# Solutions of the Cambridge Problems: From 1800 to 1820, Volume 2

Black, Young, and Young, Tavistock-Street, Covent-Garden., 1825 - Mathematics - 653 pages
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### Contents

 N 243 11 255 11 870 13 650 23 880 25 6 64 10 78 440 98
 109 369 13 379 75 388 127 413 80 420 143 458 94 460 148 507

 60 100 9 116 7 125 8 138 N 147 260 152 70 158 470 174 739 190 38 208 280 209 6 215 303 221 80 249 367 251 3 253 8 254 58 255 365 257 7 262 90 268 21 274 180 277 185 284 10 291 91 292 345676 306 10 350
 n 2 530 29 561 10 574 24 586 12 592 900 636 n 5 639 9 645 11 647 10 653 35 664 9396774 673 12 674 OPTICS 686 182 717 103 721 6789 725 6 726 132 727 208 733 n 11 740 403 745 416 746 407 23 20 4 14

### Popular passages

Page 654 - ... line and the extremities of the base have the same ratio which the other sides of the triangle have to one...
Page 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.
Page 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.
Page 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.
Page 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...
Page 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.
Page 713 - This is the same as saying that when a ray of light passes out of one medium into another, the...
Page 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...
Page 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.
Page 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...