BİRİNCİ FEN · BİRİNCİ BÂB · ÜÇÜNCÜ FASIL · Üçüncü Madde
Third Article
Concerning the Easiest Method of Addition.
O esteemed one! Know that arithmetic scholars have stated: The easiest method of addition is as follows: When two or more numbers are to be added, write the digits in the ones place beneath each other. Similarly, arrange the tens and hundreds digits so they align vertically, and finally draw a line beneath all of them. They call this the "addition line."
Thereafter, beginning from the right side, add the digit at each place value to the digit below it, observing each place value as it is completed; if the sum is less than ten, write it beneath the addition line in alignment with its place.
And if the sum reaches ten, write zero (0) in its place beneath the addition line and, accepting ten as one, add it to the digit in the tens place on the left.
If the sum of the digits in the tens place also exceeds ten, then write the excess digit below the addition line, aligning it with the tens place.
Accepting the remaining ten as one, add it to the number in the hundreds place. Thus, accept each ten as one and add it to the values on the left. For every ten found on the right is equivalent to one of what is found on its left.
And if there is no digit in the leftmost place, write the remaining digit below the addition line, aligning it with the nonexistent place. If a digit is not found beneath any place value, write that digit below the addition line in the same place value. The process proceeds as follows:
00373 + 02318 + 73514 = 76205
Verification: [432] 2/2
If the number of digits you are adding is more than three or four, add them in groups of four beneath a line. (As you continue the process downward) disregard the numbers above the addition line and add the result to the numbers below. Continue this way (with grouping) until all the numbers being added are exhausted.
Write the name of each number that has been added, i.e., which commodity each price belongs to, on the left side in alignment with its place. The method for this is as follows: Write the names of the items to which the numbers belong down the left side of a long sheet of paper, one beneath the other.
Thus, simultaneously, write the corresponding number next to each name in Hindu numerals, ensuring that the digits in the ones, tens, and hundreds places align vertically with their respective place values.
Write zero in any missing place value and apply the method described above to complete the process. The form of the operation is as follows:
Mushaf-i Sharif: 0032
Tefsir-i Ma’alim: 0654
Tefsir-i Qadi: 0710
Tefsir-i Kabir: 0891
Total: 2287
Jami' al-Bukhari: 0921
Luqat al-Qamus: 0567
Total: 3775
Merely three thousand seven hundred seventy-five (kurush).
Verification: 4/4
This way, the paper on which the operation is performed is called a "tongued ledger," and the numerals are called “black sentences.”
The verification of each number is the sum of the digits that make up the number, after subtracting nine and its multiples, and the remainder from this sum.
However, the verification of addition is done by adding the verifications of the two or more numbers being added and comparing it with the verification of the total itself.
If the two verifications are equal, then the addition has been performed correctly. Otherwise, it is incorrect.
If the verification of the addition does not come out correct, then the operation has not been done correctly. For the verification to be correct, the operation must be correct.
[22/a]