William Oughtred

108

Application de l’algèbre à géométrie.. Paris, 1705.

109

Elémens de la géométrie de l’infini, by M. de Fontenelle, Paris, 1727, p. 110.

110

Eclaircissemens sur l’analyse des infiniment petits, by M. Varignon, Paris, 1725, p. 87.

111

Application de la géométrie ordinaire et des calculs différentiel et intégral, by M. Robillard, Paris, 1753.

112

Traité de géométrie théorique et pratique, new ed., Paris, 1764, p. 15.

113

Recherches sur les courbes à double courbure, Paris, 1731, p. 13.

114

Analyse des infiniment petits, by the Marquis de L’Hospital. New ed. by M. Le Fèvre, Paris, 1781, p. 41. In this volume passages in fine print, probably supplied by the editor, contain the notation a:b::c:d; the parts in large type give Oughtred’s original notation.

115

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.

116

Chr. Clavii Operum mathematicorum tomus secundus, Mayence, 1611, Algebra, p. 39.

117

Invention nouvelle en l’algèbre, by Albert Girard, Amsterdam, 1629, p. 17.

118

La géométrie et pratique générale d’icelle, par I. Errard de Bar-le-Duc, Ingénieur ordinaire de sa Majesté, 3d ed., revised by D. H. P. E. M., Paris, 1619, p. 216.

119

Novae geometriae clavis algebra, authore P. Jacobo de Billy, Paris, 1643, p. 157; also an Abridgement of the Precepts of Algebra. Written in French by James de Billy, London, 1659, p. 346.

120

Miscellanies: or Mathematical Lucubrations, of Mr. Samuel Foster, Sometime publike Professor of Astronomie in Gresham Colledge in London, London, 1659, p. 7.

121

Quarterly Jour. of Pure and Applied Math., Vol. XLVI (London, 1915), p. 191.

122

Pietro Cossali, Origine, trasporto in Italia primi progressi in essa dell’ algebra, Vol. I, Parmense, 1797, p. 52.

123

In Is. Bullialdi astronomiae philolaicae fundamenta inquisitio brevis, Auctore Setho Wardo, Oxford, 1653, p. 1.

124

John Wallis, Algebra, London, 1685, p. 321, and in some of his other works. He makes greater use of Harriot’s symbols.

125

Euclidis data, 1657, p. 1; also Euclidis elementorum libris XV, London, 1659, p. 1.

126

John Kersey, Algebra, London, 1673, p. 321.

127

E. Wells, Elementa arithmeticae numerosae et speciosae, Oxford, 1698, p. 142.

128

Cocker’s Decimal Arithmetick, perused by John Hawkins, London, 1695 (preface dated 1684), p. 278.

129

Th. Baker, The Geometrical Key, London, 1684, p. 15.

130

Richard Sault, A New Treatise of Algebra, London (no date).

131

Richard Rawlinson in a pamphlet without date, issued sometime between 1655 and 1668, containing trigonometric formulas. There is a copy in the British Museum.

132

F. Dulaurens, Specima mathematica, Paris, 1667, p. 1.