This method had been used by the Greeks, but they did not generalize the method to cover all equations with positive roots.
Metode ini sudah dipakai oleh bangsa Yunani, tetapi mereka tidak menggeneralisasi metode ini untuk semua persamaan berakar positif.
For example, to solve the equation x 3 + ab x +a=bx} , with a and b positive, he would note that the maximum point of the curve yb x − x 3 } occurs at xb 3 {3}}}} , and that the equation would have no solutions, one solution or two solutions, depending on whether the height of the curve at that point was less than, equal to, or greater than a. His surviving works give no indication of how he discovered his formulae for the maxima of these curves.
, ia menulis bahwa titik maksimum kurva yb x − x 3 } ada di xb 3 {3}}}} , dan persamaan tersebut bisa tidak punya solusi, satu solusi, atau dua solusi, tergantung apakah tinggi kurva pada titik tersebut kurang dari, sama dengan, atau lebih besar daripada a. Karya-karyanya yang berhasil diselamatkan tidak memberi petunjuk mengenai cara ia menemukan rumus nilai maksimum kurva tersebut.
The first explicit formulation of the principle of induction was given by Pascal in his Traité du triangle arithmétique (1665).
Perumusan prinsip induksi yang eksplisit pertama dipaparkan oleh Blaise Pascal dalam Traité du triangle arithmétique (1665).
The Greeks had discovered irrational numbers, but were not happy with them and only able to cope by drawing a distinction between magnitude and number.
Bangsa Yunani menemukan bilangan irasional, namun mereka tidak senang dan hanya mampu membedakan besaran dan bilangan.
In the Greek view, magnitudes varied continuously and could be used for entities such as line segments, whereas numbers were discrete.
Dalam pandangan Yunani, besaran terus berubah dan dapat digunakan untuk beberapa hal seperti rentang garis, sedangkan bilangan bersifat diskret.
Hence, irrationals could only be handled geometrically; and indeed Greek mathematics was mainly geometrical.
Karena itu, bilangan irasional hanya dapat diselesaikan oleh geometri dan matematika Yunani memang cenderung geometris.
Islamic mathematicians including Abū Kāmil Shujāʿ ibn Aslam and Ibn Tahir al-Baghdadi slowly removed the distinction between magnitude and number, allowing irrational quantities to appear as coefficients in equations and to be solutions of algebraic equations.
Sejumlah matematikawan Islam seperti Abū Kāmil Shujāʿ ibn Aslam perlahan menghapus perbedaan antara besaran dan bilangan, sehingga memungkinkan jumlah irasional tampak seperti koefisien dalam persamaan dan solusi bagi persamaan aljabar.
He revised Ptolemy's Geography and wrote on astronomy and astrology.
Ia merevisi Geography karya Ptolomeus dan menulis tentang astronomi dan astrologi.
'Abd al-Hamīd ibn Turk (fl. 830) (quadratics)
'Abd al-Hamīd ibn Turk (fl. 830) (kuadratika)
Al-Khayyām (1048–1131) Ibn Maḍāʾ (c. 1116–1196)
Ibn Yaḥyā al-Maghribī al-Samawʾal (c. 1130 – c. 1180) Ibn Maḍāʾ (c. 1116 - 1196)
Archived from the original on 2018-12-24.
Diarsipkan dari asli tanggal 2018-12-24.
O'Connor, John J.; Robertson, Edmund F. (1999), "Arabic mathematics: forgotten brilliance?
Diakses tanggal 2013-05-27. ; Pemeliharaan CS1: Tanggal dan tahun (link) O'Connor, John J.; Robertson, Edmund F., "Arabic mathematics: forgotten brilliance?
", MacTutor History of Mathematics Archive, University of St Andrews Richard Covington, Rediscovering Arabic Science, 2007, Saudi Aramco World
Richard Covington, Rediscovering Arabic Science, 2007, Saudi Aramco World