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This is described in Chapter 3, Satarudra Samhita of Shiva Mahapurana.

Chapter 10 Rudra Samhita (Sati Khanda) of Shiva Mahapurana says:

Daksha, at command of Brahma, prayed to Durga and got Her as daughter. Chapter 11 Rudra Samhita (Sati Khanda) says:

Chapter 3, Rudra Samhita (Parvati Khanda) says:

Chapter 4 Rudra Samhita (Parvati Khanda) says

This is described in Chapter 3, Satarudra Samhita of Shiva Mahapurana.

Chapter 10 Rudra Samhita (Sati Khanda) of Shiva Mahapurana says:

Daksha, at command of Brahma, prayed to Durga and got Her as daughter. Chapter 11 Rudra Samhita (Sati Khanda) says:

Chapter 3, Rudra Samhita (Parvati Khanda) says:

Chapter 4 Rudra Samhita (Parvati Khanda) says

यदा सृष्टाः प्रजाः सर्वा न व्यवर्द्धन्त वेधसा।
तदा चिन्ताकुलोऽभूत्स तेन दुःखेन दुःखितः ॥ २॥

When there had been little evolution of the people created by Brahma, he felt extremely painful.

नभोवाणी तदाऽभूद्वै सृष्टिं मिथुनजां कुरु।
तच्छ्रुत्वा मैथुनीं सृष्टिं ब्रह्मा कर्तुममन्यत॥ ३॥

Then there was a divine sound from the sky said, "Carry on the creation produced by the couples' (i.e. the male and the female). Then Brahma thought of the creation based on the sexual relations.

 

नारीणां कुलमीशानान्निर्गतं न पुरा यतः।
ततो मैथुनजां सृष्टिं कर्तुं शेके न पद्मभूः॥४॥

Earlier to that the race had not appeared out of the sexual intercourse with the females. Therefore Brahma could not create the world based on sexual relationship earlier.

प्रभावेणा विना शम्भोर्न जायेरन्त्रिमाः प्रजाः।
एवं सञ्चिन्तयन्ब्रह्मा तपः कर्तुं प्रचक्रमे॥ ५॥

Brahma thought that the creation cannot be progressed without the influence of Šiva. Therefore he started performing tapas.

शिवाय परया शक्त्या संयुक्त परमेश्वरम्।
सञ्चिन्त्य हृदये प्रीत्या तपेशं परमं तपः।। ६॥

Then he meditated upon Siva united with the great Sakti called Parameswara (Siva) in a combined way performing severe tapas.

तीव्रेण तपसा तस्य संयुक्तस्य स्वयम्भुवः।
अचिरेणैव कालेन तुतोष स शिवो द्रुतम्॥७॥

Observing the severe austerities of Brahma, lord Siva was rapidly pleased with him within no time.

ततः पूर्णचिदीशस्य मूर्तिमाविश्य कामदाम्।
अर्द्धनारीनरो भूत्वा ततो ब्रह्मान्तिकं हरः॥८॥

Then Isvara- the form of complete consciousness, entered into the Ardhanarisvara form, representing half male and half female and he appeared before Brahmā.

यदा सृष्टाः प्रजाः सर्वा न व्यवर्द्धन्त वेधसा।
तदा चिन्ताकुलोऽभूत्स तेन दुःखेन दुःखितः ॥ २॥

When there had been little evolution of the people created by Brahma, he felt extremely painful.

नभोवाणी तदाऽभूद्वै सृष्टिं मिथुनजां कुरु।
तच्छ्रुत्वा मैथुनीं सृष्टिं ब्रह्मा कर्तुममन्यत॥ ३॥

Then there was a divine sound from the sky said, "Carry on the creation produced by the couples' (i.e. the male and the female). Then Brahma thought of the creation based on the sexual relations.

नारीणां कुलमीशानान्निर्गतं न पुरा यतः।
ततो मैथुनजां सृष्टिं कर्तुं शेके न पद्मभूः॥४॥

Earlier to that the race had not appeared out of the sexual intercourse with the females. Therefore Brahma could not create the world based on sexual relationship earlier.

प्रभावेणा विना शम्भोर्न जायेरन्त्रिमाः प्रजाः।
एवं सञ्चिन्तयन्ब्रह्मा तपः कर्तुं प्रचक्रमे॥ ५॥

Brahma thought that the creation cannot be progressed without the influence of Šiva. Therefore he started performing tapas.

शिवाय परया शक्त्या संयुक्त परमेश्वरम्।
सञ्चिन्त्य हृदये प्रीत्या तपेशं परमं तपः।। ६॥

Then he meditated upon Siva united with the great Sakti called Parameswara (Siva) in a combined way performing severe tapas.

तीव्रेण तपसा तस्य संयुक्तस्य स्वयम्भुवः।
अचिरेणैव कालेन तुतोष स शिवो द्रुतम्॥७॥

Observing the severe austerities of Brahma, lord Siva was rapidly pleased with him within no time.

ततः पूर्णचिदीशस्य मूर्तिमाविश्य कामदाम्।
अर्द्धनारीनरो भूत्वा ततो ब्रह्मान्तिकं हरः॥८॥

Then Isvara- the form of complete consciousness, entered into the Ardhanarisvara form, representing half male and half female and he appeared before Brahmā.

उमोवाच हे हरे! विधे! देवा! मुनयश्च गतव्यथा:।
सर्वे शृणुत मद्वाक्यं प्रसन्नाऽहं न संशयः।।२३।।

Uma said, "O Visnu, O Brahma, O other gods, let all of you be comfortable. Listen to my words. I am undoubtedly pleased with all of you.

चरितं मम सर्वत्र त्रैलोक्यस्य सुखावहम्॥
कृतं मयैव सकलं दक्षमोहादिकं च तत्।।२४।।

My performance always provides comforts to all the three worlds. The sport relating to the yajna of Daksa, was performed by me.

अवतारं करिष्यामि क्षितौ पूर्णं न संशयः।
बहवो हेतवोऽप्यत्र तद्वदामि महादरात्।।२५।।

I shall surely appear on earth, with full incarnation. There are several reasons for the same, which I am going to highlight with respect.

पुरा हिमाचलो देवा मेना चातिसुभक्तितः। सेवां मे चक्रतुस्तात! जननीवत्सतीतनोः।।२६।।

O Gods, earlier when I was born as Sati, then both Himalaya and Mena had severed me lovingly as parents.

इदानीं कुरुतः सेवां सुभक्त्या मम नित्यशः।
मेना विशेषतस्तत्र सुतात्वे नात्र संशयः।।२७।।

Even presently both of them are serving me with utmost devotion. Out of both of them, Menaka, serves me particularly as a daughter.

उमोवाच हे हरे! विधे! देवा! मुनयश्च गतव्यथा:।
सर्वे शृणुत मद्वाक्यं प्रसन्नाऽहं न संशयः।।२३।।

Uma said, "O Visnu, O Brahma, O other gods, let all of you be comfortable. Listen to my words. I am undoubtedly pleased with all of you.

चरितं मम सर्वत्र त्रैलोक्यस्य सुखावहम्॥
कृतं मयैव सकलं दक्षमोहादिकं च तत्।।२४।।

My performance always provides comforts to all the three worlds. The sport relating to the yajna of Daksa, was performed by me.

अवतारं करिष्यामि क्षितौ पूर्णं न संशयः।
बहवो हेतवोऽप्यत्र तद्वदामि महादरात्।।२५।।

I shall surely appear on earth, with full incarnation. There are several reasons for the same, which I am going to highlight with respect.

पुरा हिमाचलो देवा मेना चातिसुभक्तितः। सेवां मे चक्रतुस्तात! जननीवत्सतीतनोः।।२६।।

O Gods, earlier when I was born as Sati, then both Himalaya and Mena had served me lovingly as parents.

इदानीं कुरुतः सेवां सुभक्त्या मम नित्यशः।
मेना विशेषतस्तत्र सुतात्वे नात्र संशयः।।२७।।

Even presently both of them are serving me with utmost devotion. Out of both of them, Menaka, serves me particularly as a daughter.