Brigaglia, Aldo; Nastasi, Pietro Viète’s and Ghetaldi’s Apollonian reconstructions. (Italian) Zbl 0615.01004 Boll. Stor. Sci. Mat. 6, No. 1, 83-133 (1986). In this paper the authors examine in a technically clear way and by proper critical sense Viète’s and Ghetaldi’s Apollonian reconstructions. The authors point out the rôle that these reconstructions had to rationalize and to systematize the methods of solution of geometrical problems. First the authors study the problems that concern the “geometry of the contacts” in Viète, Ghetaldi and Torricelli. The problems inherent the “inclinations” are analogously examined. The third paragraph is dedicated to problems that “sub algebram non cadunt”. The work is concluded by some remarks on the successive developments (Girard, Descartes, Huygens). Reviewer: P.Freguglia MSC: 01A40 History of mathematics in the 15th and 16th centuries, Renaissance 01A45 History of mathematics in the 17th century 51-03 History of geometry Keywords:geometrical problems; inclinations Biographic References: Viète, F.; Ghetaldi, M. PDFBibTeX XMLCite \textit{A. Brigaglia} and \textit{P. Nastasi}, Boll. Stor. Sci. Mat. 6, No. 1, 83--133 (1986; Zbl 0615.01004)