so there is no contradiction in this. if it is said how did you know that what you have arrived at is knowledge related to the known as it is but rather it is ignorance that you thought was knowledge? we say if a denier denies the mathematical sciences what is said to him? is he not foolish in his mind? and it is said to him this indicates your lack of insight into mathematical matters. for if the one who studies geometry confines the premises and arranges them in the necessary form knowledge of the result is necessarily obtained in a way that is not disputed. thus is our answer in rational matters for if theoretical premises are arranged according to their conditions they provide knowledge of the result on the face of the earth that is not disputed. in it and the knowledge gained from the premises after their occurrence is necessary like the knowledge of the necessary premises that produce it. and if we wanted to reveal that to someone whose merchandise in the sciences is little then we would give him a geometric example then we would give him a rational example so that the cover would be removed for him and the hidden belief would be revealed. as for the geometric example it is that euclid drew in his book in the first figure of the first article a triangle and claimed that it was equilateral and he did not know that by the intuition of the mind but he claimed that he knew by proof by sight and his proof by the premises is that the straight lines coming out from the center of the circle to the circumference are equal from every this introduction is necessary because the circle is drawn with a compass on one opening but the straight line from the center to the circle is the opening of the compass and it is one in the sides.
فهذا لا تناقض فيه فان قيل وبم عرفتم ان ما وصلتم اليه علم متعلق بالمعلوم على ما هو به بل هو جهل ظننتموه علما قلنا ولو انكر العلوم الحسابية منكر فماذا يقال له او ليس يسفه في عقله ويقال له هذا يدل على قلة بصيرتك بالحسابيات فإن الناظر في الهندسة اذا حصر المقدمات ورتبها على الشكل الواجب يحصل العلم بالنتيجة ضرورة على وجه لا يتمارى فيه فهكذا جوابنا في المعقولات فان المقدمات النظرية اذا رتبت على شروطها افادت العلم بالنتيجة على وجه الارض لا يتمارى فيه ويكون العلم المستفاد من المقدمات بعد حصولها ضروريا كالعلم بالمقدمات الضرورية المنتجه له وإن اردنا أن نكشف ذلك لمن قلت بضاعته في العلوم فنضرب له مثالا هندسيا ثم نضرب له مثالا عقليا لينكشف له الغطاء وينجلي عن عقيدته الخفاء اما المثال الهندسي فهو ان إقليدس رسم في مصنفه في الشكل الأول من المقالة الأولى مثلثا وادعى انه متساوي الاضلاع ولا يعرف ذلك ببديهة العقل ولكنه ادعى انه يعرف بالبرهان نظرا وبرهانه بمقدمات ان الخطوط المستقيمة الخارجة من مركز الدائرة الى المحيط متساوية من كل جانب وهذه المقدمة ضرورية إذ الدائرة ترسم بالبركار على فتح واحد وانما الخط المستقيم من المركز الى الدائرة هوفتح البركار وهو واحد في الجوانب