الحمد لله الذي هدانا — Ibn Alyasmen

الحَمدُ لِلَّه الذي هَدانا

وَنَقَّحَ العُقولَ والأذهانا

Praise be to God, who guided us,

and refined intellects and minds.

وَصَلَواتُه عَلى مُحَمَّد

نَبِيِّه المختارِ طولَ الأمَدِ

And His blessings be upon Muhammad,

His chosen prophet, for all time.

والشُّكرُ للشَّيخ الفَقيه العالِم

أُستاذِنا مُحمَّدِ بن قاسِمِ

And thanks to the shaykh, the learned jurist,

our teacher, Muhammad ibn Qasim.

وَهوَ الَّذي ذَلَّلَ مَا قَدِ امتَنَع

وأَوضَح المبهَمَ حتّى قد نصَع

And he is the one who made tractable what had resisted,

and clarified the obscure until it became clear.

فالله يَجزيهِ جزيلَ الخَير

وَيَختِمُ الأخرَى لَهُ بالأجرِ

So may God reward him with abundant good,

and crown his life to come with reward.

لما بدت ليَ الجُذورُ مُغلَقَه

نَظَمتُ في أَجناسِها المحقَّقه

When roots appeared obscure to me,

I composed, on their established kinds,

أُرجوزَةً تُبَيِّنُ ما قَدِ انبهم

وَتُوَضِّح المشكِلَ مِن تِلكَ البُهَم

a rajaz poem explaining what had grown obscure,

and clarifying the difficulties among those obscurities.

يا سائِلي عَن صِفَةِ الجذورِ

اسمَع هُديتَ لِعُلَى الأمورِ

O you who ask me about the nature of roots,

listen—may you be guided to the loftiest matters.

فَإنَّها قد قُسِّمَت لِسِتَّه

الضَّرب ثمَّ الجَمع ثُمَّ القِسمَه

For they have been divided into six:

multiplication, then addition, then division;

وَبَعدَهُ التَّضعيفُ يَتلو الطَّرحا

والسّادِسُ التَّجذيرُ فيها أضحا

and after it, doubling follows subtraction;

and root extraction is the sixth among them.

فَإن أَرَدتَ ضَربَ جَذرِ العَدَد

في مِثلِهِ أو غَيرِهِ أَو عَدَد

If you wish to multiply the root of a number

by its like, another root, or a number,

فَرَبِّعهُما عَلَى انفِرادِ

واضرِبهُما كالضَّربِ للاعدادِ

then square each of the two separately,

and multiply them as you multiply numbers.

وَجَذرُ ما يَخرُجُ فَهو الخارِج

وَمِن هُنا تَبدو لَكَ المناهِج

And the root of what results is the product,

and from here the methods become clear to you.

وَالجَمعُ فَاسمَعهُ كلاماً مُجمَلا

أَن تَجمَعَ المرَبَّعَين أَوَّلا

As for addition, hear it in a concise account:

first add the two squares,

وَلتَضربنهُما كَما تَقَدَّما

وَتَأخُذَ الجّذرَ مِنَ الجميعِ

and be sure to multiply them as explained before,

and take the root of the whole.

فَذاكَ وَجهُ الجمعِ للجُذور

مِنَ الأصَمِّ أو مِنَ المجذور

That is the method for adding roots,

whether surd or exact.

وَأَوجُهُ القِسمَةِ عِندِي أَربَعَه

خُذها لَدَيكَ شَرحُها مُنَوَّعَه

I have four methods of division;

take them to hand; their explanation has several forms.

فَقِسمَةُ الفَردِ عَلى المنفَرِد

أَن تَقسشمَ التَّربيعَ قَسمَ العَدَد

To divide a single term by another single term,

divide the squared values as you divide numbers.

والجيمُ أَيضاً لا يَزالُ تَابِعاً

يُنبي عَنِ التَّجذير فيما رُبِّعا

The letter jim, too, remains appended,

indicating root extraction in what has been squared.

وَقسمَةُ الفَردِ عَلَى التركيبِ

فَقِس لَهُ وَجهاً مِنَ الضُّروبِ

To divide a single term by a compound,

apply to it a method among the procedures:

أَن تَضرِبَ التركيبَ في مُنفَصِلِه

فإن غَدا فَضلاً فَفي مُتَّصلِه

multiply the compound by its subtractive counterpart;

but if it is a difference, use its additive counterpart.

وَتَقسِمَ الفَردَ عَلَى مَا قَد بدا

مِن ضَربِكَ المركَّبين أَبَدا

And divide the single term by what has resulted

from your multiplication of the two compounds, always.

ثُمَّ اضرِب الخارجَ في المنفَصِل

إن كانَ مَفصولاً أو المتَّصِل

Then multiply the quotient by the subtractive counterpart,

if it was subtractive, or by the additive one.

فَذاكض ما يخرُجُ مِن قِسمَتِه

سُبحانَ مَن أَوضَحَ مِن حِكمَتِه

That is what results from its division.

Glory to Him who gave clarity through His wisdom.

وَقسمَةُ المركَّبِ المعلُومِ

عَلى المفرَدِ مِنَ المقسومِ

To divide the known compound

by a single term of the dividend,

أَن تَقسِمَ الأفرادَ مِمّا رُكِّبا

فَرداً عَلى فَردٍ كَما قَد رَكِّبا

divide the individual terms of which it is composed,

term by term, just as they were compounded,

كَما الَّذي قَد قُلته في القِسمَه

فَاسمَع هَداك الله رَبُّ الحِكمَه

as in what I have already said about division.

So listen—may God, Lord of wisdom, guide you.

وَإن تُرشد أَن تَقسِمَ المُرَكَّبا

عَلى مِثالِ غَيرِهِ قَد رُكِّبا

And if you are guided to divide a compound

by another similarly compounded expression,

فَلتَقسِمَنَّ مُفرَدات الأعلى

فَرداً فَفَرداً كَي توفى الأصلا

then be sure to divide the terms of the upper expression,

one by one, to account for the original quantity,

على مُركِّباتش شَطر الثاني

فيكمُلُ الكلُّ بِالامتِحانِ

by the compounds of the second part;

then the whole is completed by verification.

وشَرطُ مَا تُرِيدُ مِن صِحَّتِها

أَن تَضرِبَ الخارِجَ من قسمَتِها

And the condition for the correctness you seek

is to multiply the quotient of that division

فيما عَلَيهِ قَد قَسَمتَ أوَّلا

يَخرُج ما قَسَمتَهُ مُكَمَّلا

by what you originally divided by:

what you divided will result in full.

والجذرُ إن أَرَدتَ أَن تُضعِفَهُ

فَضَربُهُ في اثنين يُبدي ضِعفَهُ

And if you wish to double a root,

multiplying it by two gives its double.

وَإن أَرَدتَ ضِعفَهُ مِثل عَدَد

فَاضرِبهُ في عِدَّتِهِ عَلى سَدَد

And if you wish to multiply it a certain number of times,

multiply it by that count, correctly.

يَخرُجُ مَا أَرَدتَ مِن تَضعِيفِ

مِن غَير ما شَكٍّ ولا تحريفِ

What you wanted from multiplying will result,

without any doubt or distortion.

والفَضلُ مِن تَربيعكَ الجَذرَينِ

عَلى الَّذِي يَبدو مِن الاثنين

And the excess from your squaring the two roots

over what results from the two

في الضَّربِ إِن أَرَدتَ جَذرَ الباقي

فَرَبِّعِ المطلوبَ باستحقاقِ

in multiplication—if you wish the root of the remainder,

then square the sought quantity as required.

وَمِثلُ هذا طَرحك الجُذورا

فَبِالآله ثِق وكُن شَكورَا

And your subtraction of roots is like this;

so trust in God and be thankful.

وَلتَرسِم التَّجذيرَ في النَّوعَين

خَطّاً مُفرَّداً وفي نَوعَين

And mark root extraction in the two kinds

with a single line; and in two kinds,

وَلتَجعَل الجيمَ عَلى المنفَرِد

فَذاك جَذرُهُ بِغَير فَنَد

place the letter jim above the single term;

that is its root, without error.

هَذا اِصطِلاحٌ في العَمَل

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

This is a convention in calculation.

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

وَجَذرُ ما رُكِّب مِن خَطَّينِ

فاختَلَفا بِسَببِ الاسمَينِ

And for the root of what is composed of two lines,

which differ because of the two terms,

فَرَبِّع الأنصافَ مِن كِلَيهما

وانقِص مِنَ الأكبَرِ أَصغَرَيهما

square the halves of both,

and subtract the smaller of the two from the larger.

وما بَقِيَ فاكسِهِ لَفظَ الجَذرِ

وَأنقِصهُ مِن نِصفِ عَظيمِ القَدرِ

And clothe what remains in the word 'root',

and subtract it from half the greater quantity.

وَفَضلُ ما يَبقى لتأخُذ جَذرَه

واجعَلهُ مَحفوظا واكتم سرَّه

And take the root of the remainder,

keep it in reserve, and conceal its secret.

واحمِل عَلَى التَّنصيف ما نَقَصتا

ثُمَّ خُذ الجَذرَ إذا أَضَفتا

And add to the half what you subtracted,

then take the root once you have added it.

وَجَذرُكَ المحفوظُ في المنفَصِلِ

فَافصِلهُ مِن نِصفِ العَظيمِ الأطوَلِ

And your reserved root, in the subtractive case,

subtract it from half the larger, longer line.

فَذاكَ جَذرُ خَطِّكَ المرَكَّب

وهو ذو الاسمَين فافهم تُصِب

That is the root of your compound line,

and it has two terms—understand, and you will be right.

والجَذرُ إن ضَرَبتَه فِي مِثلِهِ

يَخرُج ما جَذَّرتَهُ بِكُلِّه

And if you multiply a root by its like,

the whole quantity whose root you took will result.

فَهكَذا حَدِّث عَنِ الجُذورِ

عَلى عَروضِ الرَّجَزِ المشطورِ

Thus speak of roots,

in the meter of half-line rajaz.

جَعلتُها تَذكِرةً للبادِي

وَقُدوَةً وسَدَداً لِلشّادي

I made it a reminder for the beginner,

and a model and guidance for the learner.

فَالحَمدُ للكريمِ ذي المحامِدِ

سُبحانَه سُبحانَهُ مِن ماجِدِ

So praise be to the Generous One, whose qualities merit praise.

Glory be to Him, glory be to Him—how glorious He is!

ثُمَّ الصَّلاةُ والسَّلام أَبَدا

على النَّبِيِّ العَرَبيِّ أَحمدا

Then blessings and peace forever

upon the Arab prophet, Ahmad.