By Edward O. Thorp

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**Sample text**

Bead off . , the corresponding numbers. GRAPHICS. 20 If (34) Draw four lines of lengths 7*8, 2'6 and 3'1 cms. and 0'4 inch. the last represents unity, find the product of the numbers represented by second. the the third and the ratio of the first to Continued Multiplication. EXAMPLE where u 1. Find representing the product line a, represents unity, the numbers being given by OU=u Set off along any line and along an intersecting Mark X X where l X OX3 is OD UX OD. UX% OD l the length required.

Perpendicular to the one Fig. 27. 4 lines intersecting at right angles. } 3 2 lines are B, FIG. 27 it, is as in POWERS. 27 Construct the u scale along a straight-edged piece ot paper. 2 3 OA<>, OA^ OA 4 ... on the u scale; they are A* A , A*.... Measure , OBly OB2 Measure 1 _L OB*. , on the same ... scale; they are JL A^ A*"" A' All the triangles Proof. *. For the reciprocals A =A 3 3 , etc. we have OB^OB^ OU~OA Multiplying together Similarly, BB = JL -jo, etc. For positive powers the construction stops would not be on the paper.

To-=2'3" represents, to the scale 2 cms. , the weight of a body ; represents, to the scale 1 cm. -lbs. = 7"2cms. body 11. Construct geometrically the curve xy=3'2, and find the values of ; 3'2 times the reciprocals of 1 3, 27, 4*2 and 0'8. a of divide 2 '72, 0'85, 3 '64, 1-88 in turn by 1'35. aid line 12. By straight *13. The volume of a pyramid being $ base area x height, find graphically the volume in cubic feet when the base is a rectangle, the sides of the rectangle being given by lines of 7*2 and 3 '9 cms.