THE two Correspondents having provided themselves with a sufficient number of printed Papers delineated and shadow'd conveniently for the purpose:

1. They must first of all by a mutual consent, compleat their Numerical Alphabet and Clavis Ʋniver­salis, in like manner as is done Page 5. placing in the Numerical Alphabet what Letters they please, (some Capitall, others small) from an Unite to 34. and transposing the Numbers contained in each Marginal Number of the Clavis Universalis, in any broken Order whatsoever, each of them reserving a Copy.

2. They must agree in what kind of Figure to write to each other; For by those few Schemes, Page 2, & 3. it is e­vident, that the various Figures, in which any Writing of a considerable length may be inscribed, are very numerous.

3. They are to resolve what Number of Nulls they will either prefix, adjoyn, or intermingle with that Writing; and where those Nulls shall be placed.

4. It is necessary to be concluded, whether they will transcribe what they intend to Conceal, in Upright Columns, or else by way of Diagonalls, or otherwise? as likewise whether the Transcription shall be ascending, descending, Alternate, or Retrograde?

An Example or two will clear all Doubts.

Let A. and B. be Two Correspondents:

• 1. Let their Numerical Alphabet, and Clavis Universalis, be the same with that Pag. 5.
• 2. Let it be agreed between them, to write to each other in a Parallelogram, such as is Pag. 2. Fig. I.
• 3. Let the Number of Nulls before the Writing be evermore 3, and after the Writing 4.
• 4. Let the way of Transcription be in Upright Columnes, and descending.

This done, A. writes to B. the following words: viz. This Way of Writing is of all other the most facil and expeditious, as well to unlock, as to conceale.

Scriptio Cryptographica.

State cauti, cras horâ decimâ noctis venient h [...]stes, ut invadant Urbem

Various Methods of Transcribing the Words conteyn'd in Fig. I. Pag. 2.

The First Method reads and transcribes the Writing (as before, Pag. 1.) in Upright Columnes, and descending according to the Numerical Alphabet, and the Clavis Ʋniversalis.

The 2^d Method reads and transcribes it in Upright Columnes, ascending.

The 3^d Method reads and transcribes it in Upright Columnes, descending and ascending, alternately.

The 4^th Method reads and transcribes it in Ʋpright Columnes, ascending and descending alternately.

The 5^th Method reads and transcribes it in Upright Columnes, and descending, (and that in their natural Order, as like­wise do all the following Methods!) not respecting the Numerical Alphabet, or Clavis Ʋniversalis.

The 6^th Method reads and transcribes it in Upright Columnes, ascending.

The 7^th Method reads and transcribes Fig. I. in Diagonal Lines, and descending, beginning with the first Letter [T] in the Dexter Poynt.

The 8^th Method reads and transcribes Fig. I. in Diagonal Lines, and ascending, beginning with the the same Letter [T] in the Dexter Poynt of the Figure.

The 9^th Method reads and transcribes Fig. I. in Diagonal Lines descending, and ascending alternately, from the same Letter [T.]

The 10th Method reads and transcribes Fig. I. in Diagonal Lines, ascending and descending alternately, from the same Letter [T.]

By these few Methods of transcribing this first Figure, the Ingenious and learned Reader will easily perceive, that it may yet be read and transcribed in a very great number of other different wayes and Methods, and that without altering the Transpositions of the 9 Columnes. Now, if this first Figure afford such variety of Transcriptions without new Transpositions, the other different Figures afford each of them as many more; And by the Clavis Universalis, Pag. 5. composed from the Table of Permutation, Pag. 7. it is evident, that every such Figure containing but 9 Columnes, admits of no less than Three Hundred Sixty two Thousand, eight Hundred and eighty different Tran­spositions; And others of them, as Fig. VI. and VII. containing 18 Columnes, admit of Six Thousand four Hun­dred and two Millions of Millions, of different Transpositions; More by Three Hundred seventy three Thousand, seven Hundred and five Millions; More by Seven Hundred twenty and eight Thousand; And there being in the Writing 81 Letters, they make an Oblong containing 27 Columnes and three Lines; And consequently such a Figure will admit of 10888869450418352160768000000 distinct Transpositions.

But forasmuch as Examples edifie the Reader much better than bare Words, I have in the 6th Page inserted a longer Writing than the former, in a plain Parallelogram, consisting of 34 Upright Columnes, and containing 20 Lines, excepting onely 2 Nulls at the latter end to compleat the Figure.

The Words of the Writing are in French, viz.

Thus is written, what is to be hidden.

Thus, by a bare Transposition (together with a few Nulls,) is hidden, what is above written.

Thus, by the help of the Clavis Universalis, and Numerical Alphabet, a bare Transcription discovers what was hidden.

I Am not ignorant that there are some Virtuosi of this Saeculum, who vainly perswade others, and (I believe!) deceive themselves, by pretending that they are able, by I know not what Analytick Art, to unfold all Myste­ries of this nature whatsoever, and that no Secret can be made so to wander in any Paper-Labyrinth, But they will finde an Ariadnian Clue to trace it in, and fetch it out.

I must confess, as to the ordinary Methods of Cryptography, (vulgarly termed Writing in Cypher) where they are weakly contrived, or carelesly written, it's very possible, with much pains and industry, to gather the Contents; (I have often done it my self, and seen it done by others!) But where a Cypher is dexterously composed, and made use of warily, There let any such Pretender shew his ability in making the least discovery, —& erit mihi Magnus Apollo!) In the mean time, if he please, he may contemplate the following Reflections upon the foregoing Method.

• 1. The foregoing Method is comparatively with others, wonderfully facil and practicable, forasmuch as it re­quires very little more pains than a double Transcription of the Letter to be written, (which is no more than what all States-men do, whether they write in Cypher or no!) And to uncypher or open, one single Transcription do's the Business.
• 2. Let him consider in how many Parallelograms, Triangles, and other mixt Figures, any Writing may be inscribed.
• 3. The various wayes, windings, and turnings by which any Writing may be transcribed out of any such Figures.
• 4. The many places each Line affords for inscribing Nulls, besides the beginning, and latter end; as likewise whole Columnes, which may, by a private accord, be reserved.
• 5. Into how many Millions of Millions, of Millions, of Millions, of Millions, of Millions, of distinct Orders, both the Numerical Alphabet, and Marginal Numbers of the Classis Universalis, may be transposed, as in the following Table; for an Explanation whereof, I refer the Reader to Clavius, Kircherus, and others.

Learned Tacquet in his Arithmetick, lib. 5. c. 8. affirmes, That the Permutations of 24 Letters are so nume­rous, that a Thousand Millions of able Clerks, in a Thousand Millions of Years, (and that neither sparing Dominicals or Festivals) were not able to transcribe them! And Guldinus asserts, That the Books which might be compiled of the variety of 23 Letters onely (accounting 500 Pages, or 1000 Faces to each Volumne, and 100 Lines to each Face, and 60 Letters to each Line, and not any two Words in any of those Volumnes the same!) would do more than twice cover the whole Superficies of the Earth and Sea. Nay further, he seems to be of opinion, That the Paper of those Volumnes, laid singly Sheet by Sheet, would cover the very Firmament. Now, if the Transpo­sitions of 24 Letters be so numerous, what are those of 34 (which are yet of greatest use in this Method)? The last Sum of the foregoing Table is a Number consisting of 39 Places, and that for the bare Transpositions of 34 Let­ters or Numbers: But when each of those shall come to be altered, intermingled with, and transformed by all the various Figures of Inscription, Methods of Transcription, and Nulls; I am bold to assert, that the Sum. Tot. would be greater than that of Archimedes in his ΨΑΜΜΙΤΗΣ, whereby he would express the Number of Sands, which would do more than fill the cavity of a Sphere equal to the Orb of the Fixed Stars, according to the dimensions of the Coelestial Bodies determined by Aristarchus Samius.

To apply this more closely to the purpose, suppose the Writing, as it layes hid Page 6. were given to the ablest Cryptograph-Analyst in the World, to open, or Uncypher; and grant that he knew, that it was written according to some of the Rules of the foregoing Method.

1. It is impossible for him to divine the Number of Nulls, or where they are placed.

2. It's as impossible (without being privy to the Numerical Alphabet) to know certainly how many Columnes, or how many Lines this Writing consists of, or where those Indicial Letters are placed.

3. Admit he should (which is never to be imagined!) accidentally guess at the Number of Columnes, Lines, Nulls, and Indicial Letters; yet still he is to seek in what Figure it is inscribed, that is to say, whether in a Parallelo­gram, Triangle, Trapezium, Rhomboides, Polygon Simple, Polygon Central, or some other mixt Figure, or Figures?

4. Put case he knew that it was (as it is) in a Parallelogram; He is but little nearer his ends than before, unless he knew whether the Transcription were in Upright Columnes, or Diagonalls? And that Descending, Ascending, or Retrograde? Or whether in Circular, Serpentine, or Horizontal Lines?

5. But imagin he had all these: As likewise that he knew in what Language it were written, (for that also is no small Difficulty!) He has yet another Task, which is, to finde out the true Transpositions of these 34 Columnes, by often trying, and comparing Columnes with Columnes; where there are no less than 295288899039603018847618609643519999999 false wayes, and but onely one, which is exactly true. Now how any Mortal should hope in all his life time, (were he sure to live Quadrillions of Trillions, of Billions of Methusalem's years!) to hit upon so many Heterogeneous Quasita mentioned in the Premises, for which he has in a manner no Data, it cannot enter into my Understanding. And I leave the Ingenious Reader to Judge, whether the rolling of Sicyphus his Stone up the Hill, be not a Labour as likely to succeed as His? But if all this will not satisfie, Then let such a Pretender give me leave to lead him yet a Step further, where he will quickly see, what false footing all his Zetetick and Analytick devices are like to finde upon these Steganographical Quicksands: And that it will be as easie for him to discover the way of an Eagle in the Ayre, and to mark out precisely, where that subtil Element has been devided and closed up again; as to trace a Secret through all the turnings, windings, and dark Passages of so many Cryptographical Maeanders, Unless he work (and that most profoundly!) by the Black Art, or else an Angel from Heaven, in kindness, reveal it to him.

CRYPTOGRAPHIA CRYPTOGRAPHICA duplex, triplex, quadruplex, &c. in infinitum.

LET the Correspondents A. and B. mutually agree, in all Matters of great importance, to write to each other by a Cryptographia Cryptographica Quadrupla, for which they have some private Mark. And suppose A. desire to send B. the following Intelligence:

1. It is accorded between them, that whatsoever they write, must be inscribed in 4 distinct Figures: the first whereof is to be a Rectangle Parallelogram, as Pag. 9. Fig. 1. The 2^d Figure a Rhomboides, as Pag. 9. Fig. 2. The 3^d a Rectangle Triangle, as Pag. 10. Fig. 3. And the 4^th a Trapezium, as Pag. 10. Fig. 4.

2. These 4 Figures are to be inscribed, and read as follows:

The First Figure is to be inscribed in Horizontal Lines, and to be read in Upright Columnes, and descending (ac­cording to the foregoing Precept) by the Numerical Alphabet, and Clavis Universalis. The Second Figure is likewise to be inscribed in Horizontal Lines, and to be read in Upright Columnes; that is to say, The first Upright Co­lumne of the First Figure, makes the first Horizontal Line of the Second Figure. And so the second Upright Co­lumne of the First Figure, makes the second Horizontal Line of the Second Figure; And so all the Columnes of the First Figure is to be inscribed into the Second Figure one after the other in their Order.

The Third Figure is to be inscribed in Horizontal Lines, that is, The first Upright Columne of the Second Figure makes as many, or as few Horizontal Lines of the Third Figure, as it falls out to be longer or shorter, (beginning with the Vertex or Rectangle of the Third Figure.) Thus of (o r n u s e e) the first Letter (o) makes the first Horizontal Line of the Third Figure; and (r n u) make the second; and (see) make a part of the Third, which (i r) the two first Letters of the second Upright Columne of the Second Figure make good; And the fol­lowing Letters (s C D e o o s) make the fourth Horizontal Line; And so on, till the Third Figure be fully compleated.

But now the Third Figure is to be read, (not in Upright Columnes, but) in Diagonal Lines, according to the follow­ing Method, That is to say, Beginning with the Diagonal Line (r b e t t n y, &c.) from Numb. (1) under the Hypo­tenuse of the Figure; And so ascending to the Letter (o) at the Vertex, and from thence descending to (a) which answers to Numb. (2); Then again beginning with the Letters (n n e e t y, &c.) of the Diagonal Line answering to Numb. (3) and ascending to (n) in the Angle, and from thence descending to the Letter (i) which answers to Numb. (4). Then repeating the same Thing from Numb. (5) to Numb. (6), Then from Numb. (7) to Numb. (8); And so on, till the Figure be as it were wound off to nothing.

The Fourth and last Figure is to be inscribed in Alternate Diagonals, Thus, namely of the Letters [r b e u t n y s s r o] of the first Diagonal Line of the third Figure, A. places the first Letter [r] in the Dexter Poynt of the fourth Figure. Then, leaving the two next Squares voyd, he fills the third Diagonal with the 3 next Letters [b e u] After which he leaves another Diagonal voyd, and the fourth Diagonal he fills with the Letters [t n u s s] And so he proceeds, till the whole Writing be inscribed.

This done, A. might fill the voyd Diagonals with Nulls; But supposing him to be in the Enemies Countrey, and fearing his Letter may fall into their hands, and he be constrained to open the Writing, he fills the voyd Diagonals with another Discourse altogether different from the former, viz.

After which Writing he puts six Nulls [p l s a d d] to fill up all. But of this more at large in the Method of Opening, or Discovering the forementioned Intelligence.

3. This fourth Figure is to be read in Ʋpright Columnes, according to the foregoing Method, by the Numerical Alphabet, and Clavis Ʋniversalis, and so transcribed fairly, as it ought to be sent to B. leaving onely room for 13 Letters at the beginning of the second Line.

4. Of the 13 Letters at the beginning of the 2^d Line (which are to serve for Indices, or Exponents!) the first three serve to expound the first Inscription or Figure, the three next, the second Figure; the three following serve for the third Figure, and the last three for the fourth: That is to say,

The first Letter [T] gives B. to understand, that the first Figure consists of 10 Columnes; The next Letter [f], that there are in it just 11 Lines; The third Letter [d], that there are two Nulls to compleat the Figure.

The fourth, fifth, and sixth Letters [k T s] let B. know, that the second Figure has 20 Columnes, 10 Lines, and no Nulls to compleat it. For [s] and all other Letters that are not found in the Numerical Alphabet, may be used at pleasure, to signifie Negatives; as here [s] signifies that there are no Nulls to compleat the second Figure.

The seventh, eighth, and ninth signifie, that the Base of the third Figure contains 21 Places, the Lines there­of are eleven, and the Nulls to lengthen out the last Line eleven, viz. [s p k m d a s w x n a.]

The tenth, eleventh, and twelfth denote, that the Columnes of the fourth Figure are 27, the Lines 11, and the Nulls 3. viz. [n f n.] And the thirteenth and last Letter [G] serves to inform B. that there are 6 Nulls at the latter end of the Writing, as A. sends it to him. All which may be seen by the respective Figures, in which are the 4 Transcriptions.

The Writing, as it is sent to B.

s e l r o n r F t o o s o t e n n n u m x r r k b e t c m l d r u i i s l o u b a n D e n l u e i n y A w y p c r i p a l H E u b r y I s T f d k T s p f f H f n G i n r e i i A l i d a p r e u o s o e t e t h r o d o i o e a t a u y n o d s h t t s o h y c o a t y e o n e e d T r n o y i r a n n r l n e C s d x D e C s d t t e A z l c t l a d a e r r n n S S v k f o c l l l o o a f l y u i A o g f s h s t i u a a d e g e E W A e f g e F o s s i e B S n m l o t o d e o n e t e a e n e W o L h d i e u m s p w o n k.

The Method of Discovering what is before, by a Quadruple Inscription, hidden.

1. WHen B. receives the Writing, The first thing he do's, is to draw a Line under, or to put some other Mark of distinction upon the 13 first Letters of the 2^d Line of the said Writing, which he knows to be Indices of the 4 Figures.

2. That done, by the 10^th and 11^th of those Letters, [H f] he marks with pricks, as here underneath is exprest, the first Figure of Transcription, (which by the forementioned Accord, he knows to be a Trapezium!) And then tran­scribes the Writing into that Figure, till it be compleated; as it is, Pag. 10. Fig. 4. omitting onely a certain Num­ber of Nulls, which are easily known by the 13^th and last of those Indices, viz. [G]

3. In the next place, he dashes out all the alternate Diagonal Lines of that Figure, commencing from the Letter [r] in the Dexter Poynt of the Figure exclusivè, which by the same private Agreement were destin'd for Nulls, (or at least for Disguises) And then transcribes the remainder into a Rectangle-Triangle, of whose Height and Hypotenuse, the 7^th and 8^th Letters of the 2^d Line of the Writing, are sufficient Indices, onely a certain Number of Nulls, denoted by the 12^th Index, viz. [n] are omitted.

In the 4^th place, having, by the 4^th and 5^th Indices, with poynts or pricks, determined by limits, the 3^d Figure of Transcription (which he knows is a Rhomboides) he fills and compleats it out of the Rectangle-Triangle, omit­ting onely so many Letters for Nulls, as [f] the 9^th Letter of that 2^d Line, indigates.

Lastly, By the first, 2^d, 3^d, and 6^th Letters, he determines and fills the 4^th and last Figure of Transcription, (which was the first Figure of Inscription) and consequently he has before his eyes what he sought for, which I do not believe the Understanding of any Mortal man were, by any other means than by being privy to the forementioned Accord, ever able to discover.

I have here underneath inserted the Scheme of that first Figure of Transcription, (or 4^th Figure of Inscription,) that so by it, the Reader may plainly discern the manner of performing all the rest.