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two hundred and forty ratls a unit of weight, similar to a pound, though its value varied by region, and each ratl is one hundred and forty-four dirhams. A mudd a small dry measure is sixty-four grains of wheat.
In every square, if you square the number of the square preceding it, the result of that squaring is what must be in the square after the next, acting as a doubling. For example: in the first square there is one. If we square what is in the third [square], for instance, we get what is in the fifth. If we square what we obtained in the fifth, we get what is in the ninth. If we square that, we get what is in the seventeenth. If we square that, we get what is in the thirty-third. If we square that, we get what is in the sixty-fifth. The author is describing a mathematical shortcut for calculating powers of two: $(2^n)^2 = 2^{2n}$. By squaring the values of previous squares, one jumps exponentially through the board. If we then subtract one from it, the remainder is the total of all the squares combined up to the sixty-fourth square. If we subtract it before one is taken from it, half of it is the result for the sixty-fourth square alone. By this method, the doubling of the chessboard is achieved in only five operations.
The calculation is complete.
Al-Salah [relates] from Al-Rashid Yusuf bin Abi al-Bayan that Al-Taqi bin Taymiyya The famous 14th-century theologian Ibn Taymiyya, may God have mercy on him, said: "Why, sir, do you read
The calculation is complete.
Ibn Hazm? Ibn Hazm was a famous Andalusian scholar known for his literalist approach and polemical style. The smallest lie he [Ibn Hazm] claimed the Israelites told is that they entered Egypt as seventy-two souls in the time of Joseph, peace be upon him, and at their departure with Moses son of Amram, peace be upon them, they were six hundred thousand."
Al-Rashid said: "I said to him: Is it because Ibn Hazm was a Companion of the Prophet?" He said: "No." I said: "Or a Successor The generation following the Companions?" He said: "No." So I said: "He simply did not know that two and two make four!" He [Ibn Taymiyya] asked: "For what reason?" I said: "Because a chessboard has sixty-four squares; if we double them starting from one, the numbers reach such-and-such"—and I mentioned the previous calculation—"and even then, the Israelites only counted the men." He [Ibn Taymiyya] said: "Then what of the women, children, and the elderly who had reached extreme old age, whom he did not mention?" At this, he fell silent.
Al-Safadi said: What does this mean? I said to him: This [Al-Rashid’s argument] is far-fetched, because a people fleeing for their lives from Pharaoh would, in a period of a thousand years at the least, have to carry their belongings, their banners, and what suffices them. So he fell silent. I answered him that Moses, peace be upon him, was with them, and in his hand was the Staff with which he struck the rock so that twelve springs gushed forth from it; God’s care for them carried them and aided them in everything they needed.
In summary, that which Ibn Hazm found improbable cannot be denied, even though it is a large number as they claim. I say: Abu Ishaq al-Sabi'i related from Abu 'Ubayda, from Abdullah bin Mas'ud, who said: "The Israelites entered Egypt as sixty-three people, and they departed from it as six hundred and seventy thousand." And Moses bin 'Ubayda said, on the authority of Muhammad bin Ka'b al-Qurazi, from Abdullah bin Sanad: "The family of Jacob gathered to Joseph, peace be upon him..."