A Short View of the First Principles of Differential CalculusJ. Deighton, 1824 - 198 strán (strany) |
Vyhľadávanie v obsahu knihy
Výsledky 1 - 5 z 73.
Strana 5
... the circumference and area of a circle , whose radius equal 1 , and indeed the lengths and areas of curves and the contents and surfaces of solids can seldom be accurately represented by numbers . let the sides CA , CD , CE , which 5.
... the circumference and area of a circle , whose radius equal 1 , and indeed the lengths and areas of curves and the contents and surfaces of solids can seldom be accurately represented by numbers . let the sides CA , CD , CE , which 5.
Strana 11
... - rection , take OD = perpendicu- M ΑΙ M ' CP D B lar distance of the point from 40 , measuring it in the proper direction ; complete the rectangle OP , then P is manifestly the required point . COR . 1. If in any curve , the relation 11.
... - rection , take OD = perpendicu- M ΑΙ M ' CP D B lar distance of the point from 40 , measuring it in the proper direction ; complete the rectangle OP , then P is manifestly the required point . COR . 1. If in any curve , the relation 11.
Strana 12
... curve is one , where the re- lation between the two co - ordinates is represented by an equation . The ordinates and abscissas of algebraic curves are generally represented by the letters ( y ) and ( x ) respectively , and the equation ...
... curve is one , where the re- lation between the two co - ordinates is represented by an equation . The ordinates and abscissas of algebraic curves are generally represented by the letters ( y ) and ( x ) respectively , and the equation ...
Strana 13
... curve admits of an ordinate corresponding to ( X ) , which is equal to ( Y ) , but measured downwards from the first point . Let PQ be a curve , referred to the axes 40 , OB ; ON , On the co - ordi- nates to point P , and equal to ( x ) ...
... curve admits of an ordinate corresponding to ( X ) , which is equal to ( Y ) , but measured downwards from the first point . Let PQ be a curve , referred to the axes 40 , OB ; ON , On the co - ordi- nates to point P , and equal to ( x ) ...
Strana 14
Arthur Browne (M.A.). OB , but since the curve PP ' is an algebraic curve , its nature is expressed throughout by the same equa- tion , hence the equation between y and x , will also hold good , when the curve lies below OB . and x , Now ...
Arthur Browne (M.A.). OB , but since the curve PP ' is an algebraic curve , its nature is expressed throughout by the same equa- tion , hence the equation between y and x , will also hold good , when the curve lies below OB . and x , Now ...
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.