End fed wire antenna + coaxial transformer

dare4444 wrote:
So we take a 75ohm coaxial cable (any length) from our 40m transceiver...
provided that your TRX has a 75 ohm antenna input. The cable should match your TRX.

we bundle another 75ohm coaxial cable at 1/4 wavelength
IMHO the impedance of the matching stub is not too critical. It affects mainly the position of the tapping point.

or 10m long
NO, you must take the velocity factor of the cable into account. A stub for the 40 m band made of coax with solid polyethylene dielectric wil be cca 6,6m long.

and connect its one shorted side to ground
Ït will work even if the shorted end is connected to nowhere. The ground connection is desirable for lightning and static protection, though.

and a 1/2 wave end fed wire antenna on its other end. 
YES, it is called a J-pole antenna. The coax matching stub can be coiled if necessary.

The shorted side is 0ohm impedance and its other end is several thousand ohm where we connected the end fed antenna. 
YES

Now we need to find a 75ohm low impedance tap from the end which is shorted together and grounded, to connect our first 75ohm coaxial cable to couple the transceiver with the end fed wire antenna, through this bundled coaxial transformer
resp. 50 ohm if we have a 50 ohm ended TRX.

The point should not be far from its grounded side. 
Maybe nearly 10% of the stub length, i.e. 60 cm in our case.

Ideally the feeder and the bundled coaxial transformer should be indoors, preferably near a window, for example, where the end fed wire antenna starts. It goes from the window to a tree for example, and is tied to the tree with an insulator. 
Remember both ends of the antenna wire are at high RF potential. The wire should not be reached from the window! Quality insulators must be used.

The 75ohm tapping point in the coaxial cable transformer is critical for good SWR. It's going to be narrowband
I expect any of the ham bands can be covered with reasonable SWR, perhaps with the exception of 80m.