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 17
... in reality does not and cannot exist . SCHOLIUM . By the help of this proposition it may be easily prov- ed that the meridian circles on the globular earth in- tersect the parallels of latitude at right angles , and ( 17 )
... in reality does not and cannot exist . SCHOLIUM . By the help of this proposition it may be easily prov- ed that the meridian circles on the globular earth in- tersect the parallels of latitude at right angles , and ( 17 )
Σελίδα 18
... meridian cuts the representative of any parallel of latitude at right angles , it follows that on the surface of the spherical earth every meridian in- tersects every parallel of latitude at right angles . And hence a ship steered ...
... meridian cuts the representative of any parallel of latitude at right angles , it follows that on the surface of the spherical earth every meridian in- tersects every parallel of latitude at right angles . And hence a ship steered ...
Σελίδα 54
... stereographic pro jection of the concave sphere , on the plane of PFƒ , the meridian of Arcturus ; where P represents the north pole , and the south pole . Having described Ff , the parallel of declination of Arc- turus , ( 54 )
... stereographic pro jection of the concave sphere , on the plane of PFƒ , the meridian of Arcturus ; where P represents the north pole , and the south pole . Having described Ff , the parallel of declination of Arc- turus , ( 54 )
Σελίδα 55
... meridian of Antares , forward from PF ; then Fis the point of the first transit , and K is the cotem- porary position of Antares . But by the diurnal ro- tation , Antares is apparently translated from K , along KL , to the azimuth at L ...
... meridian of Antares , forward from PF ; then Fis the point of the first transit , and K is the cotem- porary position of Antares . But by the diurnal ro- tation , Antares is apparently translated from K , along KL , to the azimuth at L ...
Σελίδα 56
... meridian rPR , which falls nearest the greater side PL , when the greater declination is toward the depressed pole . Then , by cor . 2 . prop . 30 , book 3 , Emerson's Trigonometry , sine of ( PL + PF ) : sine of ( PL PF ) : : cotangent ...
... meridian rPR , which falls nearest the greater side PL , when the greater declination is toward the depressed pole . Then , by cor . 2 . prop . 30 , book 3 , Emerson's Trigonometry , sine of ( PL + PF ) : sine of ( PL PF ) : : cotangent ...
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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...