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ABCD algebraic answer assume axis azimuth ball Baron becomes bers bisects centre centrifugal force circle complete square consequently Corollary cosine cube cubic formula curve definition demonstrated denominator Diarius Yankee distance District of Maine ditto divided divisor dollars draw earth eastwardly equal Euclid evident expressed fluent fluxion four numbers four proportional numbers fourth fraction frustum given numbers greater Hence horizontal hypotenuse IKLM increments integer irreducible fraction James James Temple John Craggs length manner Math mathematical meridian multiple multiplicand nearest pole New-Jersey New-York Newbern North-Carolina number of digits Penn Pennsylvania perpendicular Philadelphia Prize Quest prop proposition pure number radius ratio rectangle right ascension Robert Adrain root rule Scholium side similar triangles sine solution Solved straight line subtracted suppose tangent theorem Thomas Maughan tion tiple tube velocity whence whole number yards York-Town
Page 163 - What principles you proceed upon; how sound they may be; and how you apply them? It must be remembered that I am not concerned about the truth of your theorems, but only about the way of coming at them; whether it be legitimate or illegitimate, clear or obscure, scientific or tentative.
Page 176 - ... the mark will have no meaning or signification : thus if it be said that the square of — 5, or the product of —5 into —5, is equal to +25, such an assertion must either signify no more than that 5 times 5 is equal to 25 without any regard to the signs, or it must be mere nonsense and unintelligible jargon.
Page 162 - ... to demonstrate any proposition a certain point is supposed, by virtue of which certain other points are attained; and such supposed point be itself afterwards destroyed or rejected by a contrary supposition ; in that case all the other points attained thereby and consequent thereupon, must also be destroyed and rejected, so as from thenceforward to be no more supposed or applied in the demonstration.
Page 132 - I sought a method of determining quantities from the velocities of the motion or increments with which they are generated ; and calling these velocities of the motions or increments Fluxions, and the generated quantities Fluents, I fell by degrees upon the method of Fluxions, which I have made use of here in the quadrature of curves, in the years 1665 and 1666.
Page 132 - Lines are described, and therefore generated not by the apposition of parts, but by the continued motion of points ; superficies by the motion of lines ; solids by the motion of superficies ; angles by the rotation of the sides ; portions of time by a continual flux ; and so in other quantities. These geneses really take place in the nature of things, and are daily seen in the motion of bodies.
Page 136 - We must therefore be careful to distinguish between the ratio of two evanescent quantities, and the limit of their ratio ; the former ratio never arriving at the latter, as the quantities vanish at the instant that such a circumstance is aboBt to take place.
Page 31 - The fourth term is equal to the product of the second and third terms, divided by the first term.
Page xi - ... administrators, or assigns, the just and full sum of four hundred and thirty-eight dollars o'n demand, (or one year after the date of this Bond, as the fact may be,) with interest at the rate of six per cent, per annum, payable quarter yearly, (or half yearly or yearly, as the agreement may be,) to wit, on the first days of May, August, November, and February in each year, (or on any other days as the parties may agree,) then the above obligation to be void, otherwise to remain in full force...
Page 176 - ... some other quantity, as a, to which it is to be added, or from which it is to be subtracted, the mark will have no meaning or signification : thus if it be said that the square of — 5, or the product of —5 into —5, is equal to +25, such an assertion must either signify no more than that...
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