●n the c●py was right before him, let him ●ell me where he did ever read in Plautus, adducta res in fastidium. I fin●e the whole se●tence in pliny's preface to Vespas●an (out of whom in t●e precedent Paragraph he citys it) about the ●iddle: alia verò ita multis prodita, ut in factidium sint adducta, which is the very example Stephanus useth, although he doth p●emise his adducta res in fastidium. Let the Dr. tell where he ever did read 〈◊〉 Horace Ova noctuae &c. ●aedium vini adducunt▪ Did he (or any else) with the interposition of an etc) make Trochaicks? I say, and Step●anus says so too, that it is in Pliny lib. 13. cap. 15. near the end; the whole sentence runs thus; Ebriosis Ova noctuae per ●●id●um data in vino, ●aedium ejus adducunt. I doubt not but these are the places he aimed at, although he disguised and min●▪ d the Quotatio●s; if they be not, I should b● glad to augment my Stephanus with his Additions.  
These things pr●mis●d, I come to consider the doctor's proofs: Res eò adducta est: adducta vita in ex●remum: adducta res in fas●idium: rem ad muc●ones & ●…s adducere: contracta res & adducta in a●gus●um: ●es ad concordiam adduci potest: in ordinem adducere: adducere febres, s●●im, taedium vini (all in Robert Stephen) betwixt which and adducere malleum, what a vast difference there is, I leave them to umpire ●…iteretes & religiosas nacti sunt aures▪ who are the competent Judges of Elegancy, and only cast in the verdict of one or two, who are in any place (where the purity of the L●tin ●ongue flourisheth) of great esteem▪ L●saeus in his Scop● Linguae Latinae, ad purgandam Linguam à barbarie, &c. (would any think that the Doctors elegant expression, frequent in all Authors, which none but the malicious or ignorant can deny, should suffer so contumelious an expurgation?) Losaeus (I say) hath these words, Adferre plerique minus attentiutuntur pro adducere. Quod Plautus, in Pseudolo, insigni exem●lo notat. C. Attu●i hunc. P. Quid attulisti? T. Adduxi volui dic●re P▪ Quis istic est? C. Charinus. Satis igitur admonet discriminis inter ducere, reducere, adducere & abducere, quae de pers●nâ; et ●erre, adferre &c. quae de re dicuntur. Idem. Demetrium, quem ego novi, adduce; argentum non mo●or qu●… feras Cavendum igitur est ne vulgi more, (let the Dr. mark this▪ and know that this Author is authentic amongst the Ciceronians) adferre de personâ dicamus, s ●●adducere; licet et hoc de certis quibus●am rebus non ineptè dicatur. In this last clause he ●aith as ●uch as Mr. Hobbes saith, and what the Dr. proves; but th●t ever the Dr. brought an example which might resemble adducis malleum, is denied; for I have mentioned alre●dy his allegations every one, of adduco. Another Author (a fit Antagonist for the elegant Dr.) is the ●arrago ●ordidorum Verborum, ●oyned with the Epitome of L. Valla's elegancies. He saith, Acce●se, adduc Petrum, latinè dicitur pro eo quod pueri dicunt▪ adfer Petrum. And this may suffice to justify Mr. Hobbes' exception, who proceeded no further th●n this Author to tell the Doctor that adduco was used of Animals. But the Dr. replies, this signification is true, but so may the other be also▪ I s●y, if it never have been used so, it cannot be so, for we cannot coin new Latin words, no more than French or Spanish who are foreigners. Mr. Hobbes was upon the negative, and not to disprove the contrary ●p●nion. If the Dr. would be believed, he must prove it by some example (which is all the proof of elegancy) and till he do so, not to beleev● him, it is sufficient not to h●ve cause. But Dr Wallis, why not adduco for a ●ammer as well as a tree? I answer, yes, equally for either, and yet for neither; Did ever anybody go about to mo●k his Reade●s thus solemnly? I do not find, (to my best remembrance) any example of it in S●ephen, and the Dr. is not wiser than his Book; if there be, it is strange the Dr. should omit the only pertinent example, and trouble us with such impertinences for three or four pages. In Stephen there are adducer● habenas and adducere lorum, but in a different sense. It is not impossible I may guess 〈◊〉 the doctor's aim. In Tully de Nat▪ D●or (as I remember) there is this passage; x autem ille respondisset, in agro ambu●anti ra●…ulum adductum, ut remissu● esset, in oculum suum recidisse, where it signifies nothing else but to be bent, bowed, pulled back, and in that sense, the hammer of a Clock▪ or, that of a Smith, when he fetcheth his strok●▪ may be said addu●i. And this I conceive the Doctor would have us in the close think to have been his me●ning; else wh●t doth he drive at in these words? Wh●n you have done the best you can, you will not be able to find better words then adducere mall●um and reduce●…▪ to signify the two contrary motions of the Hammer, the one when you strike with it, (excellently trivial!) The other when you take it back (better and better) What to do? to fetch another stroke. If any can believe that this was his meaning, I shall justify his Latin, but must leave it to him to prove it sense. If he intended no more, why did he go about to defend the other meaning, and never meddle with this? Which yet might have been proved by this one example of mine? May not therefore his own saying be justly retorted upon him in this case, Adducis malleum, us occidas muscam?  
Another exception is▪ Falsae sunt et mult● istiusmodi (propositiones) I wish the Doctor could bring so good Parallels, and so many, out of any Author, for his Adducis malleum, as Tully affords in this case. Take one for all out of the beginning of his Paradoxes; Animadverti saepe Catonem, ●um in senatu sententiam diceret, Locos graves ex Philosophia tractare, abhorrentes ab hoc usu forensi et publico, sed dicendo consequi tamen, ut illa etiam populo pro●abilia viderentur. This is but a Solaecophanes, and h●th▪ many p●●sidents mo●e, as in the second ●ook of his Academical questions, &c.  
I cannot now stay upon each particular p●ssage; I do not see any necessity of tracing the Dr. in all hi● fegaries. Now he dis●llows tanquam diceremus, a● if we should say. But why is that l●ss tolerable than tanquam feceris, as if you had done? It should be quasi (forsooth!) Or ac si, or tanquam si, which is tuli's own word. (What is tanquam si become but one word?) tanquam si tua res agatur &c. Good Dr. leave out Tully and all Ciceronians, or you will for ever suffer for this, and your Adducis malleum. Is not this to put yourself on their verdict, when you oppose Mr. Hobbs with Tully? But the Dr. gives his reason. And though he hath had the luck in his Adducis malleum, to follow the first part of that saying, Loquendum cum vulgo, yet now it is, sentiendum cum sapientibus. For tanquam without si signifies but, a●, not, as if. It is pity the Dr. could not argue in Symbols too, that so we might not understand him, but suppose all his Papers to carry evidence with them, because they are Mathematically scratched. How does he construe this, 
Plance, tu●es alto Drusorum sanguine, tanquam  
Feceris ipse aliquid, propter quod nobilis esses.  So Coelius, one much esteemed by Cicero, who hath inserted his Epistle● into his works, saith in his fifth Epistle (Tul. Epist. sam. lib. 8. Ep▪ 5) Omnia desiderantur ab eo tanquam nihil denegatum sit ei quo mi●us paratissimus esset qui publico negotio pr●positus est. But it was not possible the Dr. should know this, it not being in Stephen, where his examples for tanquam si are.  
But the Dr. having pitched upon this criticism, and penned it, some body, I believe, put him in mind of the absurdity thereof▪ and yet the generous professor (who writes running hand and never tra●scrib●d his papers, if I am not misinformed) presumed nobody else could be more intelligent than he, who had perused Stephen. He would not retract any thing, but subjoins, That he will allow it as passable, because other modern writers, and some of the ancients, have so used it, as Mr. Hobbs hath done. I know not what Authors the Dr. meant, for, if I am not much mistaken, I do not find any in Stephen. His citation of Colum●lla is not right L. 5. cap. 5. (nor can I deduce any thing thence till I have read the passage) but if he take Juvenal and Coelius for modern Authors, I hope he will admit of Accius, N●vius, and Ca●me●ta for the only ancients. Let him think upon this▪ criticism, and never hope pardon for his Adducis malleum, which is not half so well justified, and yet none but mad men or fools reject it.  
But certainly the Dr. should not have made it his business to object Anglicisines, in whose Elench●s I doubt not but there may be found such phrases as may serve to convince him that he is an English man. However Scottified in his principles. If the Dr. doubt of it, or but desire a Catalogue, let him but signify his mind, and he shall be furnished with a Florilegium. But I am now come to the main controversy about Empusa. The Dr. saith nothing in defence of his quibble, nor gives any reason why he jumbled Languages to make a silly clinch, which will not pass for wit either at Oxford, or at Cambridge; no nor at Westmi●ster.  
It seems he had derived Empusa from {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} and {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, and said it was a kind of Hobgoblin that hopped upon one leg; and hence it was that the boys play (Fox come out of thy hole) came to be called Empusa. I suppose he means Ludus Empusae. This derivation he would have to be good, and that we may know his reading (though he hath soarce consulted any of the Authors) he saith Mr. Hobbes did laugh at it, until somebody told him that it was in the Scholiast of Aristophanes (as good a critic as Mr. Hobbes) Eust●thius, Erasmus, Coel●… Rhodiginus, Step●anus, Scapula, and Calepine. But sure he doth not think to scape so. To begin with the last, Calepine doth indeed say, uno incedit pede, unde et non●●n. But he is a modern, and I do not see why his Authority should outweigh mine, if his author's Reasons do not. He refers to Erasmus and Rhodiginus. Erasmus in the adage. Proteo mutabilior, hath these words of Empusa. Narrant autem uno videripedi (this is not to hopp) unde et nomen inditum putant, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. He doth not testify his approbation of the derivation at all, only lets you know what Etymologies some have given before him. And doth anybody think that Dr. Harmar was the first which began to show his wit (or folly) in e●ymologizing words? Coelius Rhodiginus doth not own the derivation, only ●aith Nominis ratio est, ut placet Eustathio, quia uno incedit pede; (is this to hopp?) sed nec desunt qui alterum interpretentur habere ●neum pedem, & inde appella●… Empusath; quod in Batrachis Aristophanes expressit. And then he recites the interpretation that Aristophanes' Scholiast doth give upon the text, of which by and by. If any credit be to be attributed to this allegation, his last thoughts are opposite to Dr. Wallis; and Empusa must be so called, not because she hopped upon one leg, but because she had but one, the other, being brass. But for the former derivation he refers to Eustathius.  
As to Eustathius, I do easily conjecture that the Reader doth believe; that Rodiginus doth mean Eustathius upon Homer, for that is the book of most repute and fame, his other piece being no way considerable for bulk or repute. But it is not that book nor yet his History of Ismenias, but his notes upon the 23 verse of Dionysius {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. The Poet had said of the stone Jaspis, that it was, 
{non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman},   
Upon which Eustathius thus remarks; {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} (fortè {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} Steph.) {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. This testimony doth not prove any thing of hopping, and as to the derivation, I cannot but say that Eustathius had too much of the Grammarian in him, and this is not the first time, neither in this book, nor elsewhere, wherein he hath trifled. It is observable out of the place that there were m●re Empusa's than one, as indeed the name is applied by several men to any kind of▪ frightful phantasm. And so it is used by several Authors, and for as much as phantasms are various, according as the persons affrighted have been severally educated, etc every man did impose this name upon his own apprehensions. This gave men occasion to fain Empusa as such (for who will believe that she was not apprehended as having four legs, when she appeared in the form of a Cow, dog, &c.) but as apprehended by Bacchus and his man at that time. I do not find that she appeared in any shape, but such as made use of legs in going, whence I imagine that Empusae might be opposite to the {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, which appellation was anciently fixed upon the gods (propitious) upon a twofold account, first for that they were usually essigiated as having no feet (which is evident from ancient sculpture) and secondly, for that they are all said not to walk, but rather swim, if I may so express that non gradiuntur, sed fluunt, which is the assertion of all the commentators I have ever seen upon that verse of Virgil, 
Et vera incessu patuit dea—   
This whole discourse may be much illustrated from a Passage in Heliodorus, Aethiop. L. 3. Sect. 12, 13. Calastris told Cnemon that the gods Apollo and Diana did appear unto him, Cnemen replied, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}; upon this the old Priest andswered, that both gods and demons, when they appear to men, may be discovered by the curious observer, both in that they never shut their eyes, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} 
{non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}  
{non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}  {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. Farnaby upon the place in Virgil observes, that, Deorum incessus est continuus & aequalis, non dimotis pedibus, neque transpositis, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. Cernelius Schrevelius in the new Leyden notes, saith, Antiquissima quaeque Deorum simulachra, quod observarunt viri magni, erant {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, dijque ipsi non gradiuntur sed fluunt. Their statues were said to stand rather upon columns then upon legs; for they seem to have been nothing but columns shaped out into this or that figure, the base whereof carrying little of the representation of a foot. These things being premised I suppose it easy for the intelligent Reader to find out the true Etymology of Empus●, quasi {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, or {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} from going on her feet, whereas the other gods and demons had a different gate. If any can dislike this deduction, and think her so named from {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, whereas she always went upon two legs (if her shape permitted it) though she might draw the one after her, as a man doth a wooden leg; I say if any, notwithstanding what hath been said, can join issue with the Doctor, my reply shall be, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}.  
Now as to the words of Aristophanes upon which the Scholiast descants, they are these. Speaking of an Apparition strangely shaped, sometimes like a Camel, sometimes like an ox, a beautiful woman, a dog &c. Bacchus' replies, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. The scholiast hereupon tells us that Empusa was {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} And this is all that is material in the Scholiast, except that he adds by and by, that {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} is all one with the leg of an ass, And this very text and Scholiast is that to which all the Authors he names, and more, do refer.  
I come now to Stephen, who in his Index and in the word {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, gives the derivation of Empusa. {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, gradior, inced●, (not to hop) sic Suidas {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} dictam ait {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. In the Index thus; sunt qui dictam putent {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, quod uno incedat pede, quasi {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, alterum enim pedem aeneum habet. But neither Stephen, nor any else (except Suida●, whom the Hypercritical Dr. had not seen) no not the Scholiast of Aristophanes (a better critic than Mr. Hobbes) doth relate the etymology as their own. Nay, there is not one saith, Empusa hopped on one leg, which is to be proved out of them. The great Etymological Dictionary deriveth it {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, to binder, let &c. its apparition being a token of ill luck. But as to the doctor's deduction, it saith {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. It doth only seem so. And it is strange that {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} should not alter only▪ its aspiration, but change its ν into μ, which I can hardly believe admittable in Greek, lest there should be no difference betwixt its derivatives and those of {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. When I consider the several {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} which the Grecians had, some whereof did fly, some had no legs &c. I can think that the origine of this name may have been thus. Some amazed person saw a spectrum, and giving another notice of it, his companion might answer, it is {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, &c. but he meeting with a new phantasm, cries, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} or {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, for which apprehension of his some body coined this expression of {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. It may also be possibly deduced from {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} might afterwards be reduced to the single term of Empusa. Nor do I much doubt, but that those who are conversant in Languages, and know how that several expressions are often jumbled together to make up one word upon such like cases, will think this a probable origination. I believe then that Mr. Hobbes' friend did never tell him it was in Eustathius, or that Empusa was an hopping phantasm. It had two legs, and went upon both, as a man may upon a wooden leg. {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} is also a name for Lamia, and such was that which Menippus might have married, which I suppose did neither hop nor go upon one leg, for he might have discovered it. But Mr. Hobbes did not except against the derivation (although he might justly, derivations made afterwards carrying more of fancy then of truth, and the Dr. is not excused for asserting what others barely relate, none approve) but asked him, where that is, in what Authors he read that boys play to be so called. To which question the Dr. (to show his reading and the good Authors he is conversant in) replies, In Junius' Nemenclator, Rider and Thomas' Dictionary, sufficient Authors in such a businesss, which methinks no man should say that were near to so copious a Library. It is to be remembered that the trial now is in Westminster School, & amongst Ciceronians, neither whereof will allow those to be sufficient Authors of any Latin word. Alas they are but Vocabularies; and if they bring no Author for their allegation, all that may be allowed them is, that by way of allusion our modern play may be called Ludus Empusae. But that it is so called, we must expect till some Author do give it the name. These are so good Authors that I have not either of them in my Library. But I have taken the pains to consult, first Rider; I looked in him (who was only Author of the English Dictionary) and I could not find any such thing. 'tis true in the Latin Dictionary which is joined with Rider, but made by Holyoke; (O that the Doctor would but mark!) in the Index of obsolete words, there is Ascoliasmus, Ludus Empusae, Fox to thy hole, for which word, not signification, he quoteth Junius. The same is in Yhomasius, who refers to Junius in like manner. But could the Dr. think the word obsolete when the play is still in fashion? Or doth he think that this play is so ancient, as to have had a name so long ago, that it should now be grown obsolete? As for Junius' interpretation of Empusa, it is this, Empusa, spectrum quod se in●elicibus ingerit, uno pede ingredients. Had the Dr. ever read him, he would have quoted him for his derivation of Empusa, I suppose. In Ascoliasmus he saith, Ascoliasinus, Ludus Empusae fit ubi, altero pede in aere librato unico sub●●liunt pede. {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, Pollux. Almanicè. Hinctelen. Belgi●è, Op 〈◊〉 been springhen. Hinctepin●●en Flandris. But what is it in English he doth not tell●, although he doth so in other places often. What the Dr. can pick out of the Dutch I know not; but if that do not justify him, as I think it doth not, he hath wronged 〈◊〉, and grossly imposed upon his Readers.  
But to illustrate this controversy further, I cannot be persuaded the Dr. ever looked into Junius, for if he had, I am confident, according to his wonted accurateness, he would have cited Polluxs's onomasticon into the bargain, for Junius refers to him, and I shall set down his words, that so the Reader may see what Ascoliasmus was, and all the Drs. Authors say Ludus Empusae and Ascoliasmus were one and the same thing. Jul. Pollux, Lib. 9 Cap. 7. {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. (old editions read it {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}) {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. So that Ascoliasmus, and consequently, Ludus Empusae, was a certain sport which consisted in hopping, whether it were by striving who could hop surthest, or whether only one did pursue the rest hopping, and they fled before him on both legs, which game he was to continue till he had caught one of his fellows, or whether it did consist in the boys striving who could hop longest. Or lastly, whether it did consist in hopping upon a certain bladder, which being blown up, and well oiled over, was placed upon the ground for them to hop upon, that so the unctuous bladder might slip from under them and give them a fall. And this is all that Pollux holds forth. Now of all these ways there is none that hath any resemblance with our, Fox to thy hole; but the second: and yet in its description there is no mention of beating him with gloves, as they do now adays, and wherein the play consists as well as in hopping. It might notwithstanding be called Ludus Empusae, but not in any sort our Fox to thy hole, So that the Dr. and his Authors are out; imposing that upon Junius and Pollux, which they never said. And thus much may suffice as to this point. I shall only add out of Meu●…'s Ludi Geaeci, that Ascolia were not Ludus Empus● but Bacchisacra, and he quotes Aristophanes' Scholiasts in Plutus, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. As also Hesychius; {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}.  
But I could have told the Dr. where he might have read of Empusa as being the name of a certain sport or game, and that is, in Tu●nebus adve sar. Lib. 27. Cap. 33 There he speaks of several games mentioned by I●stinian in his C●de, at the latter end of the third book; one of which he takes to be named Empusa; addding with all, that the other are games, it is indisputable, only Empusa, in li●e & causa erit, quod nemo nobis ●a ite ass●… sit Ludum esse, eùm constet spectrum queddam fuisse formas variè mutans. Sed quid vetat eo nomine Ludum fuisse? certè ad vestigia vittatae Scri●… quàm proxin è accedit. Yet ●e only is satisfied in this conjecture, till somebody else shall produce a ●etter. And now what shall I say? was not Turnebus as good a critic, and of as great Bead●…? as Dr. Wall●s? who had read over Pollux, and yet is afraid that nobody will believe 〈◊〉 to have been a game, and all he allegeth for it is, quid vetat? truly all I shall say, and so conclude this business, is, that he had read over an infinity of ●ooks, yet had not had the happiness which the Dr. had, to consult with Junius' Nomenclator, Thom●…us and rider's Dictionary, Authors sufficient in such a case.  
I now come to the Doctors last and greatest triumph, at which I cannot but stand 〈◊〉 admiration, when I consider he hath not got the victory. Had the Dr. been pleased to have conversed with some, of the fift form in Westminster school (for he needed not to have troubled the learned Master) he might have been better informed then to have exposed himself thus.  
Mr. Hobbes had said that {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} signified a mark with a hot iron; upon which saying the Dr. is pleased to play the droll thus, prithee tell me, good Tho▪ before we leave this point. (O the wit of a Divinity Dr.!) who it was told thee that {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} was a mark with an hot iron? for 'tis a notion I never heard till now (and do not believe it yet.) Never believe him again that told thee that lie, for as sure as can be, he did it to abuse thee, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} signifies a distinctive point in writing made with a pen or quill, not a mark made with a hot iron, such as they brand rogues withal; and accordingly {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, distinguo, interstinguo, are often so used. It is also used of a Mathematical point, or somewhat else that is very small, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, a moment, or the like. What should come in your cap, to make you think that {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} signifies a mark or brand with a hot iron? I perceive where the business lies; 'twas {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} ran in your mind when you talked of {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, and because the words are somewhat alike, you jumbled them both together, according to your usual care and accuratenesse, as if they had been the same.  
When I read this, I cannot but be astonished at the doctor's confidence, and applaud him who said, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. That the Dr. should never hear that {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} signifies a mark with a hot iron, is a manifest argument of his ignorance. But that he should advise Mr. H●bbes not to believe his own Readings or any man's else that should tell him it did signify any such thing, is a piece of notorious impudence. That {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} signifies a distinctive point in writing made with a pen or quill, (is a pen one thing and a quill another to write with?) nobody denies. But it must be withal acknowledged it signifies many things else. I know the Dr. is a good Historian (else he should not presume to object the want of History to another) let him tell us how long ago it is, since men have made use of pens or quills in writing; for if that invention be of no long standing; this signification must also be such, and so it could not be that from any ●allusion thereunto the Mathe maticians used it for a point. Another thing I would fain know of this great Historian, how long ago {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} and {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} began to signify inter●ungo? for if the mathematics were studied before the mystery of Printing was found out (as shall be proved when ever it shall please the Dr. out of his no reading to maintain the contrary) than the Mathematical use thereof should have been named before the Grammatical. And if this word be translatitions, and that Sciences were the effect of long contemplation, the names used wherein are borrowed▪ from talk, Mr. Hobbes did well to say that {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} precedaneously to that indivisible signification, which it afterwards had, did signify a visible mark, made by a hot iron, or the like. And in this procedure, he did no more than any man would have done; who considers that all our knowledge proceeds from our senses; as also that words do, primarily, signify things obvious to sense, and only secondarily, such as men call incorporeal. This leads me to a further consideration of this word. Hesychius (of whom it is said that he is Legendus non ●anquam L●xicographus, sed tanquam justus Author.) Interprets {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, which is a point of a greater or lesser size, made with any thing. So {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} signifies to prick or mark with any thing in a●y manner, and hath no impropriated signification in itself, but according to the writer that useth it. Thus in a Grammarian {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} signifies to distinguish by poin●ing often, sometimes, even in them, it is the same with {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, sometimes it signifies to set a ma●k, that something is wanting in that place, which marks were called {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. In matters of policy {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} signifies to disallow, because they used to put a {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} (not {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}) before his name who was either disapproved, or to be mulcted. In punishments it signifies to mark or brand, whereof I cannot at present remember any other ways then that of an hot iron, which is most us●al in Authors, because most practised by the ancients. But that the mark which the Turks●nd others do imprint without burning may be said {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, I do not doubt; no more than that H●rodian did to give that term to the ancient Britain's, of whom he says, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. Thus Horses that were branded with {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} and {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} ({non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} and {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}) were said {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. Thus in its origine {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} doth signifi● a b●end or mark with an hot Iron, ●r the like, and that must be the proper signification of {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, which is proper to {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, none but such as Dr. Wallis●an doubt. In its descendants it is no less evident, for from {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} comes Stigmosus, which signifies to be branded; Vitellianâ cicatrice Stig●●sus not Stigmatosus. So Pliny in his Epistles, as Robert Stephen citys it. And {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} (the Derivative of {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, which signifies any mark, as well as a brand, even such as remain after stripes, being black and blue) was a nickname imposed upon the Grammarian Nicanor, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}▪ And though we had not any examples of {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} being used in this sense, yet from thence for any man to argue against it (but he who knows no more than Stephen tells him) is madness, unless he will deny that any word hath lost its right signification, and is used only (by the Authors we have, although neither the Dr. nor I have read all them) in its analogical signification. I have always been of opinion, that {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} signified a single point, big or little, it matters not; and {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, a composure of many; as {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} signifies a line, and {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} a l●tter, made of several lines. For {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} signified the owl, the S●mana, the letter K, yea whole words, lines, Epigrams engraven in men's faces; and {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, I doubt not, had signified a single point, had such been used, and so it became translatitiously used by Grammarians and Mathematicians. I could give grounds for this conjecture, and not be so impertinent as the Doctor in his Sermon (where he told men that {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} was not in Homer; that from {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} came Ebrius; that Sobrietas was not bad Latin, and that Sobrius was once (as I remember) in Tully. Is this to speak suitably to the oracles of God, or rather to lash out into idle words? Hath the Dr. any ground to think these are not impertinences? Or are we, poor mortals, accountable for such idle words as fall from us in private discourses, whilst these ambassadors of Heaven droll in the Pulpit without any danger of an after reckoning?  
But I proceed to a further survey of the Doctors intolerable ignorance. His charge in the end of the School▪ Masters Rant, is, that he should remember {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} & {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} are not all one. I complained before that he hath not cited Robert Stephen aright, now I must tell him he hath been negligent in the reading of Henry Stephen; for in him he might have found that {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} was sometimes all one with {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} though there be no example in him wherein {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} is ●sed for {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. Hath not Hes●od (as Stephen rightly citeth it) in his S●u●um.  
{non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} ubi scholiasts; {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. So Johannes Di●conus upon the place, a man, who (if I may use the Drs. phrase) was as good a critic, as the Geometry professor.  
Thus much for the Doctor. To the understanding Reader, I say, that {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} is ●sed for burning with a hot iron; 〈◊〉▪ Macchab. 9 11. where speaking of Antiochus lamentable death, his body putrifying, and breeding worms, he is said {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}; being pained as if he had been pricked, or burned with hot ir●ns. And that this is the meaning of that elegant writer, shall be made good against the Doct●r, when he shall please to defend the vulgar Interpretation▪ Pausanias, in Baeoticis, speaking of Epaminondas, who had taken a town belonging to the Sicyonians called Phaebia ({non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}) wherein were many Baeotian fugitives, who ought by Law to have been put to death, saith, he dismissed them under other names, giving them only a brand or mark {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. It is true {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} is here put adverbially, but that doth not alter the case. Again Zonaras, in the third ●ome of his History, in the l●fe of the Emperor Th●ophilus, saith, that when Theophanes and another Monk had reproved the said Emperor for demolishing images, he took and s●igmatised each of them with twelve iambics in their faces. {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. A place so evident, that I know not what the Dr. can reply. This place is just parallel to what the same Author saith in the li●e of Irene, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. If the Dr. object that he is a modern Author, he will never be able to render him as inconsiderable as Adrianus Junius' Nomenclator, Th●mafius and Rider. If any will deny that he writes good Greek, Hieronymus W●lfius will tell them, his only fault is, {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, redundancy in words, and not the use of bad ones.  
Another example of {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} used in this sense, is in the Collections out of Diodorus Siculus lib. 34. as they are to be found at the end of his works, and as Photius hath transcr●bed them into his Bibliotheca. He ●aith that the Romans did buy multitudes of servants and employ them in Sicily; {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}. These are the words but of one Author, but aught to pass for the judgement of two, seeing Photius, by inserting them, hath made them his own.  
Besides, it is the judgement of a great Master of the Greek tongue, that stigmata non tam puncta ipsa qudm punctis variatam super●●ciem Gr●ci vocaverun●: I need not I suppose, name him, so gre●t a critic as the Dr. cannot be ignorant of him.  
Nor were {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} commonly, but upon extraordinary occasions, imprinted with an hot iron. The letters were first made by incision, than the blood pressed, and the place filled up with ink, the composition whereof is to be seen in Ae●ius. And thus they did use to matriculate soldiers also in the hand. Thus did the Grecian Emperor in the precedent example of Zonaras. And if the Dr. would more, let him repair to Vin●tas's Comment upon the fifteenth Epigram of Ausonius.  
And now I conceive enough hath hath been said to vindicate Mr. Hobbes, and to show the insufferable ignorance of the puny professor, and unlearned critic. If any more shall be though● necessary, I shall take the pains to collect more examples and Authorities, though I confess I had rather spend time otherwise then in matter of so little moment. As for some other pssages in his book, I am no competent judge of symbolic Stenography. The Dr. (Sir Reverence) might have used a cleanlier expression than that of a s●itten piece, when he censures Mr. Hobbes' Book.  
Hitherto the letter. By which you may see what came in to my (not square) cap to call {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} a mark with a hot iron, and that, they who told me that, did no more tell me a lie than they told you a lie that said the same of {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}; and if {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} be not right as I use it now, ●hen call these notes not {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman}, but {non-Roman} {non-Roman} {non-Roman} {non-Roman} {non-Roman} I will not contend with you for a tris●e. For howsoever you call them you are like to be known by them. Sir, the▪ calling of a Divine hath justly taken from you some time that might have been employed in Geometry. The study of Algebra hath taken from you another part, for Algebra and Geometry are not all one; and you have cast away much time in practising and trusting to Symbolical writ writings, and for the Authors of Geometry you have read, you have not examined their demonstrations to the bottom. Therefore you perhaps may be, but are not yet 〈◊〉 Geometrician, much less a good Divine. I would you had but so much ethics, as to be civil. But you are a notable critic So fare you well, and consider what honour you do either to the University where you are received for professor, or to the university from whence you came thither, by your Geometry; and what honour you do to Emanuel college by your Divinity; and what honour you do to the degree of Dr. with the manner of your Language. And take the counsel which you publish out of your Encomiast his letter; think me no more worthy of your pains, you see how I have ●ouled your fingers.  
FINIS.