Unit IV — The Infinite Line as Universal Measure & the Infinite Sphere Where Center, Diameter and Circumference Coincide¶
De Docta Ignorantia · Liber I, Capitula XVI–XXIII (1440)
Patet ergo centrum, diametrum et circumferentiam idem esse. Ex quo docetur ignorantia nostra incomprehensibile maximum esse, cui minimum non opponitur; sed centrum est in ipso circumferentia.
Clearly, therefore, center, diameter, and circumference are identical; thereby our ignorance is taught that the incomprehensible Maximum is that to which the Minimum is not opposed, and that within it the center is the circumference. — De Docta Ignorantia I.21 §3
Book I, Chapter 16 — How Metaphorically the Maximum Stands to All Things as the Maximal Line Stands to Lines¶
Original GEOMETOR Translation from the Latin · h I, nn. 42–46 · Paris 1514 fol. 6r–6v · Rotta 1913 pp. 32–35
Now that it is manifest how the infinite line is infinitely in act all those things that lie in the potency of a finite line, by transfer we grasp in like manner within the Simple Maximum how the Maximum itself is maximally in act all those things that stand in the potency of absolute simplicity. For whatsoever is possible, that the Maximum itself is maximally in act—not as arising out of the possible, but inasmuch as it maximally is; just as a triangle is drawn forth from a finite line, whereas the infinite line is not a triangle as drawn forth from a finite one, but is in act an infinite triangle identical with the line. Moreover, absolute possibility itself is nothing other in the Maximum than the Maximum itself in act, just as the infinite line is in act a sphere. In what is not maximal the case is otherwise; for there potency is not act, just as a finite line is not a triangle.
Hence we behold here the great speculation that can be drawn from this concerning the Maximum: namely, that it is of such nature that the Minimum within it is the Maximum, so that it utterly surpasses every opposition by infinity. From this principle as many negative truths could be drawn forth concerning it as could ever be written or read; indeed, all theology apprehensible by us is elicited from this great principle. Wherefore that supreme searcher of divine mysteries, Dionysius the Areopagite, says in his Mystical Theology that most blessed Bartholomew marvellously understood theology when he declared it to be at once maximal and minimal. For whoever understands this understands all things; he surpasses every created intellect. God, who is this very Maximum—as the same Dionysius says in On the Divine Names—is not this thing while not being another, nor is He somewhere while not being elsewhere; rather, just as He is all things, so too He is none of them all. For—as Dionysius concludes at the close of the Mystical Theology—above every affirmation He is the perfect and singular cause of all things, and above the removal of all things stands the excellence of Him who is simply absolved from all and beyond all. Hence in his Letter to Gaius he concludes that God is known above all mind and intelligence.
In harmony with this, Rabbi Solomon states that all the wise have agreed ‘that the sciences do not apprehend the Creator; none apprehends what He is save He Himself; and our apprehension in respect of Him is a falling short of approaching His apprehension.’ Accordingly the same thinker elsewhere concludes: ‘Praised be the Creator, in the comprehension of whose essence the inquiry of the sciences is cut short, wisdom is reckoned ignorance, and elegance of speech foolishness.’ This is that very learned ignorance which we are investigating, through which alone Dionysius strove in manifold ways to show—by no other principle, I judge, than the one just stated—that God can be found.
Let our speculation, then—elicited from the fact that infinite curvature is infinite rectitude—be applied transsumptively in the Maximum to its most simple and most infinite essence: how it is the most simple essence of all essences; how all essences of things that are, have been, or shall be exist eternally and always in act within that very essence as that essence itself, and so are all essences just as it is the essence of all; how that essence of all is each essence in such wise as to be simultaneously all of them and none singly; and how that Maximal Essence, just as the infinite line is the most adequate measure of all lines, is in like manner the most adequate measure of all essences. For the Maximum to which the Minimum is not opposed is of necessity the most adequate measure of all things—not greater, because it is Minimum; not smaller, because it is Maximum. Everything measurable falls between maximum and minimum. Infinite essence, therefore, is the most adequate and most precise measure of all essences.
To see this still more clearly, consider that if one infinite line were constituted out of infinitely many one-foot segments and another out of infinitely many two-foot segments, they would nonetheless have to be equal, since the infinite is not greater than the infinite. Just as one foot is not smaller than two feet within an infinite line, so the infinite line does not exceed one foot any more than it exceeds two feet. Nay rather, because every part of the infinite is infinite, one foot of an infinite line is convertible with the whole infinite line just as two feet are.
In like manner, since every essence within the Maximal Essence is that Maximal Essence itself, the Maximum is none other than the most adequate measure of all essences. Nor can any other precise measure of any essence whatsoever be found save that one; for all other measures fall short and can always be made more precise, as was shown most clearly above.
Book I, Chapter 17 — Profoundest Doctrines Drawn from the Same Principle¶
Original GEOMETOR Translation from the Latin · h I, nn. 47–51 · Paris 1514 fol. 6v–7r · Rotta 1913 pp. 35–38
Still further on the same theme: a finite line is divisible whereas the infinite line is indivisible, because the infinite—in which the Maximum coincides with the Minimum—has no parts. Yet a finite line is not divisible into what is not a line, because in magnitude one never arrives at a minimum than which there can be nothing smaller, as was shown earlier. Consequently a finite line is indivisible in the intelligible form of ‘line’: a one-foot line is no less a line than a one-cubit line. It remains, therefore, that the infinite line is the intelligible ratio of the finite line. In the very same way the unqualified Maximum is the ratio of all things. Now ratio is measure. Rightly, therefore, did Aristotle say in the Metaphysics that the First is the standard and measure of all things, because it is the ratio of all things.
Again: just as the infinite line, which is the ratio of a finite line, is indivisible and consequently immutable and perpetual, so too the ratio of all things, who is blessed God, is everlasting and immutable. Here opens the meaning of great Dionysius when he calls the essence of things incorruptible, and of others who said that the ratio of things is eternal—such as divine Plato himself, who (as Calcidius reports) declared in the Phaedo that as it exists in itself there is a single exemplar or Idea of all things, whereas in relation to things, which are many, there appear to be many exemplars. For when I consider a two-foot line, a three-foot line, and so onward, two features present themselves: namely, the ratio of ‘line,’ which in both and in all is one and equal, and the diversity between the two-foot and the three-foot line. Thus there seems to be one ratio of the two-foot line and another of the three-foot line. Yet it is plain that in the infinite line a two-foot line and a three-foot line are not distinct—and that infinite line is the ratio of the finite. Hence the ratio of both lines is one, and the diversity of things or lines arises not from a diversity of the ratio, which is one, but accidentally, because they do not participate in the ratio equally. Accordingly there is only one ratio of all things, participated in diverse ways.
That it is participated in diverse ways comes about because, as proved earlier, there cannot be two things equally similar and consequently participating with exact equality in one ratio. For the ratio cannot be participated in supreme equality save by the Maximum, which is that infinite ratio itself. Just as there is only one maximal Unity, so there can be only one Equality of Unity; and because this is maximal equality, it is the ratio of all things. For just as there is only one infinite line, which is the ratio of all finite lines, and by the very fact that a finite line necessarily falls short of that infinite line it cannot be its own ratio—any more than it can be simultaneously finite and infinite—so too, just as no two finite lines can be precisely equal (since precise equality, which is maximal, is none other than the Maximum itself), no two lines are found participating equally in the one ratio of all.
Furthermore, the infinite line is neither greater in a two-foot line than the two-foot line nor smaller, as was said above; and so too for a three-foot line and beyond. And since it is indivisible and one, it is whole in every finite line. Yet it is not whole in every finite line by way of participation and finitude; otherwise, were it wholly enclosed in the two-foot line, it could not be in the three-foot line, inasmuch as the two-foot line is not the three-foot line. Wherefore it is whole in each in such a way that it is in none insofar as one is distinguished from the others by finitude. The infinite line, therefore, is whole in every line in such wise that every line is in it. These two truths must be considered conjointly, and then one sees clearly how the Maximum is in every thing and in none. And because the Maximum is in every thing by the same ratio by which every thing is in it, and is that very ratio itself, this means nothing other than that the Maximum exists in itself. Thus for the Maximum to be the standard and measure of all things is nothing other than for the unqualified Maximum to be in itself, or for the Maximum to be the Maximum. Nothing, therefore, exists in itself except the Maximum, and every thing exists in itself insofar as it exists in its own ratio, because its ratio is the Maximum.
By these considerations the intellect can aid itself and, through the likeness of the infinite line, advance greatly in sacred ignorance toward the unqualified Maximum above all understanding. For here we have now clearly seen how we discover God by removing the participation of beings. All beings participate in beingness. When participation is removed from all beings, therefore, there remains most simple beingness itself, which is the essence of all things. And we behold such beingness only in most learned ignorance, because when I remove from my mind all things that participate in beingness, nothing seems to remain. Wherefore great Dionysius says that the understanding of God approaches nearer to nothing than to something. Yet sacred ignorance teaches me that what appears to the intellect as nothing is the incomprehensible Maximum.
Book I, Chapter 18 — How from the Same Principle We Are Guided to Understand Participation in Beingness¶
Original GEOMETOR Translation from the Latin · h I, nn. 52–54 · Paris 1514 fol. 7r–7v · Rotta 1913 pp. 38–40
Further still, our insatiable intellect, vigilantly and most sweetly stirred by what has gone before, asks how it may behold more clearly this participation in the one Maximum. Aiding itself once again by the example of infinite linear rectitude, it speaks as follows:
What is curved, because it admits of more and less, cannot be either maximal or minimal; nor is the curved as curved anything positive, since it is a falling away from the straight. The being that resides in the curved, therefore, comes from participation in rectitude, inasmuch as both the maximally curved and the minimally curved are none other than the straight. Hence the less curved a curve is—such as the circumference of a larger circle—the more it participates in rectitude: not by taking a fragment of it, since infinite rectitude has no parts, just as a finite straight line, the longer it is, seems to participate more largely in the infinity of the maximal infinite line. Now just as a finite straight line insofar as it is straight—into which minimal curvature resolves—participates in the infinite line by a simpler participation, whereas a curve participates not so simply and immediately, but mediately and at a remove through the medium of the rectitude in which it shares: so too certain beings participate more immediately in Maximal Beingness subsisting in itself, namely simple finite substances, whereas other beings participate in beingness not through themselves but through the medium of substances, namely accidents. Notwithstanding this diversity of participation, as Aristotle says, the straight is the measure both of itself and of the crooked; just as the infinite line is the measure of both straight and curved lines, so the Maximum is the measure of all things however diversely they participate.
Here opens the meaning of the saying that substance does not admit of more and less. This is true in the very way that a finite straight line, insofar as it is straight, admits neither more nor less; yet because it is finite, through diverse participation in the infinite line one finite line is larger or smaller in respect of another, and never are two found precisely equal. The curved, however, admits of more and less with regard to its participation in rectitude, and consequently through that participated rectitude it also admits of more and less in size like the straight. Hence it is that accidents are the nobler the more they participate in substance, and nobler still the nobler the substance in which they participate. Thus we see how there can exist only beings participating in the beingness of the First either through themselves or through others, just as only lines either straight or curved are found; and therefore Aristotle rightly divided everything in the world into substance and accident.
Of substance and accident alike, then, there is a single most adequate measure, namely the most simple Maximum itself; and although it is neither substance nor accident, from what has preceded it is manifestly plain that it more fittingly receives its name from the things participating in it immediately—substances—than from accidents. Hence greatest Dionysius calls it ‘more than substance’ or ‘supersubstantial’ rather than ‘superaccidental’; because to say ‘supersubstantial’ is greater than to say ‘superaccidental,’ it is more fittingly attributed to the Maximum. Yet ‘supersubstantial’ means ‘not substantial,’ since substance lies below it, while it stands above substance; thus negation suits the Maximum more truly, as we shall explain below concerning the names of God.
From what has been said above one might investigate much concerning the diversity and nobility of accidents and substances, for which this is not the place.
Book I, Chapter 19 — Transsumption of the Infinite Triangle to the Maximal Trinity¶
Original GEOMETOR Translation from the Latin · h I, nn. 55–58 · Paris 1514 fol. 7v–8r · Rotta 1913 pp. 40–42
Let us now be instructed in ignorance from what has been stated and proved, namely that the maximal line is the maximal triangle. The maximal line has been shown to be a triangle; and because a line is most simple, the most simple will be triune. Every angle of that triangle will be the line, since the whole triangle is the line; therefore the infinite line is triune. Yet there cannot be several infinites; therefore that trinity is unity.
Furthermore, since in geometry it is demonstrated that the angle opposite the greater side is greater, and here we have a triangle possessing none save infinite sides, its angles will be maximal and infinite. Hence no one angle is smaller than the others, nor are two greater than the third; rather, just as outside infinite quantity no quantity can exist, so outside one infinite angle no other angles can exist. Consequently each will be in the other, and all three will be one Maximum. Moreover, just as the maximal line is no more line than triangle, circle, or sphere, but in truth is all of them without composition, as has been shown, so in like manner the unqualified Maximum as linear Maximum may be called Essence; as triangular, Trinity; as circular, Unity; and as spherical, Actual Existence.
The Maximum, therefore, is triune essence, one in act; nor is essence other than trinity, nor trinity other than unity, nor actuality other than unity, trinity, or essence, even though it is most true that the Maximum is all these identically and most simply. Just as it is true that the Maximum exists and is one, so it is true that it is triune in such a manner that the truth of trinity does not contradict most simple unity, but is that unity itself.
Now this is possible in no other way than as can be attained through the likeness of the maximal triangle. Knowing from what precedes that true triangle and most simple line, therefore, we shall attain the Trinity in learned ignorance in the manner possible to man. For we observe that we do not find first one angle, next another, and third yet another, as in finite triangles, since one and another and another cannot exist within the unity of the triangle without composition. Instead, the One exists triply without numerical multiplication; wherefore most learned Augustine rightly said: ‘Once you begin to count the Trinity, you step outside the truth.’ In divine matters one must embrace contradictories within a simple concept so far as possible, anticipating them antecedently: for instance, in divine things one must not conceive distinction and indistinction as two contradictories, but conceive them antecedently in their most simple principle, where distinction is no other than indistinction; then one conceives clearly that trinity and unity are the same. Where distinction is indistinction, trinity is unity; and conversely, where indistinction is distinction, unity is trinity. So too with plurality of persons and unity of essence: where plurality is unity, trinity of persons is identical with unity of essence; and conversely, where unity is plurality, unity of essence is trinity in the persons.
All this appears clearly in our geometric example, where the most simple line is a triangle and conversely the simple triangle is linear unity. Here too we see why the angles of the triangle cannot be numbered as one, two, three, since each is in each—as the Son declares: ‘I am in the Father and the Father is in me.’ Again, the truth of a triangle requires three angles: here, then, there are most truly three angles, each one maximal, and all of them one Maximum. The truth of a triangle requires further that one angle not be another; and here likewise the truth of the unity of most simple essence requires that those three angles not be three separate things, but one—and this too holds true here. Join together antecedently, therefore, these things that seem opposed, as I said before, and you will have not ‘one and three’ or the reverse, but the Unitrine or Triune. And this is absolute truth.
Book I, Chapter 20 — Further on the Trinity, and Why a Quaternity or More Is Impossible in Divine Reality¶
Original GEOMETOR Translation from the Latin · h I, nn. 59–62 · Paris 1514 fol. 8r–8v · Rotta 1913 pp. 42–45
Furthermore, the truth of the Trinity, which is Triunity, requires that the triune be one, which is why it is called ‘triune.’ Now this enters into thought only in the way that distinct correlation unites and order distinguishes. Just as when we construct a finite triangle there is first one angle, second another, and third a third proceeding from both, and those angles bear a mutual correlation so that out of them there is a single triangle, so too infinitely in the infinite. Yet this must be conceived in such a way that priority is understood in eternity without posteriority contradicting it; otherwise priority and posteriority could have no place in the infinite and eternal. Hence the Father is not prior to the Son and the Son posterior; rather, the Father is prior in such wise that the Son is not posterior. The Father is the first Person without the Son being second afterward; just as the Father is first without priority, so the Son is second without posteriority, and the Holy Spirit in like manner third. Since more was said on this earlier, let this suffice.
Take careful note, however, regarding this ever-blessed Trinity, that the Maximum itself is triune and not fourfold or fivefold or more. Worthy of remark indeed is this truth, for any higherfoldness would clash with the simplicity and perfection of the Maximum. Every polygonal figure has the triangular figure as its simplest element, and the triangle is the minimal polygonal figure, than which none can be smaller. Now it has been proved that the unqualified Minimum coincides with the Maximum. Therefore as unity stands among numbers, so the triangle stands among polygonal figures; and just as every number resolves into unity, so all polygons resolve into the triangle. Hence the maximal triangle, with which the minimal triangle coincides, embraces all polygonal figures; for as maximal unity stands to every number, so the maximal triangle stands to every polygon. A quadrangular figure, by contrast, is manifestly not minimal, since a triangular figure is smaller than it. To the most simple Maximum, therefore, which can coincide solely with the Minimum, a quadrangular figure—which cannot exist without composition, being larger than the minimal—can in no wise belong. Indeed, to be maximal and to be quadrangular entails a contradiction: for a quadrangle could never serve as the adequate measure of triangular figures, since it would always exceed them. How then could that be the Maximum which was not the measure of all things? Nay, how could that be the Maximum which derived from another, was composite, and was consequently finite?
Now it is plain why out of the potency of the simple line there arises first—with respect to polygons—the simple triangle, next the simple circle, and next the simple sphere, and why one arrives at no figures other than these elemental ones, mutually disproportionate among finite magnitudes yet enfolding all figures within themselves. Just so, were we to conceive the measures of all measurable quantities, we would need first, for length, a maximal infinite line with which the minimum coincided; next, in like manner, for rectilinear breadth a maximal triangle; for circular breadth a maximal circle; and for depth a maximal sphere; nor could all measurable things be attained by any measures other than these four. And since all these measures would necessarily be infinite and maximal, with which the minimum coincided, and since there cannot be several maxima, we affirm that the single Maximum which must be the measure of all quantities is those four without which it could not be the maximal measure—even though, considered in itself apart from relation to measurable things, it is and can truly be called none of them, standing infinitely and disproportionately above them. Thus because the unqualified Maximum is the measure of all things, we call it those things without which we cannot understand it to be the universal standard. Although the Maximum stands infinitely above all trinity, we call it triune because otherwise we would not understand it to be the simple cause, standard, and measure of things whose unity of being is a trinity—just as among figures triangular unity consists in a trinity of angles—even though in truth, once this relation is set aside, both the name and our concept of trinity do not fit the Maximum at all, falling infinitely short of that maximal and incomprehensible truth.
We possess, accordingly, the maximal triangle as the simplest measure of all things subsisting triply—such as operations and actions subsisting triply in potency, object, and act; likewise acts of seeing, understanding, and willing, likenesses, unlikenesses, beauties, proportions, correlations, natural appetites, and all other realities whose unity of being consists in plurality, above all the being and operation of nature consisting in the correlation of agent, patient, and the common bond resulting from them.
Book I, Chapter 21 — Transsumption of the Infinite Circle to Unity¶
Original GEOMETOR Translation from the Latin · h I, nn. 63–66 · Paris 1514 fol. 8v–9r · Rotta 1913 pp. 45–47
We have offered a few remarks concerning the maximal triangle; let us in like manner subjoin some reflections concerning the infinite circle:
The circle is the perfect figure of unity and simplicity. Above it has already been shown that the triangle is a circle; thus trinity is unity. Now this unity is infinite, just as the circle is infinite; hence it is infinitely more one and more identical than any unity expressible or apprehensible by us. So great is the identity there that it precedes even all relative oppositions, since there ‘other’ and ‘diverse’ are not opposed to identity. Because the Maximum is of infinite unity, therefore, all attributes that belong to it are itself without diversity or otherness, so that its goodness is not one thing and its wisdom another, but the selfsame. For in it all diversity is identity; hence because its power is most one, it is also most strong and most infinite. So utterly one is its duration that within it the past is not other than the future, nor the future other than the present; rather they are one most unified duration, or eternity without beginning and end. So completely is beginning within it that within it even the end is the beginning.
All this the infinite circle displays: eternal without beginning or end, indivisibly most one and most capacious. Because that circle is maximal, its diameter too is maximal. And since there cannot be several maxima, that circle is so supremely one that its diameter is its circumference. Now an infinite diameter has an infinite midpoint; and the midpoint is the center. Clearly, therefore, center, diameter, and circumference are identical. Thereby our ignorance is taught that the incomprehensible Maximum is that to which the Minimum is not opposed, and that within it the center is the circumference.
You see how the whole Maximum exists most perfectly within everything simple and indivisible, because it is infinite center; outside all being, encompassing all things, because it is infinite circumference; and penetrating all things, because it is infinite diameter. Beginning of all things, because center; end of all things, because circumference; middle of all things, because diameter. Efficient cause, because center; formal cause, because diameter; final cause, because circumference. Bestowing being, because center; governing, because diameter; conserving, because circumference—and many similar truths besides.
Through the intellect you apprehend, accordingly, how the Maximum is neither identical with nor diverse from anything, and how all things are in it, from it, and through it, because it is circumference, diameter, and center—not that it is a circle or circumference, diameter, or center, but solely the most simple Maximum, investigated through these paradigms and found to encompass all things that are and are not, so that within it non-being is maximal being just as the Minimum is the Maximum. And it is the measure of every circulation from potency into act and back again from act into potency, of composition from principles down to individuals and resolution of individuals back into principles, of perfect circular forms and circular operations and motions returning upon themselves and to their beginning, and of all like things whose unity consists in a kind of circular perpetuity.
Much more concerning the perfection of unity might here be drawn from this circular figure, which for brevity’s sake I pass over, since anyone can readily work it out in keeping with what precedes. One thing only I admonish you to note well: how all theology is circular and grounded in a circle, to such a point that even the names of the attributes are verified of one another circularly—supreme justice is supreme truth, and supreme truth is supreme justice, and so for all the rest. From this, should you wish to extend your inquiry, countless theological truths hitherto hidden will become utterly manifest to you.
Book I, Chapter 22 — How the Providence of God Unites Contradictories¶
Original GEOMETOR Translation from the Latin · h I, nn. 67–69 · Paris 1514 fol. 9r–9v · Rotta 1913 pp. 48–50
That we may also experience how we are led to lofty understanding through what has preceded, let us apply our inquiry to the providence of God. Since from our earlier arguments it is manifest that God is the enfolding of all things, even of contradictories, nothing can escape His providence; for whether we do something or its opposite or nothing at all, the whole was enfolded within God’s providence. Nothing, therefore, will come to pass save in accordance with God’s providence.
Hence although God could have foreseen many things that He neither foresaw nor will foresee, and also foresaw many things that He could have refrained from foreseeing, nevertheless nothing can be added to or subtracted from divine providence. Take an analogy: human nature is simple and one; if a human being were born who was never expected to be born, nothing would be added to human nature, just as nothing would be subtracted from it were he not born, nor when those who have been born die—and this because human nature enfolds alike those who exist and those who neither exist nor ever will exist, though they could have existed. In the same way, even if something were to happen that will never happen, nothing would be added to divine providence, because it enfolds both the things that happen and those that do not happen yet can happen. Just as many things exist possibly in matter which will never come to pass, conversely whatsoever things will never come to pass yet can come to pass exist in God’s providence not possibly, but in act—without its following therefrom that those things exist in act in the unfolded world. Just as we say that human nature enfolds and embraces infinites—not only the human beings who have been, are, and will be, but those who can be though they never will be—and thus embraces mutable things immutably, as infinite unity embraces every number, so God’s infinite providence enfolds both the things that will happen and those that will not happen yet can happen, together with contraries, just as a genus enfolds contrary specific differences. And the things it knows it knows without difference of tenses: not future things as future nor past things as past, but eternally, and mutable things immutably.
Therefore divine providence is inevitable and immutable, and nothing can outstrip it; hence all things, when referred to providence itself, are rightly said to possess necessity, because in God all things are God, who is absolute necessity. Thus it is plain that things which will never come to pass exist in God’s providence in the manner aforesaid, even though they are not foreseen so as to happen. And God necessarily foresaw what He foresaw, since His providence is necessary and immutable, even though He could also have foreseen the opposite of what He foresaw. For when the enfolding is posited, the unfolded thing is not thereby posited, whereas when the unfolding is posited, the enfolding is posited. Although tomorrow I am free to read or not to read, whichever I do I do not evade providence, which embraces contraries; hence whatever I do will occur according to God’s providence.
Thus it is clear how, through the preceding principles teaching us that the Maximum precedes every opposition because it embraces and enfolds all things in every way, we apprehend what is true concerning God’s providence and like matters.
Book I, Chapter 23 — Transsumption of the Infinite Sphere to the Actual Existence of God¶
Original GEOMETOR Translation from the Latin · h I, nn. 70–73 · Paris 1514 fol. 9v–10r · Rotta 1913 pp. 50–52
It is fitting to add a few further speculations concerning the infinite sphere. In an infinite sphere we find three maximal lines—of length, breadth, and depth—concurring at the center. Yet the center of the maximal sphere equals the diameter and the circumference. Within the infinite sphere, therefore, the center equals those three lines; nay rather, the center is all of them, namely length, breadth, and depth. Hence the Maximum will most simply and infinitely be all length, breadth, and depth, which within it are one most simple, indivisible Maximum. As center, it precedes every breadth, length, and depth, and is likewise their end and their middle, because in an infinite sphere center, thickness, and circumference are identical. Just as the infinite sphere is wholly in act and most simple, so the Maximum is most simply and wholly in act; and just as the sphere is the act of line, triangle, and circle, so the Maximum is the act of all things. Every actual existence, accordingly, derives from it whatever actuality it possesses, and exists in act just insofar as it exists within that infinite act. Therefore the Maximum is the Form of forms and the Form of being, or Maximal Actual Beingness.
Hence Parmenides, reflecting with utmost subtlety, declared that God is He for whom to be anything that is, is to be everything that is. Just as the sphere is the ultimate perfection of figures, than which none is greater, so the Maximum is the most perfect perfection of all things, to such a degree that within it everything imperfect is most perfect—just as the infinite line is a sphere, curvature is rectitude, composition is simplicity, diversity is identity, otherness is unity, and so for all the rest. How indeed could any trace of imperfection reside where imperfection is infinite perfection and possibility is infinite act?
Seeing that the Maximum is like the maximal sphere, we now behold clearly how it is the sole, simplest, and most adequate measure of the entire universe and of all things existing within the universe, because within it the whole is no greater than the part, just as the infinite sphere is no greater than the infinite line. God, therefore, is the sole and simplest ratio of the whole universe; and just as the sphere arises after infinite revolutions, so God—like the maximal sphere—is the simplest measure of all revolutions. For all quickening, motion, and intelligence come from Him, in Him, and through Him, before whom a single revolution of the eighth sphere is no smaller than infinitely many revolutions, since He is the goal of all motions, in whom every motion comes to rest as in its end. For He is maximal rest, within which all motion is rest; and thus maximal rest is the measure of all motions, just as maximal rectitude is the measure of all circumferences and maximal presence—or eternity—is the measure of all times. In Him, therefore, all natural motions rest as in their goal, and every potency is perfected in Him as in infinite act; and because He is the beingness of all being and every motion tends toward being, the rest of motion is He Himself who is motion’s goal, namely the form and act of being.
Toward Him, accordingly, all beings strive. And because they are finite and cannot participate in that goal equally in comparison with one another, some participate in this goal through the mediation of others—just as the line is led into the sphere through the mediation of the triangle and the circle, the triangle through the mediation of the circle, and the circle into the sphere directly through itself.