New Plane And Solid Geometry

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(In these computations, for uniformity let it = 3. 1416. ) j 470. Also with diameters 2, 8, 11, 31, 42, 97. ^ 471. Find the radii of circles of areas 78. 5398, 2042. 8206, 4536. 4598.
472. Also the diameters of circles of areas 2123. 7166, 3318. 3072, 56. 745017.
473. Also the circumferences of circles of areas 95. 0332, 452. 3893. \y 474. Also the areas of circles of circumferences 267. 0354, 191. 6372.
475. The area of the ring formed between the circumferences of two * concentric circles of
...radii rj. , r 2, where T\ > r 2, is it (r x + r 2 ) (j\ — r 2 ).
476. The area of that portion of the ring of ex. 475 cut off by the arms of the central angle a radians is \a{r x i- r 2 ) (ri — r 2 ) ; or, if ai, a 2 are arcs bounding that portion, the area = I (cii + a 2 ) (ri — r 2 ).
Note. The remainder of the work may be omitted without destroying the integrity of the course.
APPENDIX TO PLANE GEOMETRY.
1. SUPPLEMENTARY THEOREMS IN MENSURATION.
Proposition XIX.
309. Theorem. If the sides of a triangle are a, b, c, and if s = i (a + b 4- c), s x = s — a, s 2 = s — b, s 3 = s —

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