Any space can be divided into 4 quadrants basically using two mutually perpendicular planes - the horizontal plane(HP) and the vertical plane(VP). These planes are considered to be transparent and to be of infinite size.
In first angle projections, the object is considered to be in front of VP and above HP. Hence the top view or plan of the object will be obtained below the reference line and the front view or elevation above the reference line.
In third angle projections, the object is said to be behind VP and below HP. hence the top view or plan will be obtained above the reference line and the elevation below the reference line.
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In a first angle projection, the object stands in between the observer and the plane of projection. In a third angle project, the object and the plane of projection is interchanged.
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Basically its just where you position the views of the main object, in first angle projection, if you view the object from the left, the view is drawn to the right of the object, in third angle projection, its drawn on the viewing side.
In first-angle projection, the projectors originate as if radiated from a viewer's eyeballs and shoot through the 3D object to project a 2D image onto the plane behind it. The 3D object is projected into 2D "paper" space as if you were looking at a radiograph of the object: the top view is under the front view, the right view is at the left of the front view. First-angle projection is the ISO standard and is primarily used in Europe.
The front elevation is in the centre in both projections. In 1st angle projection the end elevation is on the opposite side of the front elevation and the plan view is below the front elevation. In 3rd angle projection the plan view is above the front elevation and the end elevations are on the same side as viewed