now i must begin with congratulating you (or rather your source) on wording the matter perfectly. that is perhaps the best case against the belief that jesus can be god and it is precisely how i would have worded it, were i a muslim. yet i must say that the matter is pretty much already settled given that we are talking in terms of logic and the above source seems to possess no knowledge of the hypostatic union. without further ado, let us begin.
it must be acknowledged that the above points rest on the individual nature of the thing in question being transformed into something that is contradictory to it. hence why the following can be said (and quit correctly that is):
τhε ṿαlε'ṡ lïlÿ ;1415821 said:
Can you draw me a triangle with four sides?
as we can all see, the nature of a triangle is that it has 3 sides so the triangle can not be made to have 4 sides and suddenly remain a triangle. if we can all agree on this matter then i must move on to say that that is not what the christian says in claiming that god became man. we do not say that the divine essence was converted into a human essence so that the divine would cease to be divine. rather we say that god took on a human nature and not that he transformed the divine nature into a human one.
The Divine and human natures cannot alternate, so that the Divine should become human or the human Divine; nor can they be so commingled as that a third should be produced from the two which is neither wholly Divine nor wholly human. For, granting that it were possible for either to be changed into the other, it would in that case be only God and not man, or man only and not God. Or, if they were so commingled that a third nature sprung from the combination of the two (as from two animals, a male and a female of different species, a third is produced, which does not preserve entire the species of either parent, but has a mixed nature derived from both), it would neither be God nor man. Therefore the God-man, whom we require to be of a nature both human and Divine, cannot be produced by a change from one into the other, nor by an imperfect commingling of both in a third; since these things cannot be, or, if they could be, would avail nothing to our purpose. Moreover, if these two complete natures are said to be joined somehow, in such a way that one may be Divine while the other is human, and yet that which is God not be the same with that which is man, it is impossible for both to do the work necessary to be accomplished. For God will not do it, because he has no debt to pay; and man will not do it, because he cannot. Therefore, in order that the God-man may perform this, it is necessary that the same being should [be] perfect God and perfect man, in order to make this atonement. For he cannot and ought not to do it, unless he be very God and very man. Since, then, it is necessary that the God-man preserve the completeness of each nature, it is no less necessary that these two natures be united entire in one person, just as a body and a reasonable soul exist together in every human being; for otherwise it is impossible that the same being should be very God and very man. - Cur Deus Homo, Chapter VII
the above is a word on the matter by saint anselm of canterbury. while at this point, the above does not quite explain everything, once you have continued to read what i write, it will certainly begin to make sense.
the question now becomes whether it is logical for a person to be both god and man at the same time seeing as to be god means to be infinite and to be man is to be finite. in keeping with your simple example of a triangle and a square here is an example of the christian conception of christ (the following is what i have written on the subject for another person but i'll simply copy and paste it here):
Let us imagine a triangle. Now we all know the nature of a triangle i.e. it’s attributes, the things that make a triangle a triangle as opposed to a rectangle or circle. Good. Now let us at this point imagine a box. Once more we know what is the nature of a box and furthermore, we are also aware that the nature of a box is in direct contradiction to the nature of a triangle. Now suppose that we were to place the triangle within the box, would we then have a confusion, a mixing, an intermingling of the two essences/natures? No, we would possess one unit (the Triangle-Box if you would like) with the essences of both objects intact. The triangle would not cease to be a triangle and neither would the box cease to be a box—on the contrary we would now have a unit that possesses in its being the very attributes of both in that it is not half a box and half a triangle but rather a full (perfect) triangle and a full (perfect) box. A veritable Triangle-Box, wherein the unit is one but the essences are two. In just the same manner does the Christian speak of God becoming man. God did not cease being God, he did not convert the divine essence into a human essence; instead he took on a second nature aside from his divine nature. As such in the unit that is the individual, Christ Jesus, there are two natures with contradicting attributes simultaneously present. As with the Triangle-Box, Jesus can claim the otherwise mutually exclusive prerogatives that come with each nature because of them being simultaneously existent in his being. Such that he can increase in knowledge as man, but always have known all things as God. Such that he can pray to the father as man, yet have no need to do so as God. Such that should he will it, he is able to give his life unto death as man, and yet death never having any power or hold over him as God. He does everything as the God-Man—mystery upon mystery. In short, He is both three-sided and four-sided at the same time.
let us remember that the your point rested on the single nature being converted into its opposite yet simultaneously remaining that which makes it whatever it is (the nature of triangle being converted into that of a square yet somehow also remaining a triangle). this whole argument is blown completely out of the water when the muslim understands that christians speak of god taken on, for the purpose of salvation a second nature and not converting the divine nature into a human one. in light of this understanding by christians, the muslim objections are put to rest because they become untenable when christians are allowed to explain the matter of the hypostatic union. i must confess that given that the muslim argument was made on the premise of logic, the argument was more than easy to refute seeing as your source never even understood what christians meant by christ becoming man. his whole argument relies on the single premise that the one nature was converted into the other while the christian claim is that a second nature was taken on. this explanation averts the problem of any change to the being of god whatsoever and furthermore, is logically robust. i do not ask you to believe this but it is more than evident that the christian claim cannot be attacked in terms of logic.
now, i have answered and refuted all the above arguments. to those who would still claim that allah does not enter into his creation, can you please begin to engage my argument?