Which Son was to be Sacrificed?
Question

                I understand that Prophet Ibrahim (peace be upon him) intended to sacrifice his son, Prophet Ishmail (pbuh), according to Muslim belief. However, a non-Muslim that I had a discussion with pointed out that this is not mentioned in the Quran. Upon investigating this matter, it seems that the Quran is ambiguous as to which son is intended to be sacrificed (as least in my English translation-surah 37). Please explain the Muslim position on Prophet Ibrahim and the sacrifice, using textual evidence.
Praise be to Allah.Allaah says of His slave and Close Friend (Khaleel) Ibraaheem (peace be
    upon him) (interpretation of the meaning):
And he said (after his rescue from the fire):
    “Verily, I am going to my Lord. He will guide me!”
“My Lord! Grant me (offspring) from the
    righteous.”
So We gave him the glad tidings of a forbearing boy.
And, when he (his son) was old enough to walk with
    him, he said: “O my son! I have seen in a dream that I am slaughtering you (offering
    you in sacrifice to Allaah). So look what you think!” He said: “O my father! Do
    that which you are commanded, In shaa’ Allaah (if Allaah wills), you shall find me of
    As-Saabiroon (the patient).”
Then, when they had both submitted themselves (to the
    Will of Allaah), and he had laid him prostrate on his forehead (or on the side of his
    forehead for slaughtering);
We called out to him: “O Ibraaheem!
You have fulfilled the dream!” Verily, thus do We
    reward the Muhsinoon (good-doers).
Verily, that indeed was a manifest trial.
And We ransomed him with a great sacrifice (i.e. a
    ram);
And We left for him (a goodly remembrance) among the
    later generations.
“Salaam (peace) be upon Ibraaheem!”
Thus indeed do We reward the Muhsinoon (good-doers).
Verily, he was one of Our believing slaves.
And We gave him the glad tidings of Ishaaq (Isaac)  a Prophet from the righteous.
We blessed him and Ishaaq (Isaac). And of their
    progeny are (some) that do right, and some that plainly wrong themselves.”
    [al-Saaffaat 37:99-113)
Ibn Katheer (may Allaah have mercy on him) said: Allaah tells us that
    when His Close Friend (Khaleel) Ibraaheem migrated from the land of his people, he asked
    his Lord to grant him a righteous son, so Allaah gave him the glad tidings of a forbearing
    boy. This was Ismaa’eel (peace be upon him), because he was the first child who was
    born (to Ibraaheem, peace be upon him). There is no dispute on this point among the
    followers of the various religions [Jews, Christians and Muslims], that (Ismaa’eel)
    was the first child born to Ibraaheem.
“And, when he (his son) was old enough to walk with him” means,
    when he grew up and was able to take care of himself, like his father. Mujaahid said: “And,
    when he (his son) was old enough to walk with him” means, when he grew up and was
    able to ride and walk and work like his father did. When this happened, then Ibraaheem
    (peace be upon him) saw a dream in which he was commanded to sacrifice this son of his.
    According to a hadeeth narrated from Ibn ‘Abbaas and attributed to the Prophet 
    (peace and blessings of Allaah be upon him): “The dreams of the Prophets are Wahy
    (revelation).” So Allaah was testing His Close Friend by commanding him to sacrifice
    this beloved son who had come to him in his old age, when he was very old, and after he
    had been commanded to settle the child and his mother in the desert, in a valley in which
    there was no noise, no people, no vegetation and no animals. So Ibraaheem obeyed the
    command of Allaah and left them there, putting his trust in Allaah, and Allaah sent them
    provision, from an unexpected source. After all that, when Ibraaheem was ordered to
    sacrifice this son of his, who was his firstborn and his only child, he responded to his
    Lord and obeyed His command, hastening to do as He willed. So he told his son about it so
    as to put him at ease and not sacrifice him by force.
“He said: ‘O my son! I have seen in a dream that I am
    slaughtering you (offering you in sacrifice to Allaah). So look what you
    think!’” The forbearing boy immediately responded: “He said: ‘O
    my father! Do that which you are commanded, In shaa’ Allaah (if Allaah wills), you
    shall find me of As-Saabiroon (the patient).’” This was the best answer he
    could give, an example of obedience to his father and to the Lord of mankind. Allaah said
    (interpretation of the meaning):
“Then, when they had both submitted themselves (to the Will of
    Allaah), and he had laid him prostrate on his forehead (or on the side of his forehead for
    slaughtering).” It was said that “when they had both submitted themselves”
    meant when they had both surrendered to the command of Allaah. “and he had laid
    him prostrate on his forehead” means that he put him face down. It was said that
    he wanted to slaughter him from behind so that he would not see his face at the time of
    slaughter. This was the view of Ibn ‘Abbaas, Mujaahid, Sa’eed ibn Jubayr,
    Qutaadah and al-Dahhaak… “They both submitted themselves” means that
    Ibraaheem said Bismillaahi’r-Rahmaan ir-Raheem and said Allaahu akbar
    and the boy said La ilaaha ill-Allaah because he was about to die. Al-Saddi and
    others said that (Ibraaheem) passed the knife over the boy’s throat but it did not
    cut him at all. It was said that a sheet of copper was placed between the knife and his
    throat, and Allaah knows best. Then it was called out from Allaah:
“’O Ibraaheem! You have fulfilled the dream!’” meaning,
    the purpose has been achieved, you have been tested and your obedience and willingness to
    do what your Lord commands have been proven. An alternative sacrifice will be provided
    instead of your son, just as you willingly submitted your body to the flames and you spent
    your wealth to honour your guests. Hence Allaah said:
“Verily, that indeed was a manifest trial” meaning
    that it was an obvious test.
“And We ransomed him with a great sacrifice” means, We
    provided a ransom for his son, an alternative to be sacrificed in his stead. According to
    the best known opinion of the majority of scholars, this was a fine white horned ram.
    Al-Thawri narrated from ‘Abd-Allaah ibn ‘Uthmaan ibn Khaytham from Sa’eed
    ibn Jubayr that Ibn ‘Abbaas said: It was a ram that had grazed in Paradise for forty
    years.
It was also narrated from Ibn ‘Abbaas that the dried ram’s
    head was still hanging on the downspout of the Ka’bah. This alone is evidence that
    the one who was to be sacrificed was Ismaa’eel, because he was the one who was
    settled in Makkah and we have never heard that Ishaaq ever came to Makkah from the time he
    was little. And Allaah knows best.
See Al-Bidaayah wa’l-Nihaayah by Ibn Katheer, 1/157-158
The one who was to be sacrificed was Ismaa’eel and not Ishaaq,
    because of the reasons stated above. In his Tafseer (commentary) on these Ayaat,
    Ibn Katheer also mentioned a number of points which prove that it was Ismaa’eel who
    was to be sacrificed. These points may be summed up as follows:
Ismaa’eel was the first child of whom glad tidings were given to
        Ibraaheem. He was older than Ishaaq according to the consensus of the Muslims and the
        People of the Book (Jews and Christians). According to the scriptures of the People of the
        Book, it was stated that Allaah commanded Ibraaheem to sacrifice his only son, and in some
        manuscripts it says that he was to sacrifice his first-born son.

The first son is usually more dear than other children, so the command
        to sacrifice him is a more exacting test.

It is mentioned that glad tidings of a forbearing boy were given, and
        that he was the one who was to be sacrificed. Later in the passage it says (interpretation
        of the meaning): “And We gave him the glad tidings of Ishaaq (Isaac)  a Prophet from the righteous.” When the angels brought
        the glad tidings of Ishaaq to Ibraaheem, they said: “We give you glad tidings of a
        boy (son) possessing much knowledge and wisdom” [al-Hijr 15:53 – interpretation
        of the meaning].

Allâh said (interpretation of the meaning): “But We gave her
        glad tidings of Ishaaq, and after him, of Ya’qoob.” (Hood 11:71) meaning
        that a child called Ya’qoob would be born during their (Sara and Ishaaq’s)
        lifetimes, and he would have many descendents… and it does not sound right for
        Ibraaheem to be commanded to sacrifice him when he was little, because Allaah had promised
        that he would have many descendents.

Ismaa’eel is described here (in Soorat al-Saffaat) as being
        “forbearing” because this is very appropriate in this context. 

Tafseer Ibn Katheer, 4/15. And Allaah knows best.