Solutions of the Cambridge Problems: From 1800 to 1820, Volum 2Black, Young, and Young, Tavistock-Street, Covent-Garden., 1825 - 653 sider |
Inni boken
Resultat 1-5 av 66
Side 14
... greatest altitude through which the piston will be raised is GF . 16 . To construct the spiral whose areas are the measures of the ratios between the ordinates which terminate them , we have d . Area ± 2de = = d . log . p 2 = M × de ( M ...
... greatest altitude through which the piston will be raised is GF . 16 . To construct the spiral whose areas are the measures of the ratios between the ordinates which terminate them , we have d . Area ± 2de = = d . log . p 2 = M × de ( M ...
Side 24
... greatest ordinate is most easily found thus У = sin . = r sin . 0. ( 1 + cos . 0 ) P dy .. rcos . . ( 1 + cos . 0 ) - r sin.20 . d0 Hence when y max . or min . cos . + cos 20 -- sin.200 or cos 20+ cos . 8 2 1 .. cos . A = 14 ± -1 ± 3 16 ...
... greatest ordinate is most easily found thus У = sin . = r sin . 0. ( 1 + cos . 0 ) P dy .. rcos . . ( 1 + cos . 0 ) - r sin.20 . d0 Hence when y max . or min . cos . + cos 20 -- sin.200 or cos 20+ cos . 8 2 1 .. cos . A = 14 ± -1 ± 3 16 ...
Side 31
... greatest , being for each of these values , = 2r ( where r = radius of the circle ) . Hence if A , M. , A , M2 , A , M ,, & c . be taken = M1 C 3C 5C & c . and " " " 2 2 2 M2 P. , M , P , & c . each = 2r be drawn LA , A ̧ , the 3 3 ...
... greatest , being for each of these values , = 2r ( where r = radius of the circle ) . Hence if A , M. , A , M2 , A , M ,, & c . be taken = M1 C 3C 5C & c . and " " " 2 2 2 M2 P. , M , P , & c . each = 2r be drawn LA , A ̧ , the 3 3 ...
Side 33
... greatest ordinate of the curve is = a . y Also , since x = oo , when y = 0 , the line of abscissæ is an asymptote . The curve is convex to the axis throughout . 32 . tion is dy 313 dx = To find the greatest ordinate in the curve whose ...
... greatest ordinate of the curve is = a . y Also , since x = oo , when y = 0 , the line of abscissæ is an asymptote . The curve is convex to the axis throughout . 32 . tion is dy 313 dx = To find the greatest ordinate in the curve whose ...
Side 44
... greatest value . 2 Then , the area bao = sin − 11 + sin . -1 - √2 = 1 x + 75 - 2 = - 57 8 2 5.O ( rad.1 ) -p or If ACB be a straight line , it will be found , in like manner that the locus is a conic section . If our limits would ...
... greatest value . 2 Then , the area bao = sin − 11 + sin . -1 - √2 = 1 x + 75 - 2 = - 57 8 2 5.O ( rad.1 ) -p or If ACB be a straight line , it will be found , in like manner that the locus is a conic section . If our limits would ...
Andre utgaver - Vis alle
Solutions of the Cambridge Problems, from 1800 to 1820, Volum 2 John Martin Frederick WRIGHT Uten tilgangsbegrensning - 1836 |
Solutions of the Cambridge Problems: From 1800 to 1820, Volum 2 John Martin Frederick Wright Uten tilgangsbegrensning - 1825 |
Solutions of the Cambridge Problems, from 1800 to 1820, Volum 2 John Martin Frederick Wright Uten tilgangsbegrensning - 1836 |
Vanlige uttrykk og setninger
abscissa accelerating force altitude angular axis b₁ base bisected body centre of gravity chord circle co-declination co-ordinates cone curve cycloid cylinder denote density descending diameter distance dy dx earth ecliptic ellipse equal equation fluid given point gives Hence horizon hyperbola inclination intersection latitude latus rectum length locus logarithmic spiral moving force orbit ordinate orifice oscillation parabola paraboloid parallel perpendicular plane position problem Prop question radius ratio right angles right ascension shew sides specific gravity sphere spherical straight line substituting subtangent supposing surface tangent triangle velocity vers vertex vertical Vince weight whence whole
Populære avsnitt
Side 654 - ... line and the extremities of the base have the same ratio which the other sides of the triangle have to one...
Side 654 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Side 654 - BAC is cut off from the given circle ABC containing an angle equal to the given angle D : Which was to be done. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other.
Side 654 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Side 657 - B. less by 1 1 chains than the length of the sewer ; the expense of making it amounted to as many pounds per chain, as there were chains in the street leading to A. The sewer, however, being insufficient to carry off the water, an additional drain was made from a point in this street distant 4 chains from the bridge A., which entered the river at the same point with the sewer, and was equally inclined to the river and sewer. Now it was found that a drain down the middle of each street, at the rate...
Side 693 - Upon comparing the observations with each other, it was discovered that in both the fore-mentioned stars, the apparent difference of declination from the maxima was always nearly proportional to the versed sine of the sun's distance from the equinoctial points. This was an inducement to think that the cause, whatever it was, had some relation to the sun's situation with respect to those points.
Side 713 - This is the same as saying that when a ray of light passes out of one medium into another, the...
Side 685 - W its weight in water, its weight in vacuo will be, 1 — m 6. Three globes of the same diameter and of given specific gravities, are placed in the same straight line. How must they be disposed that they may balance on the same point of the line in vacuo and in water ? 7. If a homogeneous hemisphere, floating in a fluid, be slightly inclined from the position of equilibrium...
Side 658 - A ship, with a crew of 175 men, set sail with a supply of water sufficient to last to the end of the voyage ; but in 30 days the scurvy made its appearance, and carried off three men every day ; and at the same time a storm arose which protracted the voyage three weeks. They were, however, just enabled to arrive in port without any diminution in each man's daily allowance of water. Required the time of the passage, and the number of men alive when the vessel reached the harbor.
Side 655 - A number of persons purchased a field for £345. The youngest contributed a certain sum, the next £5 more, the third £5 more than the second, and so on to the oldest. For the greater accommodation of the seniors, the field was divided into two parts, the younger half taking a portion proportional to the sum they had subscribed ; and in order that each might have an equal share in this portion, they agreed to equalize their contributions, and each to pay ,£22. Required the number of persons and...