This can be done indirectly using interfaces. Create a public interface in the library that has the calls you need to make against that main project's class. Have the main project's class implement this interface. When the main projects starts have it pass in instance of this class in to the library project via the interface. The library should store this reference. It can now makes calls against the main projects class using this reference through the interface.
The Library Project:
Public Interface ITimeProvider
ReadOnly Property Time As Date
End Interface
Public Class LibraryClass
Private Shared _timeProvider As ITimeProvider
Public Shared Sub Init(timeProvider As ITimeProvider)
_timeProvider = timeProvider
End Sub
Public Function GetTimeString() As String
Return "The current time is " & _timeProvider.Time.ToString
End Function
End Class
The Main Project:
Public Class SimpleTimeProvider
Implements ClassLibrary1.ITimeProvider
Public ReadOnly Property Time As Date Implements ClassLibrary1.ITimeProvider.Time
Get
Return Date.Now
End Get
End Property
End Class
Public Class MainClassTest
Private Sub Form1_Load(sender As Object, e As EventArgs) Handles Me.Load
ClassLibrary1.LibraryClass.Init(New SimpleTimeProvider)
Dim test As New ClassLibrary1.LibraryClass
Console.WriteLine(test.GetTimeString)
End Sub
End Class
This example has the library project using a class that is defined in the Main project.