The Mathematical Correspondent: Containing New Eludications, Discoveries, and Improvements, in Various Branches of the Mathematics, Τόμος 1Sage and Clough, 1804 - 248 σελίδες |
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Σελίδα 2
... definition , but merely as a defcrip- tion of the three properties , by which proportional numbers are common known . These three properties are actually three different propositions de duced from the true definition of proportional ...
... definition , but merely as a defcrip- tion of the three properties , by which proportional numbers are common known . These three properties are actually three different propositions de duced from the true definition of proportional ...
Σελίδα 59
... Definition , of the word Power , in Arithmetic and Algebra . By G. BARON . IN the following paper , I contend , that , in the writings of the modern mathematicians , the powers of numbers , are inaccurately defined ; and that in ...
... Definition , of the word Power , in Arithmetic and Algebra . By G. BARON . IN the following paper , I contend , that , in the writings of the modern mathematicians , the powers of numbers , are inaccurately defined ; and that in ...
Σελίδα 60
... definition , for any number to be equal to its own first power ; it follows , that , this definition is erroneous . Further , it is also well known , that , the product resulting from any number , multiplied by itself , must be ...
... definition , for any number to be equal to its own first power ; it follows , that , this definition is erroneous . Further , it is also well known , that , the product resulting from any number , multiplied by itself , must be ...
Σελίδα 61
... definition , unity multiplied by any number , produces the first power of that number ; the product arising , from the first power of any number , multiplied by the number itself , is the second power of that number ; -the product ...
... definition , unity multiplied by any number , produces the first power of that number ; the product arising , from the first power of any number , multiplied by the number itself , is the second power of that number ; -the product ...
Σελίδα 62
... definition , agrees , exactly , with the com- mon usage of every mathematical author of the present age . Let us , therefore , next inquire , whether the same definition , will not lead us to a clear and intelligible solution , of the ...
... definition , agrees , exactly , with the com- mon usage of every mathematical author of the present age . Let us , therefore , next inquire , whether the same definition , will not lead us to a clear and intelligible solution , of the ...
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The Mathematical Correspondent: Containing, New Elucidations, Discoveries ... George Baron Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
The Mathematical Correspondent: Containing, New Elucidations, Discoveries ... George Baron Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD algebraic angled triangle answer assume azimuth ball Baron bisects Bunker's Hill centre centrifugal force circle complete square consequently Corollary cube cubic formula demonstrated denominator Diarius Yankee difference distance District of Maine ditto divisor dollars draw eastwardly equal equation Euclid evident expressed fluxion formula four numbers four proportional numbers fourth fraction frustum greater Hence horizontal hypotenuse increments integer irreducible fraction James James Temple John Craggs latitude length Let ABC mathematical meridian multiple multiplicand nearest pole New-Jersey New-York Newbern North-Carolina number of digits parallel Penn Pennsylvania perpendicular Philadelphia plane PRIZE QUEST prop proposed proposition pure number quantity question radius ratio rectangle rectilineal right angles Robert Adrain root rule SCHOLIUM side similar triangles sine Solved sterling straight line subtracted tangent theorem tion tiple tube velocity whence yards York-Town
Δημοφιλή αποσπάσματα
Σελίδα 157 - 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.
Σελίδα 126 - ... motion, by means of which they increase or decrease ; as a line by the motion of a point ; a surface by the motion of a line ; and a solid by the motion of a surface.
Σελίδα 170 - ... 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.
Σελίδα 156 - ... 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.
Σελίδα 126 - 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.
Σελίδα 126 - 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.
Σελίδα 130 - 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.
Σελίδα 25 - The fourth term is equal to the product of the second and third terms, divided by the first term.
Σελίδα 170 - ... 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...