Brahmagupta's propositions on the perpendiculars of cyclic quadrilaterals

Satyanad Kichenassamy (1)

1 LMR - Laboratoire de Mathématiques de Reims

We continue a recent analysis of Propositions XII.21-28 of Brahmagupta's Brāhma-sphuṭa-siddhānta (India, 628 A.D.), on the area and diagonals of the cyclic quadrilateral, by examining Propositions XII.29-32, that explain how to determine the perpendiculars as well as all the portions of diagonals and perpendiculars. These results include the result nowadays referred to as "Brahmagupta's theorem" (XII.30-31). Brahmagupta describes both the geometric situation and the key elements of the derivation of his results. We analyze the expression of hypotheses and derivations, using only Brahmagupta's conceptual framework, that does not include the notion of angle, and uses proportion only in a standard form (XII.25).

Mots clés: Geometry; medieval India; chord quadrilaterals; circumradius and circumcircle; mirror symmetry

Domaines: Histoire et perspectives sur les mathématiques [math.HO]; Mathématiques générales [math.GM]; Géométrie métrique [math.MG]; Histoire, Philosophie et Sociologie des sciences

Satyanad Kichenassamy. Brahmagupta's propositions on the perpendiculars of cyclic quadrilaterals. Historia Mathematica, 2012, 39 (4), pp.387-404. ⟨10.1016/j.hm.2012.07.004⟩. ⟨hal-00826942⟩