The Mathematical Correspondent: Containing, New Elucidations, Discoveries, and Improvements, in Various Branches of the MathematicsSage and Clough, 1804 |
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Σελίδα 22
... equation sub- = 49 4 49 tracted from leaves - 7y + y2 = the square = 4 roots of which ( since y is not greater than 3 ) give -y , whence y 2. The two digits originally expressed by x and xy2 , will now become x and 4x and the age of the ...
... equation sub- = 49 4 49 tracted from leaves - 7y + y2 = the square = 4 roots of which ( since y is not greater than 3 ) give -y , whence y 2. The two digits originally expressed by x and xy2 , will now become x and 4x and the age of the ...
Σελίδα 24
... equation gives r3 r2x , or r — x 2 - 3r2x + 3rx2 xr - x = r - x x2 . Hence r — x ⇒r √3 = 5√3 = 8.660254 inches = OE , x = rx ( 1 − √3 ) 1.339746 the thickness of the crust , r 2x 7.320508 = GE the height of the interior soft ...
... equation gives r3 r2x , or r — x 2 - 3r2x + 3rx2 xr - x = r - x x2 . Hence r — x ⇒r √3 = 5√3 = 8.660254 inches = OE , x = rx ( 1 − √3 ) 1.339746 the thickness of the crust , r 2x 7.320508 = GE the height of the interior soft ...
Σελίδα 27
... equation by an easy reduction becomes x2 + ex4 2mx3 + n2x en2 = 0 : which by assuming a = 50 , b = 78 and e = 35 gives x5 + 35x4 17168x3 + 12845056 x .449576960 = 0 . Hence by any of the common methods , we find x = 112 , and therefore ...
... equation by an easy reduction becomes x2 + ex4 2mx3 + n2x en2 = 0 : which by assuming a = 50 , b = 78 and e = 35 gives x5 + 35x4 17168x3 + 12845056 x .449576960 = 0 . Hence by any of the common methods , we find x = 112 , and therefore ...
Σελίδα 28
... equations we have ab2 + a2 + b2 × y + ay2 ab2 ay X d = √ a2 + b2 + 2ay · Hence by reduction , and a restoration of the values of the known quantities we obtain an equation from which y is easily found 19.008 exactly ; therefore x = b2 ...
... equations we have ab2 + a2 + b2 × y + ay2 ab2 ay X d = √ a2 + b2 + 2ay · Hence by reduction , and a restoration of the values of the known quantities we obtain an equation from which y is easily found 19.008 exactly ; therefore x = b2 ...
Σελίδα 43
... equation of the curve which is the locus of a point taken any where on the ladder . VII . QUEST . 14. by G. Baron , New - York . px ry xmx Given + to find the gen XC y ayn eral relation of the fluents . VIII . QUEST . 15. by R. Tagart ...
... equation of the curve which is the locus of a point taken any where on the ladder . VII . QUEST . 14. by G. Baron , New - York . px ry xmx Given + to find the gen XC y ayn eral relation of the fluents . VIII . QUEST . 15. by R. Tagart ...
Άλλες εκδόσεις - Προβολή όλων
The Mathematical Correspondent: Containing New Eludications ..., Τόμος 1 George Baron Πλήρης προβολή - 1804 |
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 algebraic characters answer arises by multiplying assume ball Baron bisects centre centrifugal force circle consequently Coroll Corollary cosine cube cubic formula demonstrated denominator Diarius Yankee difference distance ditto draw eastwardly equal equation Euclid evident expressed fluxion formula four numbers fourth fraction frustum greater Hence horizontal increments James James Temple John Craggs John Gummere latitude length Let ABC loxodromic mathematical Mathematical Correspondent meridian mon language multiple multiplicand nearest pole New-Jersey New-York Newbern North-Carolina number of digits parallel Pennsylvania perpendicular Philadelphia plane principles PRIZE QUEST product that arises prop proposition pure number radius ratio rectangle rectilineal right angles Robert Adrain root rule SCHOLIUM side signs similar triangles sine solutions Solved straight line subtracted suppose tangent theorem third tion tiple tube velocity whence whole number York-Town
Δημοφιλή αποσπάσματα
Σελίδα 149 - 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 148 - ... 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 122 - 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 149 - C's part being lost by his death, it is required to divide the whole sum, properly, between the other two. Ans. A's part is $ 57,142$, and B's $ 42,857}.
Σελίδα 19 - The fourth term is equal to the product of the second and third terms, divided by the first term.
Σελίδα 197 - ... the product of the sum and difference of any two quantities, is equal to the difference of their squares.
Σελίδα 18 - If the answer is to be greater, place the greater of the two remaining numbers for the second term, and the less number for the first term; but if it is to be less, place the less of the...
Σελίδα 68 - ... They themselves also speak in the most contemptuous manner of Col. Jared Mansfield, superintendent of the Military Academy at West Point. The writer has a copy of No. 2. stitched in a blue cover, on which is an advertisement of a Lecture delivered in New York by G. Baron, which contains (as he says) "a complete refutation of the false and spurious principles, ignorantly imposed on the public, in the 'New American Practical Navigator,
Σελίδα 118 - ... 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 118 - These geneses really take place in the nature of things, and are daily seen in the motion of bodies. And after this manner the ancients, by drawing moveable right lines along immoveable right lines, taught the genesis of rectangles.