P. HISTORY OF ' AATHEMATICAL - School of Mathematics

REFERENCES TO EIGHTEENTH-CENTURY WRITERS CITED IN THE TARLE
I. William Leybourn, Janua Mathomatic­
2. William Jones, S7Jf'Opne palmariorum matheesoe (London, 1706),p. 240.
3. William Jones, PhiL>eophirol Tranaoctione (London, 1753), p. 560. S
•. John Wilson, Trigontnrr.«;rv (Edinburgh, 1714), p, 41, 43.
Ii. Edward Wells, The Yau7l{/ Genlleman'. Trigonometry (London, 1714), p, 15,17.
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6. Jakob Kresa, Ana/lin••pecioea Trigonomelriae (Pragae, 1720), p. 288.
7. John Keill, Elemente 0/ Trigonometry (Dublin, 1726), last page. ~
8. Philip Ronayne, Treatise 0/ Algebra (London, 1727), Book II.
9. Friedrich Christian Maier, Trigonometria in Commenlarii Academiae Srient. Pelropolitanae ad annum t 7117, Vol. II, p. 12-30. ~
10. L. Euler, Commenlarii Acad.....iae Scient. Pelropolilanae, ad annum t 7119, Pet. 1735.
11. John Ward, P081humoue Worke (London, 1730), p. 437. ~
12. Thomse Simpson, Treati.e 0/ Fluziima (London, 1737), p. 176, 192.
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13. Thomas Simpson, Doctrins and Application 0/ Fluxion« (London, 1750), p. 278-88.
... L. Euler, Introduclio in analllnn infinilorum (Berlin, 1748), Vol. I, p. 93, 94, 103, 104. ~
15. Leonard Euler, Hi8lairs de I'Acadbnie de Berlin (Berlin, 1753), p. 223-57, 258-93. Euler exerted himself to arithmetise trigonometry and to use sin z, ~
COS z, and tan Z B8 (unctions of 2:. His efforts along this line are especially displayed in his article, "Svbsidium calcvli sinvvm," of 1754, where, conscious
of the importance of his innovation. he states: "Simili autem modo mihi equidem angulorum sinus tangenteBque primus in calculum ita traDstulisae videor,
ut instar reliquarum quantitatum tractari, cunctaeque operationee sine vllo impedimento peragi possent. . . . . Tamen haec ipsa notandi ratio post modum ~ .....
vniversae analysi tanta attulit adiumenta, vt nouum fere campum patefecisse videatur, in quo Geometrae non sine notabili elaborauerint fructu. Ac si
quidem ipsus Analysis praestantiam spectamus, eam praecipue soli idoneo quantitates signis denotandi modo tribuendam esse deprehendimus, quo minus §?
erit mirandum, si commoda sinuum in algorithmum introductio tantum lucri attulerit." ("Similarly I believe that I have first introduced the sines and
cosines of angles into the calculus, so that they can be treated like other quantities and can be dealt with in extended operations without any hindrance t""'
..•. so that this very mode of designation brings to general analysis great aid, that almost a new field is thereby seen to be opened up, in which geometers
Z
have worked not without great results. And if we behold the excellence of analysis we recognize that it must be attributed to the mode of denoting quantities
by signs, hence it is less to be marveled if the skilful introduction of the sine into the algorithm has brought such great advantage.")
16. C. E. L. Camus, Caur. do matMmatique, 2. Partie (nouv. M.; Paris, 1755), p. 402. ~
17. A. G. Kistner, An/angegrands der Arilhmeti6:. Geometrie . . . . Trigonometris (Gllttingen, 1758), p, 339-47.
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18. D'Aiembert, Recherches aur differene poinle imporians du SlIeleme du Monds (Paris), Vol. 1(1754), p. 130,131; Vol. 11(1754), p. 35; Vol. III (1756), p. 11,
158.
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19. E. Waring, Miscellanea ana/II/tea (Cambridge, 1762), p, 66, 91, 141.
20. Antoine Remi Mauduit, Prinripee d' Aetronomi. Spherique (Paris, 1761i).
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