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In Sura 3, Verse 13, the verse in English translation is
Already there has been for you a sign in the two armies which met - one fighting in the cause of Allah and another of disbelievers. They saw them [to be] twice their [own] number by [their] eyesight. But Allah supports with His victory whom He wills. Indeed in that is a lesson for those of vision.
I know that the context of this verse is Battle of Badr. But who saw who twice ? The Muslims or disbelievers ?
The matter can be explained by other verses were Allah says:
And already had Allah given you victory at [the battle of] Badr while you were few in number. Then fear Allah ; perhaps you will be grateful. (3:123)
And [remember] when He showed them to you, when you met, as few in your eyes, and He made you [appear] as few in their eyes so that Allah might accomplish a matter already destined. And to Allah are [all] matters returned. (8:44)
These verses show that in fact the Muslims were few, but Allah showed both parties smaller to each other for reasons we are not to discuss here and which are the topic of this question: What is the secret behind showing both adversaries as few in the others eyes in the battle of Badr? (unanswered so far).
Nevertheless both interpretations may come to mind if we recite verse (3:13) in different qira'at without having prior knowledge of the grammatical position of the verb and the observer or "acting person" as meant by the scholars of qir'aat.
But first we must be aware that the beginning of the verse:
Already there has been for you a sign in the two armies which met
"you" here is referring to the disbelievers or the Jews (according ibn Kathir).
Further note that the qira'at of this verse differ especially when it comes to the verb "to see" and its context, the majority recites:
يَرَوْنَهُمْ
which can be translated:
they see them
This is referring to the Muslims who see the army of the Kufar (smaller than it actually is or in the context of our discussed verse twice as many as they were themselves). So it describes the perspective of the Kufar (Muslims: "they"; Kufar: "you). And Nafi', his teacher abu Ja'afar and Yaqoob recite:
تَرَوْنَهُمْ
Which can be translated:
you see them
referring to the Muslims, but changing the observer: here the Muslims are addressed and it is them who observe the Kufar (Muslims: "you"; Kufar: "they").
Ibn Kathir (for example) quoted in his tafsir the following interpretations:
They saw them with their own eyes twice their number)
means, the idolators thought that the Muslims were twice as many as they were, for Allah made this illusion a factor in the victory that Islam had over them. It was said that the meaning of Allah's statement,
(They saw them with their own eyes twice their number)
is that the Muslims saw twice as many idolators as they were, yet Allah gave them victory over the disbelievers. 'Abdullah bin Mas'ud said, "When we looked at the disbelievers' forces, we found that they were twice as many as we were. When we looked at them again, we thought they did not have one man more than we had. (Source qtafsir)
Allah said,
﴿قَدْ كَانَ لَكُمْ ءَايَةٌ﴾
(There has already been a sign for you) meaning, O Jews, who said what you said! You have an Ayah, meaning proof, that Allah will make His religion prevail, award victory to His Messenger, make His Word apparent and His religion the highest.
﴿فِي فِئَتَيْنِ﴾
(In the two armies) meaning, two camps,
﴿الْتَقَتَا﴾
(that met) in combat (in Badr),
﴿فِئَةٌ تُقَـتِلُ فِى سَبِيلِ اللَّهِ﴾
(One was fighting in the Cause of Allah) the Muslims,
﴿وَأُخْرَى كَافِرَةٌ﴾
(And as for the other, in disbelief) meaning, the idolators of Quraysh at Badr. Allah's statement,
﴿يَرَوْنَهُمْ مِّثْلَيْهِمْ رَأْىَ الْعَيْنِ﴾
(They saw them with their own eyes twice their number) means, the idolators thought that the Muslims were twice as many as they were, for Allah made this illusion a factor in the victory that Islam had over them.
It was said that the meaning of Allah's statement,
﴿يَرَوْنَهُمْ مِّثْلَيْهِمْ رَأْىَ الْعَيْنِ﴾
(They saw them with their own eyes twice their number) is that the Muslims saw twice as many idolators as they were, yet Allah gave them victory over the disbelievers. Abdullah bin Masud said, ''When we looked at the disbelievers' forces, we found that they were twice as many as we were. When we looked at them again, we thought they did not have one man more than we had. So Allah's statement,
﴿وَإِذْ يُرِيكُمُوهُمْ إِذِ الْتَقَيْتُمْ فِى أَعْيُنِكُمْ قَلِيلاً وَيُقَلِّلُكُمْ فِى أَعْيُنِهِمْ﴾
(And (remember) when you met, He showed them to you as few in your eyes and He made you appear as few in their eyes.) ﴿8:44﴾''.
When the two camps saw each other, the Muslims thought that the idolators were twice as many as they were, so that they would trust in Allah and seek His help. The idolators thought that the believers were twice as many as they were, so that they would feel fear, horror, fright and despair. When the two camps stood in lines and met in battle, Allah made each camp look smaller in the eyes of the other camp, so that they would be encouraged to fight each other,
﴿لِّيَقْضِيَ اللَّهُ أَمْراً كَانَ مَفْعُولاً﴾
(so that Allah might accomplish a matter already ordained.) ﴿8:42﴾ meaning, so that the truth and falsehood are distinguishable, and thus the word of faith prevails over disbelief and deviation, so that the believers prevail and the disbelievers are humiliated. In a similar statement, Allah said,
﴿وَلَقَدْ نَصَرَكُمُ اللَّهُ بِبَدْرٍ وَأَنتُمْ أَذِلَّةٌ﴾
(And Allah has already made you victorious at Badr, when you were a weak little force) ﴿3:123﴾. In this Ayah ﴿3:13﴾ Allah said,
﴿وَاللَّهُ يُؤَيِّدُ بِنَصْرِهِ مَن يَشَآءُ إِنَّ فِى ذَلِكَ لَعِبْرَةً لاوْلِى الاٌّبْصَـرِ﴾
(And Allah supports with His victory whom He wills. Verily, in this is a lesson for those who understand.) meaning, this should be an example for those who have intelligence and sound comprehension. They should contemplate about Allah's wisdom, decisions and decree, that He gives victory to His believing servants in this life and on the Day the witnesses stand up to testify. (Source: copied from the tafsir of ibn katheer on these ayat)
