In this study, we focus on the composition of the Virgin and Child with Saint Anne by Leonardo da Vinci. The composition is considered first from the point of view of graphs and the genealogy of the Christ is analyzed accordingly. Then, the composition of the masterpiece is studied from the perspective of scientific knowledges in geometry. The many ellipses or part of ellipses in the composition are detailed. This study permits us to revisit the movement of the figures. Knowledges on celestial mechanics at the time of Leonardo are presented and themes like destiny and resurrection are examined consequently. Finally, the representation of instabilities and turbulences is considered in the painting and the renewal of forms is examined.