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Analysis Per Quantitatum Series, Fluxiones, AC Differentias: Cum ...
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Abfciffa Šquatio Šquationem Šquationis Afymptoton Arcus Area CurvŠ AreŠ Aream Arearum Areis bx▓ cafu coefficientes Conchoidalis Conica COROL crura cruris Curva omnis cujus Curvarum data decima deeft deinceps in infinitum Diametri Diametrum dimenfionum duŠ funt effe ejufdem figni Epiftola erit eſt evadit ex▓ exiftente fecundi Generis femper feries fexagefima fic deinceps figura figurŠ fint five fluens fluentes Fluxio fluxiones fubftituo funt Šquales funt impoffibiles fupra Geometria gx▓ hŠc eft Species Hyperbola Hyperbolis ifta illŠ inŠquales Infinitas infinite ipfius Methodum migrat nempe Newtoni omnibus omnis cujus Ordinata Ordinatarum Ordinatim applicata Ovali Parabola poffunt poteft Prop puncta punctis Punctum duplex quadrari Quadratura QuŠ Species quŠratur quŠvis quantitas quantitates Quotiente Quotientis radices duŠ radices funt radix recta Refolvenda relatio Seriei termini terminorum terminus ey tertia valores
Page 34 - ... the shortest the nature of the thing admits of, for a general one,) I can compare them. And so, if any two figures expressed by such equations be propounded, I can by the same rule compare them, if they may be compared. This may seem a bold assertion, because it is hard to say a figure may or may not be squared or compa[red] with another, but it is plain to me by the fountai[n I] draw it from. thou[gh] I will not undertake to prove it to others.
Page 34 - I say there is no such curve line, but I can, in less than half a quarter of an hour, tell whether it may be squared, or what are the simplest figures it may be compared with, be those figures conic sections or others. And then, by a direct and short way, (I dare say the shortest the nature of the thing admits of, for a general one,) I can compare them. And so, if any two figures expressed by such equations be propounded, I can...
Page 34 - ... not excepting the method of reducing roots to fractions. The advantage of the way I follow you may guess by the conclusions drawn from it, which I have set down in my answer to M. Leibnitz ; though I have not said all there. For there is no curve line expressed by any equation of three terms, though the unknown quantities affect one another in it, or the indices of their dignities be surd quantities, A ft.