Our diagram shows this, and also, by a dotted line, the only other possible position in which it could fulfil the conditions, if it were then of any practical use.
A BURDEN OF PINS
If one pin could be dropped into a vessel this week, two the next, four the next, and so on, doubling each time for a year, the accumulated quantity would be 4,503,599,627,370,495, and their weight, if we reckon 200 pins to the ounce, would amount to 628,292,358 tons, a full load for 27,924 ships as large as the Great Eastern, whose capacity was 22,500 tons.
No. CIV.—MEMORIES OF EUCLID
When at the signpost which said “To A 4 miles, to B 9 miles” on one arm, and on the other “To C 3 miles, to D —— miles,” and the boy whom I met could only tell me that the farm he worked at was equidistant from A, B, C, and D, and nearer to them than to the signpost, and that all the roads ran straight, I found, thanks to memories of Euclid, that I was 12 miles from D.
Since B A and D C intersect outside the circle at the signpost E,
| therefore | A E × E B = C E × E D. |
| but | A E × E B = 4 × 9 = 36, |
| therefore | C E × E D = 36, |
| and | C E = 3, therefore E D = 12. |
Q.E.D.