1. **State the problem:** Simplify the ratio $580\text{ ml} : 1.12\text{ L} : 104\text{ ml}$.\n\n2. **Convert all quantities to the same unit:** Since 1 L = 1000 ml, convert $1.12\text{ L}$ to ml:\n$$1.12 \times 1000 = 1120\text{ ml}$$\nSo the ratio becomes $580 : 1120 : 104$.\n\n3. **Write the ratio as fractions to simplify:**\n$$580 : 1120 : 104 = \frac{580}{104} : \frac{1120}{104} : \frac{104}{104} = \frac{580}{104} : \frac{1120}{104} : 1$$\n\n4. **Simplify each fraction:**\n$$\frac{580}{104} = \frac{\cancel{4}145}{\cancel{4}26} = \frac{145}{26}$$\n$$\frac{1120}{104} = \frac{\cancel{8}140}{\cancel{8}13} = \frac{140}{13}$$\n\n5. **Find a common denominator to express all parts as integers:**\nThe denominators are 26 and 13. The least common multiple is 26.\n\nConvert $\frac{140}{13}$ to denominator 26:\n$$\frac{140}{13} = \frac{140 \times 2}{13 \times 2} = \frac{280}{26}$$\n\nSo the ratio is now:\n$$\frac{145}{26} : \frac{280}{26} : 1 = 145 : 280 : 26$$\n\n6. **Simplify the integer ratio $145 : 280 : 26$ by dividing by their greatest common divisor (GCD):**\n- GCD of 145, 280, and 26 is 1 (since 145 factors as $5 \times 29$, 280 factors as $2^3 \times 5 \times 7$, and 26 factors as $2 \times 13$).\n\nTherefore, the simplified ratio is:\n$$145 : 280 : 26$$\n\n**Final answer:** The simplified ratio is $145 : 280 : 26$.