Diophantus of Alexandria/Arithmetica/Book 1
Problems by Diophantus of Alexandria: Arithmetica Book $\text I$
Problem $1$
- To divide a given number into two having a given difference.
Problem $2$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 2
Problem $3$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 3
Problem $4$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 4
Problem $5$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 5
Problem $6$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 6
Problem $7$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 7
Problem $8$
- What number must be added to $100$ and to $20$ (the same number added to each) so that the sums are in the ratio $3 : 1$?
Problem $9$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 9
Problem $10$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 10
Problem $11$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 11
Problem $12$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 12
Problem $13$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 13
Problem $14$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 14
Problem $15$
- Two numbers are such that:
- if the first receives $30$ from the second, they are in the ratio $2 : 1$
- if the second receives $50$ from the first, they are in the ratio $1 : 3$.
What are these numbers?
Problem $16$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 16
Problem $17$
- The sums of $4$ numbers, omitting each of the numbers in turn, are $22$, $24$, $27$ and $20$ respectively
What are the numbers?
Problem $18$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 18
Problem $19$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 19
Problem $20$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 20
Problem $21$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 21
Problem $22$
- To find $3$ numbers such that, if each give to the next following a given fraction of itself, in order, the results after each has given and taken may be equal.
That is:
Let $\dfrac 1 p, \dfrac 1 q, \dfrac 1 r$ be given.
The exercise is to find a set of $3$ natural numbers $\set {x, y, z}$ such that:
| \(\ds x - \frac x p + \frac z r\) | \(=\) | \(\ds m\) | ||||||||||||
| \(\ds y - \frac y q + \frac x p\) | \(=\) | \(\ds m\) | ||||||||||||
| \(\ds z - \frac z r + \frac y q\) | \(=\) | \(\ds m\) |
where $m$ is a natural number.
Problem $23$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 23
Problem $24$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 24
Problem $25$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 25
Problem $26$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 26
Problem $27$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 27
Problem $28$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 28
Problem $29$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 29
Problem $30$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 30
Problem $31$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 31
Problem $32$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 32
Problem $33$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 33
Problem $34$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 34
Problem $35$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 35
Problem $36$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 36
Problem $37$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 37
Problem $38$
Diophantus of Alexandria/Arithmetica/Book 1/Problem 38