الحَمدُ لِلَّه الذي هَدانا

وَنَقَّحَ العُقولَ والأذهانا

Praise be to Allah who guided us

And refined our minds and thoughts

وَصَلَواتُه عَلى مُحَمَّد

نَبِيِّه المختارِ طولَ الأمَدِ

And blessings upon Muhammad

His chosen prophet for all time

والشُّكرُ للشَّيخ الفَقيه العالِم

أُستاذِنا مُحمَّدِ بن قاسِمِ

Thanks to the learned scholar and jurist

Our teacher Muhammad ibn Qasim

وَهوَ الَّذي ذَلَّلَ مَا قَدِ امتَنَع

وأَوضَح المبهَمَ حتّى قد نصَع

He who made easy what was difficult

And clarified the ambiguous to lucidity

فالله يَجزيهِ جزيلَ الخَير

وَيَختِمُ الأخرَى لَهُ بالأجرِ

May Allah reward him abundantly

And conclude his life with virtue

لما بدت ليَ الجُذورُ مُغلَقَه

نَظَمتُ في أَجناسِها المحقَّقه

When roots seemed obscured to me

I composed, in verified categories

أُرجوزَةً تُبَيِّنُ ما قَدِ انبهم

وَتُوَضِّح المشكِلَ مِن تِلكَ البُهَم

A poem that clarifies ambiguities

And elucidates those conundrums

يا سائِلي عَن صِفَةِ الجذورِ

اسمَع هُديتَ لِعُلَى الأمورِ

O you who ask about the nature of roots

Listen to my guide for lofty matters

فَإنَّها قد قُسِّمَت لِسِتَّه

الضَّرب ثمَّ الجَمع ثُمَّ القِسمَه

They are divided into six kinds

Multiplication, addition, division

وَبَعدَهُ التَّضعيفُ يَتلو الطَّرحا

والسّادِسُ التَّجذيرُ فيها أضحا

Followed by doubling, subtraction

And sixth, taking the root, is evident

فَإن أَرَدتَ ضَربَ جَذرِ العَدَد

في مِثلِهِ أو غَيرِهِ أَو عَدَد

If you want to multiply a root

By itself or another number

فَرَبِّعهُما عَلَى انفِرادِ

واضرِبهُما كالضَّربِ للاعدادِ

Square them individually

And multiply as with numbers

وَجَذرُ ما يَخرُجُ فَهو الخارِج

وَمِن هُنا تَبدو لَكَ المناهِج

The root of the product is the result

And from this, methodologies become clear

وَالجَمعُ فَاسمَعهُ كلاماً مُجمَلا

أَن تَجمَعَ المرَبَّعَين أَوَّلا

And addition, listen to it generally

Is that you first square the two

وَلتَضربنهُما كَما تَقَدَّما

وَتَأخُذَ الجّذرَ مِنَ الجميعِ

Then multiply them as mentioned before

And take the root of the total

فَذاكَ وَجهُ الجمعِ للجُذور

مِنَ الأصَمِّ أو مِنَ المجذور

That is how to add roots

Of integers or of surds

وَأَوجُهُ القِسمَةِ عِندِي أَربَعَه

خُذها لَدَيكَ شَرحُها مُنَوَّعَه

And for me the cases of division are four

Take them, their explanation is varied

فَقِسمَةُ الفَردِ عَلى المنفَرِد

أَن تَقسشمَ التَّربيعَ قَسمَ العَدَد

Dividing an odd number by itself

Is dividing its square by the number

والجيمُ أَيضاً لا يَزالُ تَابِعاً

يُنبي عَنِ التَّجذير فيما رُبِّعا

Jim also always follows

To indicate taking the root of what was squared

وَقسمَةُ الفَردِ عَلَى التركيبِ

فَقِس لَهُ وَجهاً مِنَ الضُّروبِ

And dividing an odd number by a compound

Divide it as one case of methods

أَن تَضرِبَ التركيبَ في مُنفَصِلِه

فإن غَدا فَضلاً فَفي مُتَّصلِه

That you multiply the compound by its singular

If there is a remainder, then in its annex

وَتَقسِمَ الفَردَ عَلَى مَا قَد بدا

مِن ضَربِكَ المركَّبين أَبَدا

And divide the odd number by what results

From your multiplying the two compounds

ثُمَّ اضرِب الخارجَ في المنفَصِل

إن كانَ مَفصولاً أو المتَّصِل

Then multiply the quotient by the singular

If it's detached or annexed

فَذاكض ما يخرُجُ مِن قِسمَتِه

سُبحانَ مَن أَوضَحَ مِن حِكمَتِه

That is what results from its division

Glory to the One who clarified His wisdom

وَقسمَةُ المركَّبِ المعلُومِ

عَلى المفرَدِ مِنَ المقسومِ

And dividing a known compound

By a singular divisor

أَن تَقسِمَ الأفرادَ مِمّا رُكِّبا

فَرداً عَلى فَردٍ كَما قَد رَكِّبا

Is dividing its singular components

One by one as they were compounded

كَما الَّذي قَد قُلته في القِسمَه

فَاسمَع هَداك الله رَبُّ الحِكمَه

As I already said about division

Listen, God guides to wisdom

وَإن تُرشد أَن تَقسِمَ المُرَكَّبا

عَلى مِثالِ غَيرِهِ قَد رُكِّبا

And if you want to divide a compound

By another like it, compounded

فَلتَقسِمَنَّ مُفرَدات الأعلى

فَرداً فَفَرداً كَي توفى الأصلا

Divide the top singulars

One by one to fulfill the principle

على مُركِّباتش شَطر الثاني

فيكمُلُ الكلُّ بِالامتِحانِ

By the bottom compounds' halves

The total is complete with testing

وشَرطُ مَا تُرِيدُ مِن صِحَّتِها

أَن تَضرِبَ الخارِجَ من قسمَتِها

The condition for its validity

Is multiplying the quotient from its division

فيما عَلَيهِ قَد قَسَمتَ أوَّلا

يَخرُج ما قَسَمتَهُ مُكَمَّلا

By what you originally divided

The complete result emerges

والجذرُ إن أَرَدتَ أَن تُضعِفَهُ

فَضَربُهُ في اثنين يُبدي ضِعفَهُ

And if you want to double a root

Multiplying by two reveals its double

وَإن أَرَدتَ ضِعفَهُ مِثل عَدَد

فَاضرِبهُ في عِدَّتِهِ عَلى سَدَد

And if you want its double as a number

Multiply it by its count, properly

يَخرُجُ مَا أَرَدتَ مِن تَضعِيفِ

مِن غَير ما شَكٍّ ولا تحريفِ

The desired doubling emerges

Without doubt or distortion

والفَضلُ مِن تَربيعكَ الجَذرَينِ

عَلى الَّذِي يَبدو مِن الاثنين

And the remainder from squaring your two roots

Over what appears from the two

في الضَّربِ إِن أَرَدتَ جَذرَ الباقي

فَرَبِّعِ المطلوبَ باستحقاقِ

In multiplication, if you want the root of the remainder

Square the desired, as is fitting

وَمِثلُ هذا طَرحك الجُذورا

فَبِالآله ثِق وكُن شَكورَا

The same for subtracting roots

So trust the device and be grateful

وَلتَرسِم التَّجذيرَ في النَّوعَين

خَطّاً مُفرَّداً وفي نَوعَين

And represent taking the root in two ways

With a single line and in two ways

وَلتَجعَل الجيمَ عَلى المنفَرِد

فَذاك جَذرُهُ بِغَير فَنَد

And put Jim on what is singular

That is its root without difficulty

هَذا اِصطِلاحٌ في العَمَل

........................

This is terminology for practice

........................

وَجَذرُ ما رُكِّب مِن خَطَّينِ

فاختَلَفا بِسَببِ الاسمَينِ

And the root of what is compounded of two lines

Which differ due to the two names

فَرَبِّع الأنصافَ مِن كِلَيهما

وانقِص مِنَ الأكبَرِ أَصغَرَيهما

Square the halves of both

And subtract the smaller from the larger

وما بَقِيَ فاكسِهِ لَفظَ الجَذرِ

وَأنقِصهُ مِن نِصفِ عَظيمِ القَدرِ

And what remains, multiply by the root term

And subtract it from the larger half

وَفَضلُ ما يَبقى لتأخُذ جَذرَه

واجعَلهُ مَحفوظا واكتم سرَّه

The remainder, take its root

And keep it hidden, conceal its secret

واحمِل عَلَى التَّنصيف ما نَقَصتا

ثُمَّ خُذ الجَذرَ إذا أَضَفتا

And carry to halving what was subtracted

Then take the root when they are added

وَجَذرُكَ المحفوظُ في المنفَصِلِ

فَافصِلهُ مِن نِصفِ العَظيمِ الأطوَلِ

And your root kept in the singular

Separate it from the larger half's half

فَذاكَ جَذرُ خَطِّكَ المرَكَّب

وهو ذو الاسمَين فافهم تُصِب

That is the root of your compound line

The one with two names, so understand precisely

والجَذرُ إن ضَرَبتَه فِي مِثلِهِ

يَخرُج ما جَذَّرتَهُ بِكُلِّه

And if you multiply a root by its like

What you rooted entirely emerges

فَهكَذا حَدِّث عَنِ الجُذورِ

عَلى عَروضِ الرَّجَزِ المشطورِ

This is how to speak of roots

In recurring rajaz meter

جَعلتُها تَذكِرةً للبادِي

وَقُدوَةً وسَدَداً لِلشّادي

I made it a reminder for the initiate

And an example and guide for the adept

فَالحَمدُ للكريمِ ذي المحامِدِ

سُبحانَه سُبحانَهُ مِن ماجِدِ

So praise to the Bountiful, of endless praise

Glory to Him, Glory to Him, the Majestic

ثُمَّ الصَّلاةُ والسَّلام أَبَدا

على النَّبِيِّ العَرَبيِّ أَحمدا

Then blessings and peace forever

Upon the Arab Prophet Ahmad