These cards are tall and narrow at 103 mm by 51 mm (4 in by 2 in). So holding them in one hand can be a little awkward. The 40 card deck in the question is a Primiera Bolognese pattern. Alta Carta labels them as L0061 and notes:
This pattern will soon vanish. There is only one manufacturer left that prints such cards. This does not surprise me, because these cards appear very inconvenient to play with.
The book "On Games of Chance" by Girolamo Cardano described Primero with a hand size of four cards:
Two cards are dealt each player
...
After the first round of betting, two more cards are dealt to each player
Corner and edge indices (see history below) enabled using only one hand. I printed some replica cards and held 5 in a hand with relative ease:

History of the indices we use today
The New York Consolidated Card Company began printing cards in 1832. Their patented design in 1875 is credited with popularizing corner markings to allow fanning your cards for better visualization.
It was not uncommon to hold your hand of 4 or 5 cards in two hands at the time:
Corner and edge indices enabled people to hold their cards close together in a fan with one hand (instead of the two hands previously used). [emphasis added]
They were originally called "squeezers" and not well received by customers, but are now referred to as "indices".