There are n straight lines in a plane, no two of which are parallel and no three of which pass through the same point. How many additional lines can be generated by means of point of intersections of the given lines.

Answer

To solve the problem, we need to determine how many additional lines can be formed by the intersection points of n straight lines in a plane, given that no two lines are parallel and no three lines meet at a single point.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have n lines in a plane.
- No two lines are parallel, which means every pair of lines will intersect at a unique point.
- No three lines intersect at the same point, ensuring that all intersection points are distinct.

2. **Finding Intersection Points**:
- To find the number of intersection points formed by these n lines, we need to select pairs of lines.
- The number of ways to select 2 lines from n lines is given by the combination formula \( \binom{n}{2} \).
- Thus, the number of intersection points (let's denote it as P) is:
\[ P = \binom{n}{2} = \frac{n(n-1)}{2} \]

3. **Generating Additional Lines**:
- Each intersection point can be connected to other intersection points to form additional lines.
- To form additional lines, we need to select pairs of intersection points.
- The number of intersection points we have is \( P \), and we need to select 2 points from these \( P \) points.
- The number of ways to select 2 points from P points is given by \( \binom{P}{2} \).

4. **Calculating Additional Lines**:
- Substituting \( P \) into the combination formula, we have:
\[ \text{Additional Lines} = \binom{P}{2} = \binom{\frac{n(n-1)}{2}}{2} \]
- This can be calculated as:
\[ \binom{P}{2} = \frac{P(P-1)}{2} = \frac{\frac{n(n-1)}{2} \left(\frac{n(n-1)}{2} - 1\right)}{2} \]

5. **Final Expression**:
- After simplifying, we find the total number of additional lines that can be formed by the intersection points of the given lines.

### Final Answer:
The number of additional lines that can be generated by the points of intersections of the given lines is:
\[ \frac{n(n-1)(n(n-1)/2 - 1)}{8} \]