Answer

Jain scriptures do not usually state the modern phrase “do not eat potatoes, onions, carrots, etc.” in one single line. The rule comes from the scriptural doctrine of:

• Ahimsa toward plant-bodied beings
• Vanaspati-kāya jīvas — plant-bodied living beings
• Sādhāraṇa / Anantakāya vanaspati — plant bodies inhabited by innumerable/infinite souls
• Ascetic food rules prohibiting raw plants, roots, bulbs, sprouts, and similar living plant substances

The most relevant scriptural and traditional textual places are these:

Specific Citations

• Ācārāṅga Sūtra, Book 1, Lecture 1
  This foundational Śvetāmbara Āgama teaches that plants are living beings and that injury to plant life is violence. It compares plant life with human life in birth, growth, decay, and vulnerability to cutting or injury.
  Translation available in the public-domain English translation of the Ācārāṅga Sūtra.
• Ācārāṅga Sūtra, Book 2, food-conduct rules for monks and nuns
  This section gives detailed rules that monks and nuns should not accept raw plant substances, including seeds, sprouts, roots, stems, knots, bulbs, lotus parts, and similar living vegetable matter.
  This is one of the clearest canonical bases for avoiding living plant substances, especially roots, bulbs, and sprouts.
• Gommatasāra Jīvakāṇḍa, by Ācārya Nemicandra Siddhānta-cakravartī
  This Digambara text classifies living beings and explains plant-bodied souls, including sādhāraṇa vanaspati, meaning common-bodied or group-bodied plant life. This is closely connected with the Jain idea behind anantakāya.
• Tattvārtha Sūtra, Chapter 2
  The Tattvārtha Sūtra, accepted by both major Jain traditions, classifies one-sensed beings and includes plant-bodied beings. While it is not a dietary manual, it gives the philosophical foundation for why plant life is treated as living and why unnecessary harm to it is avoided.

Explanation

The Jain avoidance of root vegetables is based on the belief that many underground roots, bulbs, and tubers are connected with anantakāya or sādhāraṇa vanaspati. This means that one physical body may be the support of innumerable living beings.

So, when such a root or bulb is uprooted, cut, cooked, or eaten, Jain tradition considers it to involve a much greater amount of violence than eating a fruit or grain that is permitted under household discipline.

Examples traditionally avoided include:

• Potato
• Onion
• Garlic
• Carrot
• Radish
• Turnip
• Sweet potato
• Ginger
• Turmeric root
• Yam and similar tubers

Important Clarification

For monks and nuns, the rules are stricter and are directly connected to Āgamic conduct. For householders, the practice is followed as part of Jain dietary discipline to reduce violence as much as possible.

The scriptural basis is therefore not merely “root vegetables are forbidden” as a modern food list, but the deeper Jain principles that:

• plants are living beings,
• some plant bodies contain innumerable souls,
• uprooting destroys the whole plant,
• roots and bulbs often continue sprouting, showing active life,
• and avoidable violence should be minimized.

About Links

You asked for links to translations. I can only provide links from JainKnowledge.com. If a relevant JainKnowledge.com translation page is available, it should be preferred. I cannot provide external links here.

Takeaway

The Jain rule against root vegetables is grounded in the scriptures’ teaching on ahimsa, plant-bodied souls, and especially sādhāraṇa/anantakāya vanaspati. The clearest scriptural foundation is found in the Ācārāṅga Sūtra and the doctrinal classification of living beings found in texts like the Tattvārtha Sūtra and Gommatasāra Jīvakāṇḍa.