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One's Ascendant, or Lagna, is the degree of the rāśi (or sign) which is rising on the eastern horizon at the time of one's birth. The Most Effective Point (MEP) of the Ascendant - Lagna, is that point of the zodiacal belt that coincides with the position of the horizon at the time of birth, for a given place of birth. 
This is more specifically called the Udaya Lagna to differentiate it from charts in which other points are used to determine the first house of the horoscope (see below.) The Udaya Lagna is the most influential and important sign within the natal chart, and the characteristics of that sign will to some extent be impressed upon the personality of the person or event being born. This sign will be considered the first house of the horoscope, and the enumeration of the other houses follows in sequence through the rest of the signs of the zodiac. In this way, the Lagna does not only delineate the rising sign, but also all the other houses in the chart.
However, the Ascendant is not the only Lagna used in Jyotiṣa. Another important Lagna is the Janma Rāśi, which is the rāśi (or sign) in which the moon is found at birth. A Candra Lagna chart, which is also an important tool used to analyze the horoscope, is a chart in which the Moon's house is treated as the first house of the horoscope and the enumeration of the other houses are made starting from that rāśi and continuing in sequence throughout the rest of the zodiac signs. The astrologer will use the Candra Lagna to see the personality from the perspective of his or her mind, since the Moon is predominant symbol of the mind among planets.
The Rāśi Cakra (that is, the horoscope where the first house is the house in which the rising sign is found) is the still the most important natal chart, but charts can be cast for different analytical purposes. The primary Lagnas (that is, houses designated as the First House, from which the rest of the houses are enumerated) used to analyze the horoscope are:
- Udaya lagna (rising sign, or Ascendant as first house)
- Candra Lagna (first house counted from the sign of the natal Moon, used to anlayze mind, memory and mental activity, and also used to help determine how fertile a woman will be.)
- Sūrya Lagna (ascendant counted from sign where the natal Sun is located)
- Kāraka Lagna (significator taken as ascendant for all grahas)
- Varṇaḍā Lagna (for social company)
- Śrī Lagna (for prosperity and marriage)
- Indu Lagna (for wealth)
- Horā Lagna (for financial prosperity)
- Gati Lagna (for name and fame)
Lastly, there are some Lagnas which are determined by factors outside the chart, and are used for electional and horary charts. These are:
- Dig Lagna (first house is determined by compass direction)
- Śabda Lagna (first house is determined by the "words a client utters")
- Sparṣa Lagna (first house is determined by a part of the body which is touched)
- Nāma Lagna (first house is determined by the numerology of the person's name)
The term Ārūḍha Pada is also known as "Pada". Ārūḍha literally means "mount" and refers to the IMAGE of a sign falling on another due to "reflection of the rays emanating from it and being reflected by its lord.
Keeping the reflection in view, the Kāraka (Significator) can be taken to be the Moon. Count from a sign to its lord. Then count as many signs from the lord to arrive at the ĀRŪḌHA PADA. For example, if the Lagna Lord (Lagneśa) is in the fifth house, then count five signs from the Lagneśa to arrive at the ninth house. This ninth house becomes the Ārūḍha Pada for the Lagna.
Exception: The Ārūḍha Pada cannot be in the same sign or the seventh from it. In case this happens, then choose the tenth house therefrom. For example, if the Lagneśa is in the 4th house, then the Ārūḍha Lagna should be in the 4th from the 4th house i.e. the 7th house. But since this is not allowed, the tenth therefrom should be chosen. The tenth from the 7th house is the 4th house and the 4th house becomes the Ārūḍha Lagna.
Ārūḍha of 1st house is also called PADA LAGNA or ĀRŪḌHA LAGNA. Ārūḍha Lagna stands for "manifestation of self, in this Māyā(illusory) world". In this manner Ārūḍha Pada can be computed for all the houses. They are called Dhana Pada (2nd), Bhrātṛpada (3rd), Mātṛ Pada (4th), Mantrapada (5th), Śatrupada (6th), Dāra Pada (7th), Roga pada (8th), Bhāgyapada (9th), Rājyapada (10th), Lābhapada (11th) and Upapada (12th). Jaimini discussed Ārūḍha Lagna (AL) and Upapada (UL) extensively in his classical treatise.
- The Essentials of Vedic and thantrik Astrology, by Komilla Sutton, The Wessex Astrologer Ltd, England, 1999, p.96.
- "Sri Ramana Maharshi's Moksha", by Sri Sankara Bhagavadpada, Yogi Impressions, India, 2008, p.49 http://hinduworldastrology.net/index.php?module=book&action=samples#
- Vedic Astrology: A Guide to the Fundamentals of Jyotish, by Ronnie Gale Dreyer, Samuel Weiser, York Beach ME, 1997, pp. 47–49.
- Light on Life: An Introduction to the Astrology of India, by Hart deFouw and Robert Svoboda, Penguin, 1996, pp.45–46.