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Chap. 1. On the resolution of simple equations in which more than one unknown number appears. p. 153
Chap. 2. On the so-called Regula Cœci rule of the silent/hidden (referring to Diophantine analysis), where three or more unknown numbers are to be determined from two equations. p. 171
Chap. 3. On compound indeterminate equations, where only the first power of one unknown number appears. p. 178
Chap. 4. On the way to make these irrational formulas $\sqrt{(a + bx + cxx)}$ rational. p. 183
Chap. 5. On cases where the formula $a + bx + cxx$ can never become a square. p. 202
Chap. 6. On cases in whole numbers where the formula $axx + b$ becomes a square. p. 213
Chap. 7. On a special method to make the formula $ann + 1$ a square in whole numbers. p. 226
Chap. 8. On the way to make this irrational formula $\sqrt{(a + bx + cxx + dx^3)}$ rational. p. 239
Chap. 9. On the way to make this irrational formula $\sqrt{(a + bx + cxx + dx^3 + ex^4)}$ rational. p. 250
Chap. 10. On the way to make this irrational formula $\sqrt[3]{(a + bx + cxx + dx^3)}$ rational. p. 264
Chap. 11. On the resolution of this formula $axx + bxy + cyy$ into factors. p. 275
Chap. 12. On the transformation of this formula $axx + cyy$ into squares, or even higher powers. p. 288
Chap. 13. On some formulas of this type, $ax^4 + by^4$, which cannot be made into a square. p. 302
Chap. 14. Resolution of some questions that belong to this part of analysis. p. 315
Chap. 15. Resolution of such questions for which cubes are required. p. 366