From where did Jesus draw the notion of salt losing its saltiness, for his usage "You are the salt of the earth"

The history of salt is actually very interesting. A deeper study of the subject perhaps not fitting for this format is definitely justified. I will however provide a brief summery.

Salt is History has had many influences, not just in biblical history but also through out the entire world. It was one of the first industries; roads were called Salt Roads.

Not only did salt serve to flavor and preserve food, it made a good antiseptic, which is why the Roman word for these salubrious crystals (sal) is a first cousin to Salus, the goddess of health. Of all the roads that led to Rome, one of the busiest was the Via Salaria, the salt route; over which Roman soldiers marched and merchants drove oxcarts full of the precious crystals up the Tiber from the salt pans at Ostia. A soldier’s pay—consisting in part of salt—came to be known as solarium argentum, from which we derive the word salary. A soldier’s salary was cut if he “was not worth his salt,” a phrase that came into being because the Greeks and Romans often bought slaves with salt.

A Brief History of Salt- Time Magazine source http://time.com/3957460/a-brief-history-of-salt/

Uses of Salt:

1. Spice

2. Antiseptic

3. Preservative

4. Fertilizer

5. Currency

6. Religious uses Hebrew Sacrifices, early Baptisms

7. Funeral Rituals

Taken from New advent: sourcehttp://www.newadvent.org/cathen/13403b.htm

Its use in the Church belongs exclusively to the Roman Rite. The Ritual knows two kinds of salt for liturgical purposes, the baptismal salt and the blessed salt.

The former, cleansed and sanctified by special exorcisms and prayers, is given to the catechumen before entering church for baptism. According to the fifth canon of the Third Council of Carthage it would seem that salt was administered to the catechumens several times a year. This use of salt is attested by St. Augustine (Confessions I.11) and by John the Deacon. St. Isidore of Seville speaks of it (De off., II, xxi), but in the Spanish Church it was not universal.

The other salt is exorcized and blessed in the preparation of holy water for the Asperges before high Mass on Sunday and for the use of the faithful in their homes. The present formula of blessing is taken from the Gregorian Sacramentary (P.L., LXXVIII, 231). Both baptismal salt and blessed salt may be used again without a new benediction.

The appendix of the Roman Ritual has a blessing of salt for the use of animals and another in honour of St. Hubert. The Roman Pontifical orders salt to be blessed and mixed in the water (mixed in turn with ashes and wine) for the consecration of a church. This is also from the Gregorian Sacramentary. Again salt (not specially blessed) may be used for purifying the fingers after sacred unctions.

Also from New Advent, concerning the Old Testiment and Jewish uses of Salt.

Salt, always used for the seasoning of food and for the preservation of things from corruption, had from very early days a sacred and religious character.

The Prophet Eliseus employed it to make palatable the waters of a well (2 Kings 2:19 sqq.). The Orientals used it to cleanse and harden the skin of a newborn child (Ezekiel 16:4); by strewing salt on a piece of land they dedicated it to the gods; in the Jewish Law it was prescribed for the sacrifices and the loaves of proposition (Leviticus 2:13). In Matthew 5:13, salt symbolizes wisdom, though perhaps originally it had an exorcistic signification.

The daily offerings in the temple included salt:

Whatsoever sacrifice thou offerest, thou shalt season it with salt: neither shalt thou take away the salt of the covenant of thy God from thy sacrifice. In all thy oblations thou shalt offer salt. Leviticus 2:13

The value of salt in ancient times was significant in every way, people were taxed on it, Salt was a major commodity in the ancient world. New uses are found for Salt all the time, Naturalist in todays world are trying to get away from using chemicals so common in modern society, salt answer many problems for basic household uses, like cleaning or in my case, killing flea eggs because a hairy beast of a dog that I own is a flea bag. Pouring salt all over the carpets was done to kill any unhatched eggs the fleas may have left behind.

A person could really do a college dissertation on the uses of salt and it's relevance to biblical teaching, I can only scratch the surface. I suggest you take this answer with "A Grain of Salt" Oh, 8.verbal expressions, another great use of salt, anyone “worth their salt” knows that.