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In the Kalki purana chapter 4 verse 15 it stated that:
Being pleased by their devotional service, I incarnate, along with Goddess Lakshmi, in every millennium."
What is meant by this verse? A millenium is 1000 years. There are 10 avatars of Vishnu per kalpa. Is it a mistake? Do they mean a kalpa or mahayuga?
This seems a translation issue, here is the Sanskrit shloka and Hindi translation of Kalki Purana 4.15:
The religion of the Brahmanas is to render pure devotional service unto Me. Being pleased by their devotional service, I incarnate, along with Goddess Laksmi (Shri), from age to age.
There are infinite avatars of Vishnu, few of them are given in this post:
10 or 24 are most famous among all avatars but they are not the only avatars.
The phrase संभवामि युगे युगे (sambhavami yuge yuge) is there in Shrimad Bhagavad Gita 4.8 too:
परित्राणाय साधूनां विनाशाय च दुष्कृताम्।
धर्मसंस्थापनार्थाय संभवामि युगे युगे।।4.8।।
And here is how different scholars translated it:
[Lord Shri Krishna to Arjuna]: Paritranaya, for the protection; sadhunam, of the pious, the followers of the virtuous path; vinasaya, for the destruction; duskrtam, of the evil-doers, of the sinful ones; and also dharmasamsthapanarthaya, for establishing virtue fully;-for that purpose, sambhavami, I manifest Myself; yuge yuge, in every age. -English Translation Of Sri Shankaracharya's Sanskrit Commentary By Swami Gambirananda
[Lord Shri Krishna to Arjuna]: For the protection of the good and also for the destruction of the wicked, for the establishment of Dharma, am I born from age to age. -English Translation By Swami Adidevananda
[Lord Shri Krishna to Arjuna]: For the protection of the pious, the destruction of the evil-doers, and establishing virtue, I manifest Myself in every age. -English Translation By Swami Gambirananda
[Lord Shri Krishna to Arjuna]: For the protection of the good, for the destruction of the wicked and for the establishment of righteousness, I am born in every age. -English Translation By Swami Sivananda
[Lord Shri Krishna to Arjuna]: For the protection of the good people, and for the destruction of evil-doers, and for the purpose of firmly establishing righteousness, I take birth in every age. -English Translation By By Dr. S. Sankaranarayan
[Lord Shri Krishna to Arjuna]: To protect the righteous, to destroy the wicked and to establish the kingdom of God, I am reborn from age to age. -English Translation by Shri Purohit Swami
Sanskrit word used is "Yuga" and translation you quoted is given by by Bhumipatidas. Gaudiya Sampradaya (ISKCON) Swamis and Acharyas translate "Yuga" as millenium.
यो धर्मो ब्राह्मणाना हि सा भक्तिर्मम पुप्फला ।
तयाहं तोषितः श्रीशः सम्भवामि युगे युगे ॥ १५The dharma of the brahmanas is to render pure devotional service unto Me .Being pleased by their devotional service, I incarnate, along with Goddess Laksmi, in every millennium.
This quote is similar to Bhagavadgita Gita 4.8
परित्राणाय साधूनां विनाशाय च दुष्कृताम् ।
धर्मसंस्थापनार्थाय सम्भवामि युगे युगे ॥८॥paritrāṇāya sādhūnāḿ vināśāya ca duṣkṛtām
dharma-saḿsthāpanārthāya sambhavāmi yuge yugeTo deliver the pious and to annihilate the miscreants, as well as to reestablish the principles of religion, I Myself appear, millennium after millennium.
Yuga is translated as "Age" or "Millenium" or to convey a time that occurs at required intervals. Here is how A Mahadeva Sastri translates it in his translation of commentary of Bhagavadgita.
- For the protection of the good, for the destruction of evil-doers, for the firm establishment of religion, I am born in every age.
There are 10 avatars of Vishnu per kalpa. Is it a mistake?
Lord Vishnu avatars are infinite if we consider cyclic nature of time. However, Puranas mention some avatars of Lord Vishnu. There's no rule that Lord Vishnu has to take only 10 Avatars in a Kalpa. Also, refer this post for chronological order of Vishnu's avatars.
