So when starting a tweet with '@persons_Twitter_handle' (followed by quoted text) only the addressed account & all people following BOTH (the one sending the tweet & recipient) can read this tweet, intended for a wider public (all followers)
This 'public direct messaging' can be avoid once a tweet starts with any other character than '@'. Often a '.' (full stop) is used.
Since a couple of month however, Twitter provides us with a superb other method of displaying the content of other tweets: embedding !
Once you use this method the entire 'original' tweet will be made available to your audience.
You just have to 'open' the tweet you intend to 're-publish', then right-click on 'Details' (to the right of Date/Time of tweet) and copy the link of this tweet.(method of 'copy&paste' might be different when using MAC OSX or other Operating System)
2013 #NobelPrize recap: Physics to François Englert & Peter W. Higgs for the theory of how particles acquire mass http://t.co/E4HITGgl62link: https://twitter.com/Nobelprize_org/status/389013387637977088
— Nobelprize_org (@Nobelprize_org) October 12, 2013
Then you write your introduction text and you add ('paste') the link to your tweet. By using this method is also possible to 'circumvent' the 140 character limitation of Twitter, which is even less when you try to put all quoted text between quotation marks & provide the author's name.