Of Number and Magnitude

First we will consider of number, and of the science mathematical appropriate to it, called Arithmetic: and afterward of magnitude, and its science, called geometry. But that name does not content me; of which a word or two shall be said hereafter. How immaterial and free from all matter Number is, who does not perceive? Indeed, who does not wonder at it greatly? For neither pure Element, nor Aristotle's Fifth Essence, is able to serve as the proper matter of Number. Nor yet will the purity and simplicity of Spiritual or Angelic Substance be found proper enough for it. And therefore the great and godly philosopher Anitius Boetius said: All things (which from the very first original being of things have been framed and made) do appear to be formed by the reason of Numbers. For this was the principal example or pattern in the mind of the Creator. O comfortable allurement, O ravishing persuasion, to deal with a Science whose Subject is so Ancient, so pure, so excellent, so surpassing all creatures, so used by the Almighty and incomprehensible wisdom of the Creator in the distinct creation of all creatures: in all their distinct parts, properties, natures, and virtues, by order and most absolute number, brought from Nothing to the formality of their being and state. By the property of numbers, therefore, learned by us by all possible means (to the perfection of the Science), we may both wind and draw ourselves into the inward and deep search and view of all creatures' distinct virtues, natures, properties, and forms; and also arise further, climb, ascend, and mount up (with speculative wings) in spirit to see in the Glass of Creation the Form of Forms, the Exemplar Number of all things numerable, both visible and invisible, mortal and immortal, corporeal and spiritual. Part of this profound and divine Science had Joachim the prophet attained: by Formal, Natural, and Rational Numbers, foreseeing, concluding, and foretelling great particular events long before their coming. His books yet remaining are good proof of this; and the noble Earl of Mirandula, besides that, a sufficient witness that Joachim in his prophecies proceeded by no other way than by Formal Numbers. And this Earl himself, in Rome,

(A.D. 1488.)

* set up 900 Conclusions, in all kinds of sciences, openly to be disputed; and among the rest, in his Mathematical Conclusions (in the eleventh Conclusion) he has in Latin this English sentence: By Numbers, a way is had to the searching out and understanding of every thing able to be known. For the verifying of which Conclusion, I promise to answer the 74 questions written below by the way of Numbers. Which Conclusions I omit here to rehearse: as well avoiding superfluous prolixity, as because the works of Joannes Picus are commonly available. But in any case I would wish that those Conclusions were read diligently and understood by such as are earnest observers and considerers of the constant law of numbers, which is planted in natural and supernatural things, and is prescribed to all creatures inviolably to be kept. For so, besides many other things in those Conclusions to be marked, it would appear how sincerely, and within my bounds, I disclose the wonderful mysteries to be attained by numbers.

Of my former words it is easy to gather that Number has a triple state: one in the Creator; another in every creature (in respect of its complete constitution); and the third in Spiritual and Angelic Minds, and in the Soul of man. In the first and third state Number is termed Number Numbering. But in all creatures otherwise, Number is termed Number Numbered. And in our Soul Number bears such sway, and has such affinity with it, that some of the old philosophers taught the human Soul to be a self-moving Number. And indeed in us, though it is a mere accident, yet such an accident is it that before all creatures it had perfect being in the Creator, eternally. Number Numbering, therefore, is the discretion that discerns and distinguishes things. But in God the Creator this discretion in the beginning produced all things orderly and distinctly. For his Numbering then was his Creating of all things. And his continual Numbering of all things is the conservation of them in being; and where and when he will lack a Unit, there and then that particular thing shall be discreated. Here I stop. But our separating, distinguishing, and Numbering creates nothing; of Multitude considered it makes a certain and distinct determination. And although these things are weighty and truths of great importance, yet (by the infinite goodness of the Almighty Ternary) artificial methods and easy ways are made by which the zealous philosopher may come near this Ida of many rivers, this Mountain of Contemplation, and more than Contemplation. And also, though Number be a thing so immaterial, so divine, and eternal, yet by degrees, little by little, stretching forth and applying some likeness of it — first to spiritual things, then bringing it lower to things sensibly perceived, as of a momentary sound repeated, then to the least things that may be seen, numerable, and at length (most grossly) to a multitude of any corporeal things seen or felt — and so from these gross and sensible things we are trained to learn a certain image or likeness of numbers, and to use art in them to our pleasure and profit. So gross is our conversation, and dull our apprehension, while mortal Sense in us rules the commonwealth of our little world. By this we say, Three lions are three, or a ternary. Three eagles are three, or a ternary.

(☞)

Which * ternaries are each the union, knot, and uniformity of three discrete and distinct units. That is, we may in each ternary thrice separately point out and show a part: One, One, and One. Where in numbering we say One, two, Three. But how far these visible Ones differ from our indivisible Units (principally considered in pure arithmetic) no one is ignorant. Yet from these gross and material things may we be led upward by degrees, so informing our rude imagination toward the conceiving of Numbers absolutely — not supposing, nor admixing any created thing, corporeal or spiritual, to support, contain, or represent those Numbers imagined — that at length we may be able to find the number of our own name gloriously exemplified and registered in the book of the Trinity most blessed and eternal.

But further understand that vulgar practitioners have Numbers otherwise in sundry considerations, and extend their name further than to Numbers whose least part is a Unit. For the common accountant, reckoning master, or arithmetician, in his using of Numbers, imagines lesser parts of a Unit, and calls them Fractions. As of a Unit he makes a half, and thus notes it, ½; and so of other (infinitely diverse) parts of a Unit. Indeed he further has fractions of fractions, etc.

First we will consider number, and the mathematical science proper to it, called Arithmetic; and afterward of magnitude, and its science, called geometry. But that name does not satisfy me; a word or two about that will come later. How immaterial and free from all matter number is, who does not perceive it? Yes, who does not marvel at it? For neither pure element, nor Aristotle's quintessence, can serve as the proper matter of number. Nor will the purity and simplicity of a Spiritual or Angelic Substance be found proper enough for it. And therefore the great and godly philosopher Anitius Boetius said: All things (which from the very first original being of things have been framed and made) appear to be formed by the reason of Numbers. For this was the principal example or pattern in the mind of the Creator. What a comfort, what a rapture, to deal with a Science whose Subject is so ancient, so pure, so excellent, so far above all creatures, and so used by the almighty and incomprehensible wisdom of the Creator in the distinct creation of all creatures: in all their distinct parts, properties, natures, and virtues, brought by order and the most absolute number, from Nothing, to the form of their being and state. Therefore, learning the property of Numbers by every possible means (to the perfection of the Science), we may both wind and draw ourselves into the inward and deep search and view of all creatures' distinct virtues, natures, properties, and Forms; and also further arise, climb, ascend and mount up (with speculative wings) in spirit, to see in the mirror of creation the Form of Forms, the model Number of all things numerable: both visible and invisible, mortal and immortal, bodily and spiritual. Part of this profound and divine Science the prophet Joachim had attained: by Formal, Natural and Rational Numbers, foreseeing, concluding and foretelling great particular events long before they came. His books still remaining are good proof of this; and the noble Earl of Mirandula (besides that) is a sufficient witness that Joachim, in his prophecies, proceeded by no other way than by Formal Numbers. And this Earl himself, in Rome,

In the year 1488.

He set up 900 conclusions in all kinds of sciences, openly to be disputed, and among the rest, in his Mathematical Conclusions (in the eleventh Conclusion) he has in Latin this English sentence: "By Numbers, a way is had to the searching out and understanding of every thing able to be known." To verify which Conclusion, I promise to answer the 74 questions written below by the way of Numbers. Which Conclusions I omit here to repeat, both to avoid needless length and because the works of Ioannes Picus are commonly available. But in any case I would wish that those Conclusions were read carefully and understood by such as are earnest observers and considerers of the constant law of numbers, which is planted in natural and supernatural things, and is prescribed to all creatures to be kept inviolably. For so, besides many other things to be noted in those Conclusions, it would appear how sincerely, and within my bounds, I disclose the wonderful mysteries to be attained by numbers.

From my earlier words it is easy to gather that Number has a threefold state: one in the Creator, another in every Creature (in respect of its complete constitution), and the third in Spiritual and Angelic Minds and in the Soul of man. In the first and third state, Number is called Number Numbering. But in all Creatures, otherwise, Number is called Number Numbered. And in our Soul, Number holds such sway and has such an affinity with it that some of the old Philosophers taught that the human Soul is a Number moving itself. And indeed, in us, though it is only an accident, yet it is such an accident that before all Creatures it had perfect being in the Creator, eternally. Number Numbering, then, is the discretion that discerns and distinguishes things. But in God the Creator this discretion, in the beginning, produced all things orderly and distinctly. For his Numbering then was his Creating of all things. And his continual Numbering of all things is their conservation in being; and wherever and whenever he will lack a Unit, there and then that particular thing will be uncreated. Here I stop. But our separating, distinguishing, and Numbering creates nothing; of Multitude considered it makes a certain and distinct determination. And although these things are weighty truths of great importance, yet (by the infinite goodness of the Almighty Ternary) Artificial Methods and easy ways are made by which the zealous Philosopher may draw near to this river-rich Ida, this Mountain of Contemplation, and more than Contemplation. And also, though Number is a thing so immaterial, so divine, and eternal, yet by degrees, little by little, stretching forth and applying some likeness of it—first to Spiritual things; then bringing it lower to things sensibly perceived, such as a momentary sound repeated; then to the smallest things that can be seen and numbered; and at length (most coarsely) to a multitude of any bodily things seen or felt—so from these coarse and sensible things we are trained to learn a certain Image or likeness of numbers, and to use Art in them for our pleasure and profit. So coarse is our dealing and dull our apprehension, while mortal Sense rules the commonwealth of our little world. By this we say, three lions are three, or a Ternary. Three eagles are three, or a Ternary.

Note this.

Such Ternaries are each the Union, knot, and Uniformity of three separate and distinct Units. That is, in each Ternary we can three times separately point out and show a part: One, One, and One. Whereas in Numbering we say One, two, Three. But how far these visible Ones differ from our Indivisible Units (principally considered in pure arithmetic) no one is ignorant. Yet from these coarse and material things we may be led upward, degree by degree, training our crude imagination toward the conceiving of Numbers absolutely (supposing no created thing, bodily or spiritual, to support, contain, or represent those Numbers imagined), that at length we may be able to find the number of our own name, gloriously exemplified and registered in the book of the most blessed and eternal Trinity.

But further understand that ordinary practitioners consider Numbers in various other ways, and extend the name further than to Numbers whose least part is a Unit. For the common reckoner, master of accounts, or arithmetician, in his use of Numbers, imagines parts smaller than a Unit and calls them Fractions. From a Unit he makes a half, and notes it thus, ½, and so of other (infinitely various) parts of a Unit. And further, he has Fractions of Fractions, etc.