Three primary 18th century violin treatises (Geminiani, Leopold Mozart and L'Abbé Fils - the Italian, the German and the French) were all created within the space of the decade 1751-1761 and summarize the traditions they represent. A paradox exists, however, in that both too few and too many details of violin playing are known. Certain questions cannot be answered with assurance; the bewildering array of answers within the boundaries of accepted practice leads to the conclusion that there is not one but a variety of 18th century styles.
Geminiani, whose works provide a vital link between the Italian tradition from Corelli to Tartini, was a student of Corelli in Rome and Scarlatti in Naples, and came to England in 1714 (15?) shortly after the death of Corelli, never returning to Italy. He enjoyed a fantastic success as a virtuoso in England, playing for King George with Handle as accompanist (1715). He later had immense prestige as a composer, teacher and theorist. Burney is said to have a malicious prejudice against Geminiani; in Naples Burney said Geminiani was discharged from the opera orchestra in Lucca for "frequent absences." 
Geminiani wrote a substantial amount of music for his treatises, including twelve compositions for The Art of Playing the Violin. Donington characterizes Geminiani as being only a "moderately good composer,"  but Boyden clarifies this consideration of the value of the composer's works by stating that they are undervalued and unfortunately overshadowed by Vivaldi. Geminiani nevertheless had an illustrious reputation as a teacher, influenced a large circle of pupils and was one of the most deeply respected, influential and celebrated violin virtuoso of his time. He was also a financial success in London and Dublin, and known for his vigorous and elegant English prose style.
Geminiani was on good terms with leading figures such as the Earl of Essex (who is said to have rescued him from debtor's prison due to the composer's predilection for acquiring paintings). His contemporaries considered him superior as a player even to Veracini. Tartini characterized him as "the violent one"  and Burney noted his "overwhelming technical audacity." 
Reprints, translations and imitations of his works indicate that the composer was widely read by the musical public of the 18th century. It was at one time thought that The Art of Playing the Violin was a reprint of an anonymous violin method, Volens Nolens, published in London in 1695. All of this is cleared up in Boyden's article Acta Musicologica, February, 1960. A simplified version of Geminiani's work was printed after his death by Stephen Philpot (pupil of Festing) and an abbreviated version was printed in Boston by John Boyles. After the composer's death a number of merely imitative violin tutors for amateurs were published, exploiting the composer's name when he was no longer able to defend himself.
Though The Art of Playing the Violin is said by Boyden to be merely of archeological use if considered apart from the original instrument, it has significant historical importance and much of the material is still applicable to contemporary technique. The treatise was written during the last period of the composer's life, and was the most successful of his works. Though certainly not the first violin method, it was the first mature exposition of this kind of material and covered very adequately the technical groundwork necessary to cope with almost any violinistic problems of the time, aside from exceptionally virtuosic pieces such as the Locatelli Caprices. It was the first violin treatise addressed to professional violinists, reflecting their practices, particularly those in the Italian tradition of Corelli and his pupils. The work is based on long-established traditions which had dominated Europe for two centuries. Instruction of this sort was fundamental to the education of the post-Corelli generation; Locatelli, Veracini and Geminiani himself. All the pieces in both works are based on English, Scottish and Irish folksongs, reflecting the composer's absorption of his adopted environment.
A Treatise of Good Taste in the Art of Music is a brief, interesting, second part of Geminiani's writing on the subject of "good taste," a technical phrase which during those days denoted the ability to use ornamentation in the refined and cultured manner; both works have tables of ornaments carefully described, and even have some part of the text in common. Artists at that time were expected to use their imaginations and the music that one undoubtedly heard was submerged beneath the bare surface of the score, as for examples in Corelli's Adagios, which are written very plainly but are reputed to have been performed by Corelli in a very ornate fashion. Geminiani's belief was that technique was inseparable from emotional expression; an expressive performance was required by means of dynamic swells, ornaments and vibrato. The composer meant expression in a general sense, not in the descriptive, as in the French bird-calls he so detested.
Geminiani was furiously impatient with the French predilection for dance music (versus the abstract Italian sonata) with its "wretched Rule"  of the down-bow. He opposed the idea of imitating bird calls, whistles, etc. [Not until 1750 did French aestheticians concede that music need not represent anything concretely.] Geminiani's notion that the singing voice is the most appropriate model for violin sound is still very much useful.
Geminiani's work looks to the future with respect to chromatic fingering, extensions and contrations of fingerings and the continuous vibrato. However, compared to Mozart's work (1756), Geminiani's looks primarily to the past. His way of holding the instrument is relatively old-fashioned (though the frontspiece shows a different hold than that mentioned in the text, and one more likely suitable to his fingerings). Unlike Mozart, Geminiani mentioned nothing about certain matters which relate to the technical equipment of later violinists (consecutive trills, trills in thirds and sixths), and he mentions nothing about harmonics and the technique of using higher positions to preserve the same tone color within a passage. A primarily difference with Mozart is Geminiani's use of what amounts to a continuous vibrato. Mozart recommends that vibrato be restricted to a closing note or any sustained tone: "Performers there are who tremble consistently on each note as if they had palsy." 
Organization of the Treatise
I. Subject area:
Position violin is held: general controversy over collarbone or chin hold, and where chin is held; middle, right or left?
Position bow is held; implied bow grip above the nut.
a. Chromatic fingering; one finger per note, rediscovered in 20th century
b. Extension and contraction; a speciality of Geminiani
c. Frequent shifts. Burney states that Geminiani claims invention of the half-shift but the composer's claim, if accurate, is doubtful. Geminiani favors larger shifts to reduce the number of shifts.
Vibrato; continuous, not just an ornament
Seven positions ("orders")
Multiple stops; unisons to octaves
Bowing; detests the "rule of the down-bow"
Tempo Rubato: notorious for, mentions nothing of.
Notes inégales; forbids these saying they "alter and spoil the piece."