O ponto é o princípio ou a origem da linha, mas não sua causa; o instante é o princípio ou a origem da atividade [mas não a causa do ato]; o ponto de partida é o princípio do movimento, mas não a causa do movimento; as premissas são os princípios do argumento, mas não sua causa.

Burchio. Even if this be true I do not wish to believe it, for this Infinite can neither be understood by my head nor brooked by my stomach. Although, to tell the truth, I could yet hope that Philotheo were right, so that if by ill luck I were to fall from this world I should always find myself on firm ground.

We are wont to say that it was not in our power to choose the parents who fell to our lot, that they have been given to men by chance; yet we may be the sons of whomsoever we will. Households there are of noblest intellects; choose the one into which you wish to be adopted; you will inherit not merely their name, but even their property, which there will be no need to guard in a mean or niggardly spirit; the more persons you share it with, the greater it will become. These will open to you the path to immortality, and will raise you to a height from which no one is cast down. This is the only way of prolonging mortality — nay, of turning it into immortality. Honours, monuments, all that ambition has commanded by decrees or reared in works of stone, quickly sink to ruin; there is nothing that the lapse of time does not tear down and remove. But the works which philosophy has consecrated cannot be harmed; no age will destroy them, no age reduce them; the following and each succeeding age will but increase the reverence for them, since envy works upon what is close at hand, and things that are far off we are more free to admire. The life of the philosopher, therefore, has wide range, and he is not confined by the same bounds that shut others in. He alone is freed from the limitations of the human race; all ages serve him as if a god. Has some time passed by? This he embraces by recollection. Is time present? This he uses. Is it still to come? This he anticipates. He makes his life long by combining all times into one.

Thus Democritus and Epicurus, [16] who maintained that everything throughout infinity suffereth renewal and restoration, understood these matters more truly than those who would at all costs maintain belief in the immutability of the universe, alleging a constant and unchanging number of particles of identical material that perpetually undergo transformation, one into another.

Philotheo. No corporeal sense can perceive the infinite. None of our senses could be expected to furnish this conclusion; for the infinite cannot be the object of sense-perception; therefore he who demandeth to obtain this knowledge through the senses is like unto one who would desire to see with his eyes both substance and essence. And he who would deny the existence of a thing merely because it cannot be apprehended by the senses, nor is visible, would presently be led to the denial of his own substance and being. Wherefore there must be some measure in the demand for evidence from our sense-perception, for this we can accept only in regard to sensible objects, and even there it is not above all suspicion unless it cometh before the court aided by good judgement. It is the part of the intellect to judge, yielding due weight to factors absent and separated by distance of time and by space intervals. And in this matter our sense-perception doth suffice us and doth yield us adequate testimony, since it is unable to gainsay us; moreover it advertiseth and confesseth his own feebleness and inadequacy by the impression it giveth us of a finite horizon, an impression moreover which is ever changing. Since then we have experience that sense-perception deceiveth us concerning the surface of this globe on which we live, much more should we hold suspect the impression it giveth us of a limit to the starry sphere.

Sixteenthly, efficient infinity would be utterly incomplete without the [infinite] effect thereof, as we cannot conceive that such an effect [of infinity] should be the efficient infinity itself. Furthermore, if such were or could be the effect, this doth in no way detract from that which must appertain to every veritable effect, wherefore theologians name action ad extra or transitive in addition to imminent action, so that thus it is fitting that both one and the other be infinite.

Eighthly, none of our sense-perceptions is opposed to the acceptance of infinity, since we cannot deny infinity merely because we do not sensibly perceive it; but since sense in itself is included in infinity, and since reason doth confirm infinity, therefore needs must that we posit infinity. Moreover, if we consider well, sense doth present to us an infinite universe. For we perceive an endless series of objects, each one contained by another, nor do we ever perceive either with our external or our internal sense, an object which is not contained by another or similar object.

Lastly before our eyes one thing is seen to bound another; air is as a well between the hills, and mountains between tracts of air, land bounds the sea and again sea bounds all lands; yet in truth there is nothing outside to limit the universe ... so far on every side spreads out huge room for things, free from limit in all directions everywhere. [6]

From the testimony of our sight then we should rather infer the infinite, since there is no object which doth not terminate in another, nor can we experience aught which terminateth in itself.

Passing alone to those realms
The object erst of thine exalted thought,
I would rise to infinity: then I would compass the skill
Of industries and arts equal to the objects. [18]
There would I be reborn: there on high I would foster for thee
Thy fair offspring, now that at length cruel
Destiny hath run her whole course
Against the enterprise whereby I was wont to withdraw to thee.
Fly not from me, for I yearn for a nobler refuge
That I may rejoice in thee. And I shall have as guide
A god called blind by the unseeing.
May Heaven deliver thee, and every emanation
Of the great Architect be ever gracious unto thee:
But turn thou not to me unless thou art mine.

Escaped from the narrow murky prison
Where for so many years error held me straitly,
Here I leave the chain that bound me
And the shadow of my fiercely malicious foe
Who can [19] force me no longer to the gloomy dusk of night.
For he who hath overcome the great Python [20]
With whose blood he hath dyed the waters of the sea
Hath put to flight the Fury that pursued me. [21]
To thee I turn, I soar, O my sustaining Voice;
I render thanks to thee, my Sun, my divine Light,
For thou hast summoned me from that horrible torture, [22]
Thou hast led me to a goodlier tabernacle; [23]
Thou hast brought healing to my bruised heart.

Thou art my delight and the warmth of my heart; [24]
Thou makest me without fear of Fate or of Death;
Thou breakest the chains and bars
Whence few come forth free.
Seasons, years, months, days and hours — The children and weapons of Time — and that Court
Where neither steel nor treasure [25] avail
Have secured me from the fury [of the foe].
Henceforth I spread confident wings to space;
I fear no barrier of crystal or of glass;
I cleave the heavens and soar to the infinite.
And while I rise from my own globe to others
And penetrate ever further through the eternal field,
That which others saw from afar, I leave far behind me. [26]

Sixthly, if we posit a finite world, it is impossible to escape acceptance of the void, if void is that which containeth naught.

Seventhly, this space in which is our world would without it be indeed a void, since where the world is not, there we must infer a void. Beyond our world then, one space is as another; therefore the quality of one is also that of the other; wherefore too this quality cometh to action, for no quality is eternally without action, and indeed it is eternally linked to action or rather is itself action, for in eternity there is no distinction between being and potential being [nor therefore between action and potential action].

The intellect being developed to the comprehension of a certain definite and specific form, and the will to a love commensurate with such comprehension; the intellect does not stop there, but by its own light it is prompted to think of this: that it contains within itself the germ of everything intelligible and desirable, until it comes to comprehend with the intellect the depth of the fountain of ideas, the ocean of every truth and goodness. So that it happens, that whatever conception is presented to the mind, and becomes understood by it, from that which is so presented and comprehended it judges, that above it, is other greater and greater, and finds itself ever in a certain way discoursing and moving with it.

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"First, in his suppositions, he proceeds from unnatural foundations, pretending there are parts of the infinite; there are none who can support this, for there are no partial infinities; this is an implied contradiction, that infinity has a lesser part and a greater part, but you approach infinity no more quickly if you count by hundreds than by threes, for infinity has an infinity of hundreds no less than an infinity of threes. Infinite distance is measured in infinite feet equally with infinite miles, and when we would speak of parts of an infinite distance, we don't say "a hundred miles" or "a thousand parasangs", as these describe parts of a finite distance; they are in fact parts only of a finite whole, to which they have a proportion; they cannot be said to be parts of that to which they have no proportion. Thus a thousand years isn't part of eternity, because it has no proportion to the whole, but is instead a partial measure of time, like ten thousand years or a hundred thousand centuries."

Fourteenthly, if infinite active power doth actuate corporeal and dimensional being, this being must necessarily be infinite; otherwise there would be derogation from the nature and dignity both of creator and of creation.