Sol 6.1

  1. الحمدُ للهِ عَلى ما اَلَهما

    وَمَنَّ مِن تعلِيمِه وفَهَّما

    Praise be to God for what He inspired,

    and for the teaching He bestowed and the understanding He gave.

  2. وَصَلَوات اللهِ طولَ الأبَدِ

    عَلى النَّبِيِّ المُصطَفى مُحَمَّدِ

    And God's blessings throughout eternity

    be upon the chosen Prophet, Muhammad.

  3. والشكرُ لِلحَبَرِ الذكيِّ العالِم

    أُستاذِنا مُحمَّدِ بن قاسِمِ

    And thanks to the intelligent, learned scholar,

    our teacher, Muhammad ibn Qasim.

  4. فهو الَّذي بينّ ما قَد اَشكَلا

    وَقَرَّبَ القَاصي حَتَّى سَهُلا

    For he is the one who clarified what was obscure,

    and brought the distant within reach until it became easy.

  5. جَزَاهُ رُبُّ النّاسِ عَنّا خَيرا

    وأجزَلَ الأجرَ لَهُ في الأخرى

    May the Lord of mankind reward him well on our behalf,

    and grant him abundant reward in the hereafter.

  6. كَلَّفَ مَن لا بُدَّ مِن إسعافِهِ

    وَلاَ أرَى وَجهاً إلى خِلافِهِ

    One whom I must oblige charged me,

    and I see no way to oppose him,

  7. أَن أُوضح الجَبريَّةَ المُقَدَّمَه

    في أَحرُفٍ قَلِيلةٍ مُنَظَّمه

    to explain the introductory algebra,

    in a few words arranged in verse,

  8. موزونَةٍ عَلَى عَروضِ الرَّجَز

    كثيرة المعنَى بلفظٍ موجَز

    measured in the rajaz meter,

    rich in meaning and concise in expression.

  9. فَلَم أًَزَل مُعتضذِراً عَن هَذا

    وَلَم أَجد عَن أمرِهِ مَلاذا

    So I kept pleading to be excused from this,

    but found no refuge from his command.

  10. فَقُلتُها قولاَ عَلى اعتِذاريَ

    فَليغفِر الزَّلَّةَ فِيها القاري

    So I composed it despite my plea to be excused;

    let the reader pardon any slip in it.

  11. عَلى ثَلاثَةٍ يدورُ الجَبرُ

    المالُ والأعدادُ ثُمَّ الجذرُ

    Algebra revolves around three things:

    the square, the numbers, and then the root.

  12. فالمالُ كلُّ عَدَدٍ مُربَّعِ

    وَجَذرُهُ واحِدُ تِلكَ الأضلُعِ

    A square is any squared number,

    and its root is one of those sides.

  13. والعَدَدُ المُطلَقُ مَا لَم يُنسب

    لِلمالِ أَو للجَذرِ فافهَم تُصِب

    An absolute number is one not ascribed

    to a square or a root; understand, and you will be right.

  14. والشَّيءُ والجَذرُ بمَعنَى واحِدٍ

    كَالقُولِ في لَفظِ أبٍ وَوالِدِ

    The 'thing' and the root have the same meaning,

    as with the words 'father' and 'begetter'.

  15. فَبَعضُها يَعدِلُ بعضاً عَدَدا

    مُرَكَّباً مَع غَيرِهِ أو مُفرَدا

    Some of these equal others in quantity,

    whether combined with another or standing alone.

  16. فَتِلكَ سِتٌّ نَصفُها مُركَّبَه

    وَنِصفُها بَسيطَةٌ مُرَتَّبه

    These make six: half are compound,

    and half are simple, arranged in order.

  17. أَوَّلُها في الاصطِلاحِ الجارِي

    أَن تَعدِلَ الأموالَ للأجذارِ

    The first, in the customary terminology,

    is to set squares equal to roots.

  18. وَإن تَكُن عَادَلتَ الأعدادَا

    فَهِي تَليها فافهَمِ المُرادا

    If you equate them instead to numbers,

    that follows it; understand what is meant.

  19. وَإن تُعَادِل بالجذورِ عَدَدا

    فَتِلك تَتلوها عَلى ما حُدِّدا

    And if you equate roots to a number,

    that follows next, as specified.

  20. فَاقسِم عَلى الأموال إن وَجَدتَها

    واقسِم عَلَى الأجذارِ إن عَدِمتَها

    So divide by the number of squares, if they are present;

    and divide by the number of roots if squares are absent.

  21. فَهَذِهِ المسائِلُ البَسيطَه

    خَارِجُها الجَذرُ سوى الوَسيطَه

    These are the simple problems;

    their quotient is the root, except in the middle case,

  22. فَإنَّما يَخرُجُ فِيها المالُ

    بِحَسبِ ما قَد اقتَضَى السُّؤالُ

    where only the square results,

    as the question requires.

  23. واعلَم هداكَ رَبُّنا أنَّ العَدَد

    في أوَّلِ المُرَكَّباتِ انفَرَد

    Know—may our Lord guide you—that the number

    stands alone in the first compound case.

  24. وَوَحَّدوا أيضا جُذور الثّانِيه

    وَأَفرَدوا أموَالهم في التالِيه

    They also isolated the roots in the second,

    and set their squares alone in the next.

  25. فَرَبَّع النِّصفَ مِنَ الأشَياء

    وَاحمِل عَلَى الأعداد باعتِناءِ

    So square half the number of 'things',

    and carefully add it to the numbers.

  26. وَخُذ مِنَ الَّذي تَناهَى جذرُه

    ثمَّ انقصِ التَّنصيفَ تفهَم سِرَّه

    Take the root of the resulting total;

    then subtract the half, and you will understand its secret.

  27. فَما بقي فَذاكَ جَذرُ المال

    وَهذِه رابِعَةُ الأحوال

    What remains is the root of the square,

    and this is the fourth case.

  28. واسقِط مِن التَّربيع في الأخرى العدد

    وجَذرُ ما يَبقى عَلَيهِ يُعتَمَد

    Subtract the number from the squared half in the next case,

    and rely upon the root of what remains.

  29. فانقِصه من تَنصيفِك الأجذارا

    وإن تَشَأ جَمَعتَهُ اختيارا

    Subtract it from half your number of roots;

    and, if you wish, you may instead add it.

  30. فَذاكَ جذرُ المَالِ بالنُّقصان

    وَذاكَ جَذرُ المالِ بالحُملان

    That is the root of the square by subtraction,

    and that is the root of the square by addition.

  31. وَإن غَدا التربيعُ مِثلَ العَدَدِ

    فَجذرُه التَّنصِيفُ دونَ فَنَد

    If the squared half equals the number,

    then its root is the half, without error.

  32. وَإن يكُن يُربى عَلَيهِ العَدَد

    أَيقَنتَ أنَّ ذاكَ لا يَنعَضِد

    But if the number exceeds the squared half,

    you can be certain that this cannot hold.

  33. وَإذ فَرَغنا مِن بَيانِ الخامِسَه

    فلنُوضِّح الآنَ بَيانَ السَادِسَه

    Now that we have finished explaining the fifth,

    let us now make the sixth clear.

  34. فَاجمَع إلى أعدادِكَ التَّربيعا

    واستَخرِجَن جَذرَهُما جَمِيعا

    Add the squared half to your numbers,

    and extract the root of their sum.

  35. وَاحمِل عَلى التَّنصيفِ مَا أَخَذتا

    فَذلِك الجذرُ الَّذي أرَدتا

    Add what you obtained to the half,

    and that is the root you sought.

  36. وَحُطّ الأموالَ إذا ما كَثُرت

    واجبُر كُسورَها إذا ما قَصُرَت

    Reduce the squares when they are too many,

    and make their fractions whole when they fall short,

  37. حَتى يَصيرَ الكلُّ مالاً مُفرَدا

    وَخُذ بِذاك الاسمِ مِمّا قَد عدا

    until the whole becomes a single square,

    and apply the same proportion to the remaining terms.

  38. أَو فاضرِب الأموالَ في الأعدادِ

    وكن عَلى ما مَرَّ ذا اعتِمادِ

    Or multiply the number of squares by the numbers,

    and rely on the method already given.

  39. وَاقسِم نَظيرَ الجَذرِ من بَعد عَلى

    عَدَدِ الأموالِ وخُذ ما أُصِّلا

    Then divide the value corresponding to the root by

    the number of squares, and take the resulting root.

  40. وَكُلَّما استَثنيتَ في المسائِل

    صَيّره إيجاباَ مَع المُعادِل

    Whenever you subtract a term in a problem,

    make it positive on the other side of the equation.

  41. وَبَعدَما تَجبُر فَلتُقابِل

    بِطَرحِ مَا نَظيرُهُ مُماثِل

    After restoring, proceed to balance,

    by subtracting whatever has an equal counterpart.

  42. ثُمَّ أَقولُ بَعدُ في المنازِل

    مقالَ إيجازٍ بِلفظٍ شامِل

    Then I shall speak further of the degrees,

    in a brief account with comprehensive wording.

  43. الجَذرُ في الأولى يَليه المالُ

    وبَعدَهُ كَعبٌ لَهُ استقلالُ

    The root is first, followed by the square,

    and after it the cube, standing on its own.

  44. وهكذا رَكب عَلَيهِ أَبَدا

    مَا بَلَغت ومَأ تَناهَت عَدَدا

    And so keep building upon it without end,

    however far you go, whatever number they reach.

  45. وَما ضَربتَه فَخُذ مَنازلَه

    تَعرِف بذَاك الأخذ أُسّاً لِحَاصِلِه

    For whatever you multiply, take its degrees;

    you will thereby know the exponent of its product:

  46. ثلاثة لِكُلِّ كَعبٍ كرَّرا

    واثنان للمالِ مَتَى ما ذُكرا

    three for every repeated cube,

    and two for a square whenever it is mentioned,

  47. وواحدٌ للجَذرِ لا يَنحَرِف

    وَلَيسَ لللأعدادِ أُسٌّ يُعرف

    and one for a root, without variation.

    Numbers have no recognized exponent.

  48. وإن ضَرَبتَ عَدَداً في جِنس

    فالخارجُ الجِنسُ بِغَيرِ لَبسِ

    If you multiply a number by a kind of term,

    the product is that kind, without ambiguity.

  49. وَخارجُ القِسمَةِ في النَّوعَين

    مَقامُهُ عَد بِغَير مَين

    For the quotient of division between two kinds,

    reckon its degree without error.

  50. وَقِسمَةُ الأعلى مِنَ الجِنسَينِ

    خَأرِجُها زِيادَةُ الأسَّين

    When dividing the higher of the two kinds,

    the quotient's degree is the difference of the two exponents;

  51. أَعني بِهذا مالَهُ مِن مَنزِلَه

    وَعَكسُه جَوابُه كالمسأَله

    by this I mean the degree it possesses.

    In the reverse, its answer remains like the original problem.

  52. وَضَربُ كُلِّ زايِدٍ وَناقِصِ

    في نَوعِهِ زِيادةٌ للفاحِصِ

    Multiplying any positive or negative term

    by one of its own sign gives a positive result to the examiner.

  53. وَضربُهُ في ضِدِّهِ نُقصانُ

    فَافهَم هَداكَ المَلكُ الدّيَان

    Multiplying it by its opposite gives a negative result.

    So understand—may the King, the Judge, guide you.

  54. ثُمَّ صَلاةُ الله والسَّلام

    عَلَى النَّبِيِّ ما انجَلى الظَّلام

    Then may God's blessing and peace

    be upon the Prophet as long as darkness lifts.