وَللكَفّاتِ في المجهولِ وجهٌ

وَللكَفّاتِ في المجهولِ وجهٌ

إذا هُوَ قَد بَدا لم يُبقِ جَهلا

إذا هُوَ قَد بَدا لم يُبقِ جَهلا

And the balance pans have a method for the unknown;

The unknown has a face

once it has become clear, it leaves no ignorance.

When it appears, ignorance is no more

فَخُذ عَدَدَين واسقِط فَهُما ما

فَخُذ عَدَدَين واسقِط فَهُما ما

اَرَدتَ مُقابِلاً فَضلاً فَفَضلا

اَرَدتَ مُقابِلاً فَضلاً فَفَضلا

So take two numbers and subtract; for they are what

Take two numbers and subtract what

you intended, comparing one excess after another.

You want as surplus or surplus

فَتضنقُص أو تَزيدُ فَسَمِّ هذا

فَتضنقُص أو تَزيدُ فَسَمِّ هذا

خَطأَ الكَفّات لا أَخطََت فِعلا

خَطأَ الكَفّات لا أَخطََت فِعلا

Then you fall short or exceed; call this

So you decrease or increase, then call this

the error of the balance pans—may you never err in practice.

The error of the unknown, not its deeds

فَزايدُهُنَّ يُثبتُ فَوقَ خضطٍّ

فَزايدُهُنَّ يُثبتُ فَوقَ خضطٍّ

وَناقِصُهُنَّ يُثبتُ مِنهُ سُفلا

وَناقِصُهُنَّ يُثبتُ مِنهُ سُفلا

So their excess is recorded above a line,

Increasing it affirms above the line

and their deficit is recorded below it.

Decreasing affirms below

فَأولى كَفَّتَيكَ اضرِب في الأَقصى

فَأولى كَفَّتَيكَ اضرِب في الأَقصى

مِنَ الخطأَين والأُخرى في الأعلى

مِنَ الخطأَين والأُخرى في الأعلى

Then multiply the first of your two pans by the farther

So your first unknown, multiply by the highest

of the two errors, and the other by the upper one.

Of the two errors, and the other by the greatest

فَحَيثُ تَخالَفَ الخَطآن فَاجمَع

فَحَيثُ تَخالَفَ الخَطآن فَاجمَع

وَحَيثُ تَجَانسا حُطَّ الاَقَلاّ

وَحَيثُ تَجَانسا حُطَّ الاَقَلاّ

So, when the two errors differ in sign, add;

Where the two errors differ, add

and when they share a sign, subtract the smaller.

Where they agree, subtract the lesser

وَتَقسِم ما جَمَعتَ لَدى اختلاف

وَتَقسِم ما جَمَعتَ لَدى اختلاف

عَلَى الخَطأَين مَجموعَين كَلاّ

عَلَى الخَطأَين مَجموعَين كَلاّ

And divide what you added, when they differ,

And divide what you added at difference

by the two errors, both added together.

By the two errors added both

فَيَخرُج مالُكَ المجهول شَمساً

فَيَخرُج مالُكَ المجهول شَمساً

يُرِكَ الجضهلَ عنه قَد تَوَلاّ

يُرِكَ الجضهلَ عنه قَد تَوَلاّ

Then your unknown quantity emerges as a sun,

So your unknown comes out a sun

showing you that ignorance of it has departed.

That leaves ignorance behind, having departed