Sir Isaac Newton's Two Treatises: Of the Quadrature of Curves and Analysis by Equations of an Infinite Number of Terms, Explained : Containing the Treatises Themselves, Translated Into English, with a Large Commentary ; in which the Demonstrations are Supplied where Wanting, the Doctrine Illustrated, and the Whole Accommodated to the Capacities of Beginners, for Whom it is Chiefly Designed
James Bettenham, at the expense of the Society, 1745 - 479 σελίδες
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alſo ariſing aſſumed Baſe becauſe belonging betwixt Caſe Circle Conic Sečtion conſequently conſidered converging Series correſponding Curve propoſed Curve whoſe Ordinate curvilinear Area demonſtrated denotes deſcribed Dimenſions diminiſhed diſcovered Diviſor eaſily Ellipſe equal Equation Explica expreſſed Expreſſion fince find the Area finite firſt Term flowing Quantity Fluent Fluxions Form Fraćtion given Hyperbola increaſes infinite Series inſerting itſelf juſt laſt leſs likewiſe Logarithm Meaſure Method of Fluxions moſt multiplied muſt negative Number obſerved Ordinate BC Parabola plication poſitive Progreſſion Prop propoſed Propoſition quadrable Quadrature of Curves reaſoning Relation repreſented reſpect right Line Root ſaid ſame Manner ſame thing ſay ſecond Sečtor ſee Series's ſeveral ſhall ſhew ſhewn ſimple ſince Sir Iſaac ſmall ſome ſought ſquared ſtand ſtill ſubſtituting Subtangent ſubtract ſuch ſuppoſe Tangent thence theſe thoſe tion Treatiſe uſe Value vaniſh Velocity whence Wherefore whoſe Abſciſs whoſe Area
Σελίδα 270 - When a ray of light passes from one medium to another, it is refracted so that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities in the two media.
Σελίδα viii - Just so it is in the mind ; would you have a man reason well, you must use him to it betimes, exercise his mind in observing the connection of ideas, and following them in train. Nothing does this better than mathematics, which therefore I think should be taught all those who have the time and opportunity, not so much to make them mathematicians, as to make them reasonable creatures...
Σελίδα viii - I have mentioned mathematics as a way to settle in the mind a habit of reasoning closely and in train; not that I think it necessary that all men should be deep mathematicians, but that, having got the way of reasoning, which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge, as they shall have occasion.
Σελίδα 34 - I. The length of the space describ'd being continually (that is, at all times) given; to find the velocity of the motion at any time propos'd.
Σελίδα 329 - ... ratio between two whole numbers the impossibility of the problem of rectification is not inferable. The quadrature of the circle stands and falls with the problem of rectification. This is based upon the truth above mentioned, that a circle is equal in area to a right-angled triangle, in which one side is equal to the radius of the circle and the other to the circumference. Supposing, accordingly, that the circumference of the circle were rectified, then we could construct this triangle. But...
Σελίδα 288 - COROLLARY. The measure of the surface of a spherical triangle is the difference between the sum of its three angles and two right angles. For if s =-J- of the surface of the sphere, 180°xm=s X(A + B + C— 180°).
Σελίδα viii - Reafoning, which that ftudy neceffarily brings the Mind to, they might be able to transfer it to other parts of Knowledge as they fhall have occafion. For in all forts of Reafoning, every fmgle Argument mould be managed as a Mathematical Demonftration, the Connection and dependence of Ideas...
Σελίδα 2 - AB, the ordinate BC and the curve line ACc ; and the sides of the triangle CET...
Σελίδα viii - ... times, exercife his mind in obferving the connection of ideas, and follow them in train. Nothing does this better than mathematics, which therefore, I think, fhould be taught all thofe who have the time and opportunity, not fo much to make them mathematicians, as to make them reafonable creatures...