For the sake of practice the learner may now solve the following PROBLEMS: 1. The basis of a triangle, the angle opposite to it, and the sum of the two remaining sides being given, to construct the triangle. 2. The basis of a triangle, the angle opposite to it, and a line equal to the difference of the two remaining sides being given, to construct the triangle. 3. The basis of a triangle, the angle opposite to it, and a side of the square, which is equal to the sum of the squares upon the two remaining sides, being given, to construct the triangle. 4. The basis of a triangle, the angle opposite to it, and a side of the square, which is equal to the difference between the squares upon the two remaining sides, being given, to construct the triangle. 5. The basis of a triangle, the angle opposite to it, and the sum of the height and the two remaining sides, being given, to construct the triangle. 6. The basis of a triangle, the angle opposite to it, and the sum of the height and difference between the two remaining sides, being given, to construct the triangle. 7. The basis of a triangle, the angle opposite to it, and the difference between the sum of the two remaining sides and the height, being given, to construct the triangle. 8. The basis of a triangle, the angle opposite to it, and the difference between the difference of the two remaining sides, and the height of the triangle, being given, to construct the triangle. 9. The basis of a triangle, the angle opposite to it, and the ratio of the sum of the two remaining sides to the height of the triangle being given, to construct the triangle. 10. The basis of a triangle, the angle opposite to it, and the ratio of the difference between the two remaining sides to the height of the triangle, being given, to construct the triangle. 11. The basis, height, and sum of the two remaining sides of a triangle being given, to construct the triangle. 12. The basis, height, and difference between the two remaining sides of a triangle being given, to construct the triangle. 13. The basis and height of a triangle, together with the ratio of the two remaining sides, being given, to construct the triangle. 14. The basis and height of a triangle, and a square equal to the rectangle of the two remaining sides, being given, to construct the triangle. 15. The basis and height of a triangle, and a square which is equal to the sum of the squares upon the two remaining sides, being given, to construct the triangle. 16. The basis and height of a triangle, and a square which is equal to the difference between the squares upon the two remaining sides, being given, to construct the triangle. 17. The angle opposite to the basis of a triangle, the sum of the basis and height, and that of the two remaining sides, being given, to construct the triangle. 18. The angle opposite to the basis of a triangle, the sum of its basis and height, and the difference of the two remaining sides of the triangle, being given, to construct the triangle. 19. The angle opposite to the basis of a triangle, the sum of its basis and height, and the ratio of the two remaining sides, being given, to construct the triangle. 20. The angle opposite to the basis of a triangle, the sum of its basis and height, and the square equal to the rectangle of the two remaining sides, being given, to construct the triangle. 21. The angle opposite to the basis, the sum of the basis and height, and the sum of the three sides, being given, to construct the triangle. 22. The angle opposite to the basis, the sum of its basis and height, and the difference between the sum of the two remaining sides and the basis, being given, to construct the triangle. 23. The angle opposite to the basis, the sum of its basis and height, and the difference between the basis and the difference of the two remaining sides, being given, to construct the triangle. 24. The angle opposite to the basis, the sum of the basis and height, and the ratio of the sum of the two remaining sides to the basis, being given, to construct the triangle. 25. The angle opposite to the basis, the sum of the basis and height, and the ratio of the difference between the two remaining sides to the basis, being given, to construct the triangle. 26. The angle opposite to the basis, the height, and the square, which is equal to the sum of the squares upon the two remaining sides, being given, to construct the triangle. 27. The angle opposite the basis, the height and the sum of the three sides, being given, to construct the triangle. 28. The angle opposite to the basis, the height, and the radius of the circumscribed circle, being given, to construct the triangle. 29. The angle opposite to the basis, the radius of the inscribed circle, and the sum of the three sides, being given, to construct the triangle. 30. The angle opposite to the basis, the radius of the inscribed circle, and the ratio of the sum of the two remaining sides to the basis, being given, to construct the triangle. 31. The angle opposite to the basis, the radius of the inscribed circle, and the square whose area is equal to that of the rectangle of the sum of the two remaining sides and the basis, being given, to construct the triangle. 32. The angle opposite to the basis, the radius of the inscribed circle, and the square whose area is equal to the difference between the sum of the squares of the two remaining sides and the square upon the basis, being given, to construct the triangle. 33. The basis, the line drawn from the vertex of the opposite angle to the middle of the basis, and the sum of the two remaining sides, being given, to construct the triangle. 34. The basis, the line drawn from the vertex of the opposite angle to the middle of the basis, and the difference between the two remaining sides, being given, to construct the triangle. 35. The perpendiculars, dropped from the three vertices upon the opposite sides, being given, to construct the triangle. 36. The lines drawn from the three vertices to the middle of the opposite sides being given, to construct the triangle. |