A Short View of the First Principles of Differential CalculusJ. Deighton, 1824 - 198 strán (strany) |
Vyhľadávanie v obsahu knihy
Výsledky 1 - 5 z 15.
Strana 2
... unity . This line is called a linear unit . If a square , and a cube be described upon it , they are called respectively a plane and a solid unit . PROP . I. If any line be a multiple of a linear unit , it is capable of being ...
... unity . This line is called a linear unit . If a square , and a cube be described upon it , they are called respectively a plane and a solid unit . PROP . I. If any line be a multiple of a linear unit , it is capable of being ...
Strana 3
... unity , and has no common measure with it , then there is no number , whether whole or fractional , by which this line can be represented , but an approxi- mation may be made to it by decimals , to any re- quired degree of exactness ...
... unity , and has no common measure with it , then there is no number , whether whole or fractional , by which this line can be represented , but an approxi- mation may be made to it by decimals , to any re- quired degree of exactness ...
Strana 51
... unity , ( x ) is in each case less than unity . A function may have more than one maximum or minimum value . Suppose p ( x ) = ( x− a ) ( x − b ) ( x − c ) ( x − d ) ( x − e ) , where ( a ) , ( b ) , ( c ) , ( d ) , ( e ) , are ...
... unity , ( x ) is in each case less than unity . A function may have more than one maximum or minimum value . Suppose p ( x ) = ( x− a ) ( x − b ) ( x − c ) ( x − d ) ( x − e ) , where ( a ) , ( b ) , ( c ) , ( d ) , ( e ) , are ...
Strana 58
... unity , and multiplying by the differential of its root . CASE 1. LET the root be a simple algebraic quantity ( x ) ; and let ( n ) be the power to which it is raised ; then d.x " = nx2 - 1dx . Let u = x " , then u ' = ( x + h ) " = x ...
... unity , and multiplying by the differential of its root . CASE 1. LET the root be a simple algebraic quantity ( x ) ; and let ( n ) be the power to which it is raised ; then d.x " = nx2 - 1dx . Let u = x " , then u ' = ( x + h ) " = x ...
Strana 72
... unity , it must at length become negative ; and , consequently , that , when x = 0 , that differential coefficient becomes infinite , and , therefore , in this case , Taylor's theorem fails . COR . 5. If p ( x ) be any rational function ...
... unity , it must at length become negative ; and , consequently , that , when x = 0 , that differential coefficient becomes infinite , and , therefore , in this case , Taylor's theorem fails . COR . 5. If p ( x ) be any rational function ...
Časté výrazy a frázy
1+p² A'PQ a²+x² abscissa algebraic algebraic curve Analytics angle LSP arc PQ assume axes calculated cient circle A"PQ circle of curvature circle Pq co-ordinates coeffi common logarithm consequently considered contrary flexure convex curve APQ cylinder d²p dp dp dp² dx² Dx³ equal equation finite function ƒ² ƒ³ given line greater than SQ Hence horizontal axis hyp.log initial line length less lies linear unit logarithmic spiral manifest Mathematics maximum minimum negative ordinate parabola parallelopiped perpendicular point of contrary positive Prop proposition R₂ radius of curvature radius vector rect rectangle represented second differential coefficient series D spiral is concave straight line substituted suppose tangent Taylor's theorem
Populárne pasáže
Strana xvii - Excudent alii spirantia mollius aera, Credo equidem, vivos ducent de marmore vultus, Orabunt causas melius, caelique meatus Describent radio et surgentia sidera dicent; Tu regere imperio populos, Romane, memento : Hae tibi erunt artes, pacisque imponere morem, Parcere subiectis, et debellare superbos.
Strana xvii - Excudent alii spirantia mollius aera, credo equidem, vivos ducent de marmore vultus, orabunt causas melius, caelique meatus describent radio et surgentia sidera dicent : 850 tu regere imperio populos, Romane, memento (hae tibi erunt artes), pacisque imponere morem, parcere subiectis et debellare superbos.
Strana 50 - The differential of the product of any number of functions is equal to the sum of the products which arise by multiplying the differential of each function by the product of all the others: d(uts) = tsdu + usdt -4- utds.
Strana 5 - The area of a rectangle is equal to the product of the length by the breadth.
Strana 44 - It was also shown in the same article, that the differential of the sum of any number of functions is equal to the sum of their...
Strana 67 - Show how to divide a straight line into two parts so that the sum of the squares on the parts shall be equal to the square on a given line.
Strana 74 - The sum of the logarithms of two numbers, is the logarithm of the product of those numbers; and the difference of the logarithms of two numbers, is the logarithm of the quotient of one of the numbers divided by the other. (Art. 2.) In Briggs' system, the logarithm of 10 is 1.
Strana 133 - ... the angle which the tangent to the curve at that point makes with the axis of strain ; I will call this angle <f>.
Strana 1 - If two sides and the included angle of a triangle are given, show how to solve the triangle. Ex. The two sides are 345, 174 feet respectively, and the included angle is 37° 20'; find the remaining angles of the triangle. log.,» 5'19 = -715167, log. tan. 71° 20/ = 10-471298. log.,0 1-71 = -232996, log. tan. 44° 17
Strana 24 - If three magnitudes of the same kind are so related that the first is greater than the second, and the second greater than the third, then the first is greater than the third.