The question of infinity is another topic of importance for proving the existence of God. We proceed as follows: An infinite line is an impossibility. For let the lines _a_------------_b_ be infinite in the _c_------|-----_d_ _e_ directions _b_, _d_. Take away from _cd_ a finite length = _ce_, and pull up the line _ed_ so that _e_ coincides with _c_. Now if _ed_ is equal to _ab_, and _cd_ was also equal to _ab_ by hypothesis, it follows that _ed_ = _cd_, which is impossible, for _ed_ is a part of _cd_. If it is shorter than _cd_ and yet is infinite, one infinite is shorter than another infinite, which is also impossible. The only alternative left is then that _ed_ is finite. If then we add to it the finite part _ce_, the sum, _ce_ + _ed_ = _cd_, will be finite, and _cd_ being equal to _ab_ by hypothesis, _ab_ is also finite. Hence there is no infinite line. If there is no infinite line, there is no infinite surface or infinite solid, for we could in that case draw in them infinite lines. Besides we can prove directly the impossibility of infinite surface and solid by the same methods we employed in line.
We can prove similarly that an infinite series of objects is also an impossibility. In other words, infinite number as an actuality is impossible because it is a contradiction in terms. A number of things means a known number; infinite means having no known number. A series is something that has beginning, middle and end. Infinite means being all middle. We have thus proved that an actual infinite is impossible, whether as extension or number. And the Bible also alludes to the finiteness of the universe in the words of Isaiah (40, 12): "Who hath measured the waters in the hollow of his hand...," intimating that the universe is capable of being measured.
We must prove next that no finite body can have an infinite power. For let the line _ae_ ------------- be a finite line having an infinite _a_ _b_ _c_ _d_ _e_ power. Divide into the several parts _ab_, _be_, _cd_, _de_, etc. If every one of the parts has an infinite power, _ab_ has an infinite power, _ac_ a greater infinite power, _ad_ a still greater, _ae_ a still greater, and so on. But this is absurd, for there cannot be anything greater than the infinite. It follows then that each of the parts has a finite power; and as the sum of finites is finite, the line _ae_ also has a finite power. All these principles we must keep in mind, for we shall by means of them prove later the existence and incorporeality of God.[235]