Note 115 — Chapter IV · OUGHTRED’S INFLUENCE UPON MATHEMATICAL PROGRESS AND TEACHING

The tendency during the eighteenth century is shown in part by the following data: Jacobi Bernoulli Opera, Tomus primus, Geneva, 1744, gives B.A::D.C on p. 368, the paper having been first published in 1688; on p. 419 is given GE:AG=LA:ML, the paper having been first published in 1689. Bernhardi Nieuwentiit, Considerationes circa analyseos ad quantitates infinitè parvas applicatae principia, Amsterdam, 1694, p. 20, and Analysis infinitorum, Amsterdam, 1695, on p. 276, have x:c::s:r. Paul Halcken’s Deliciae mathematicae, Hamburg, 1719, gives a:b::c:d. Johannis Baptistae Caraccioli, Geometria algebraica universa, Rome, 1759, p. 79, has a.b::c.d. Delle corde ouverto fibre elastiche schediasmi fisico-matematici del conte Giordano Riccati, Bologna, 1767, p. 65, gives P:b::r:ds. “Produzioni mathematiche” del Conte Giulio Carlo de Fagnano, Vol. I, Pesario, 1750, p. 193, has a.b::c.d. L. Mascheroni, Géométrie du compas, translated by A. M. Carette, Paris, 1798, p. 188, gives √3:2::√2:Lp. Danielis Melandri and Paulli Frisi, De theoria lunae commentarii, Parma, 1769, p. 13, has a:b::c:d. Vicentio Riccato and Hieronymo Saladino, Institutiones analyticae, Vol. I, Bologna, 1765, p. 47, gives x:a::m:n+m. R. G. Boscovich, Opera pertinentia ad opticam et astronomiam, Bassani, 1785, p. 409, uses a:b::c:d. Jacob Bernoulli, Ars Conjectandi, Basel, 1713, has n-r.n-1::c.d. Pavlini Chelvicii, Institutiones analyticae, editio post tertiam Romanam prima in Germania, Vienna, 1761, p. 2, a.b::c.d. Christiani Wolfii, Elementa matheseos universae, Vol. III, Geneva, 1735, p. 63, has AB:AE=1:q. Johann Bernoulli, Opera omnia, Vol. I, Lausanne and Geneva, 1742, p. 43, has a:b=c:d. D. C. Walmesley, Analyse des mesures des rapports et des angles, Paris, 1749, uses extensively a.b::c.d, later a:b::c:d. G. W. Krafft, Institutiones geometriae sublimoris, Tübingen, 1753, p. 194, has a:b=c:d. J. H. Lambert, Photometria, 1760, p. 104, has C:π=BC²:MH². Meccanica sublime del Dott. Domenico Bartaloni, Naples, 1765, has a:b::c:d. Occasionally ratio is not designated by a.b, nor by a:b, but by a, b, as for instance in A. de Moivre’s Doctrine of Chance, London, 1756, p. 34, where he writes a, b::1, q. A further variation in the designation of ratio is found in James Atkinson’s Epitome of the Art of Navigation, London, 1718, p. 24, namely, 3..2::72..48. Curious notations are given in Rich. Balam’s Algebra, London, 1653.