How do I collect Spell Cards?

I'm currently attempting to play Touhou: the Embodiment of Scarlet Devil. I've figured out that my own Spell Cards are what I use for my bombs, but when I go to Score in the menu, I see that there is an entry for Spell Cards. Clicking on that, there are 64 entries, some of which I've acquired, so I'm assuming this is a collection of some sort.

The problem is I don't really know how I collected them and what exactly the numbers next to them mean. For example, next to No. 02 Night Sign "Night Bird", I have 1/2 while for No. 03 Darkness Sign "Demarcation" I have 2/2.

I assume this means that for No. 02, I have 1 out of the 2 "cards" available to collect and for No. 03, I've collected all the cards available to collect. How do I know which I have and which I don't? How do I collect these things in the first place? I've noticed them pop up during the boss fights, but what are the specific criteria I need to meet in order to successfully collect them?

Edit: And now I've just noticed after doing some more (failed) playthroughs that these numbers are... increasing? The numbers for the cards I listed are now 3/4 and 4/4, respectively. I thought the last number was increasing with my playthrough attempts, but I've got some at 3 and some at 5 when I've currently tried 4 times, so I'm not sure if this is correct.

2 Answers

You collect a spell card by defeating it without using a bomb, being hit, or running out of time.

The number (e.g. 3/4) is the number of times you've captured the spell card, followed by the number of times you've attempted the spell card in total.

To add some details to Jonathan Drain's answer. If I am correct, the total number only considers "real plays". Practices doesn't count.

I understand your edited point. For my personal score, I assumed that the number of attempt is how many times you tried the spell card. That's means if a boss & mid boss are the same character (e.g. EoSD Level 4: Hong Meilin), you can have 5 try for mid boss spell card but only 4 tries for her last spell card because you have already died...(R.I.P.)