# 7. arithmetic & number theoretic recreations a. Fibonacci numbers

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## Ff. 98v-99r, pp. 197 198. Furnace with 3 fires: (10, 15, 20).

Johann Widman. Op. cit. in 7.G.1. 1489. (On pp. 131-132, Glaisher mentions the following.) Ff. 136r 138v: Eyn fasz mit dreyen Czapfen; Von der Mulen; Leb, wolff, hunt; Schiff. (Cistern problem; 3 mills; lion, wolf, dog eating a sheep; ship with 3 sails.)

Calandri. Arimethrica. 1491.

## Ff. 66v-67r, prob. 92. Basin has inlets which fill it in 1, 2, 3 hours and outlet which empty it in 2, 3, 4 hours, i.e. (1, 2, 3, -2, -3, -4). How long to fill? He follows with remarks that all such problems can be done similarly. Cf della Francesca.

Blasius. 1513. F. F.iii.r: Decimatertia regula. Three rivers can water a field in (1, 2, 3) days. Gets 13 1/11 hours for all three -- so he is using 24 hour days.

Tagliente. Libro de Abaco. (1515). 1541.

## Prob. 119, f. 58v. Cask with two taps -- (4, 6).

Tonstall. De Arte Supputandi. 1522.

## Quest. 33, p. 166. Three architects building a house, (30, 40, x) in 15.

Riese. Die Coss. 1524.

## No. 118, p. 56. Three windmills can grind 20, 17, 15 per day. How long to do 24?

Cardan. Practica Arithmetice. 1539.

## Chap. 66, section 126 (misprinted 123), ff. kk.vi.v - kk.vii.r (p. 181). Cistern:  (1, 2, 3,  4, -5, -3/4).

Gemma Frisius. Arithmetica. 1540. (20, x) in 14 -- man & wife drinking a cask of wine. ??NYS -- Latin given in H&S, p. 71.

Recorde. Second Part. 1552. 1668, pp. 329-330: A question of water, the eighth example. (6, 8, 9, 12).

Tartaglia. General Trattato, 1556, art. 74, p. 248v; art. 176 177, p. 261v; art. 187 188, pp. 262r 262v.

## Art. 188: (10, 5, 4).

Buteo. Logistica. 1559.

## Prob. 62, pp. 268-269. Cistern, (+2, -3).

Gori. Libro di arimetricha. 1571.

## F. 74v (pp. 82 83). Cistern empties in (4, 6) hours. Ship with three sails, (3, 4, 5) days.

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