Two important prayers Catholics pray are the Rosary and the Seven Sorrows Chaplet. They involve repetitions of the Hail Mary and the Our Father, along with some other prayers. They are prayed in a specific order, but the words of the prayers are not the primary purpose of the prayers. They are instead meant to help people delve deeper into the mysteries of the faith.
During the Seven Sorrows prayer we reflect on and meditate on seven sorrows in Mary's life that relate directly to Jesus. In the Rosary we reflect on 15, or 20, events in Jesus' life and Mary's life that have some significance and contain some mystery of faith. These sets are broken up into sets of 5, so on any day of the week we pray while meditating on 5 mysteries. By taking the time to think about these events and place our emotions and our imagination in them, the prayers can gain new significance when thought of in those contexts. We make a deeper, more thorough, connection to the faith and experience the mystery in a more complete way.
Though there are a lot of published things about what one might reflect on for any of these events, there is no single right answer. Each event is multi-faceted. Each time you approach them, you are in a different state of mind and in different circumstance. Plus as you continue to pray these, your sense of them deepens over time.
The seven sorrows are: the prophecy of Simeon, the flight into Egypt, the loss at the temple, the meeting on the way of the cross, the Crucifixion, the taking down of the body, and the burial. These events are not in isolation from each other, nor are they in isolation for other events outside the seven. This gives more room to reflect on the significance of the events, to experience her sorrows with her, to see the life and death of Jesus in a new light.
The Rosary is similar in that we are asked to meditate on mysteries in Jesus' life (and conception) while praying the formula of prayers. The standard set of mysteries have changed over time, and one can find more mysteries to pray during the Rosary which were used more commonly in the past to vary it up. The current standard 20 are 4 sets of 5 and include the 5 Luminous Mysteries added by Saint Pope John Paul II. The first set of 5 are the Joyful Mysteries: the Annunciation, the Visitation, the Nativity, the Presentation, the Finding at the Temple. The Presentation and the Finding coincide with two of the Sorrows above. The second set of 5 are the Sorrowful Mysteries are: the Agony in the Garden, the Scourging at the Pillar, the Crowning with Thorns, the Carrying of the Cross, the Cruxifiction. The third set of 5 are the Glorious Mysteries: the Resurrection, the Ascension, the Pentecost/Descent of the Holy Ghost/Spirit, the Assumption of Mary in to Heaven (Catholic doctrine not held by other denominations), and the Crowning in Heaven (as found in the Book of Revelation, where some other denominations seem to maintain that we can not know that is Mary and could be Israel or the church as the Body of Christ, or perhaps other ideas I'm not familiar with. I think it's a stretch. Even if the alternate interpretations are right, Mary is surely among them. Who is going to push her aside and be the first to be crowned? She's His mom for God's sake. Let her have the Crown.) The 5 Luminous Mysteries are: the Baptism by John the Baptist, the Wedding at Cana, the Declaration of the Kingdom of Heaven, The Transfiguration, and the Eucharist.
There are 7 days in a week, and 4 sets of Mysteries (now). The Luminous ones are done on Thursdays only, leaving the others to be done on the other days. Any book on the Rosary or any youtube video where you can do the Rosary along with the video will state what days the set of mysteries are for.
Additionally it has been suggested, I do not know the source, that it is good to meditate on one of the Mysteries of the Rosary for 15 minutes on its own. I do not recall if it is suggested for once a week or daily. At Fatima, and in other apparitions, Mary asked us to pray the Rosary daily. Some people pray more than the five sets of mysteries per day, which are called decades because they consist of 10 Hail Marys along with an Our Father to start, the Glory Be and the Fatima Decade Prayer to finish. Some people add the Flame of Love to the Hail Marys which came from an apparition in Hungary in the middle of the 20th century.
I will post more about these prayers, eventually. Feel free to start praying them. There are variations on how to do it, and I hope to include those here soon. But more than praying them, meditating on the mysteries along with some prayers is good. It has been said that one or two good decades prayed with focus and without distractions is better than rushing through the words without any real depth of meditation or with many distractions.
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