# Vieta sentence example

vieta

- He was selected by the executors of Franciscus Vieta to revise and edit his manuscript works, a task which he discharged with great ability.
- The development of symbolic algebra by the use of general symbols to denote numbers is due to Franciscus Vieta (Francois Viete, 1540-1603).
- This appears to have been due in the first instance to Albert Girard (1595-1632), who extended Vieta's results in various branches of mathematics.
- Franciscus Vieta (Francois Viete) named it Specious Arithmetic, on account of the species of the quantities involved, which he represented symbolically by the various letters of the alphabet.
- About the beginning of the 17th century various mathematical works by Franciscus Vieta were published, which were afterwards collected by Franz van Schooten and republished in 1646 at Leiden.Advertisement
- This writer, after having published an edition of Stevin's works in 1625, published in 1629 at Amsterdam a small tract on algebra which shows a considerable advance on the work of Vieta.
- Girard is inconsistent in his notation, sometimes following Vieta, sometimes Stevin; he introduced the new symbols ff for greater than and ï¿½ for less than; he follows Vieta in using the plus (+) for addition, he denotes subtraction by Recorde's symbol for equality (=), and he had no sign for equality but wrote the word out.
- He follows Vieta in assigning the vowels to the unknown quantities and the consonants to the knowns, but instead of using capitals, as with Vieta, he employed the small letters; equality he denoted by Recorde's symbol, and he introduced the signs > and < for greater than and less than.
- His notation is based on that of Vieta, but he introduced the sign X for multiplication, - for continued proportion, :: for proportion, ' and denoted ratio by one dot.
- Ritter,' Vieta was brought up as a Catholic, and died in the same creed; but there can be no doubt that he belonged to the Huguenots for several years.Advertisement
- On the completion of his studies in Iaw at Poitiers Vieta began his career as an advocate in his native town.
- After the accession of Henry of Navarre to the throne of France, Vieta filled in 1589 the position of councillor of the parlement at Tours.
- We know of one important service rendered by Vieta as a royal officer.
- Vieta's writings thus became very quickly known; but, when Franciscus van Schooten issued a general edition of his works in 1646, he failed to make a complete collection, although probably nothing of very great value has perished.
- The form of Vieta's writings is their weak side.Advertisement
- Vieta is wont to be called the father of modern algebra.
- On the other hand, Vieta was well skilled in most modern artifices, aiming at a simplification of equations by the substitution of new quantities having a certain connexion with the primitive unknown quantities.
- While these writings were generally intelligible, and therefore of the greatest didactic importance, the principle of homogeneity, first enunciated by Vieta, was so far in advance of his times that most readers seem to have passed it over without adverting to its value.
- During the three centuries that have elapsed between Vieta's day and our own several changes of opinion have taken place on this subject, till the principle has at last proved so far victorious that modern mathematicians like to make homogeneous such equations as are not so from the beginning, in order to get values of a symmetrical shape.
- Vieta himself, of course, did not see so far as that; nevertheless the merit cannot be denied him of having indirectly suggested the thought.Advertisement
- This formula must have been known to Vieta in 1593.
- A second took place when Vieta pointed to Apollonius's problem of taction as not yet being mastered, and Adriaan van Roomen gave a solution by the hyperbola.
- Vieta, however, did not accept it, as there existed a solution by means of the rule and the compass only, which he published himself in his Apollonius Gallus (1600).
- In this paper Vieta made use of the centre of similitude of two circles.
- Considered as a history of algebra, this work is strongly objected to by Jean Etienne Montucla on the ground of its unfairness as against the early Italian algebraists and also Franciscus Vieta and Rene Descartes and in favour of Harriot; but Augustus De Morgan, while admitting this, attributes to it considerable merit.Advertisement
- This problem, also termed the " Apollonian problem," was demonstrated with the aid of conic sections by Apollonius in his book on Contacts or Tangencies; geometrical solutions involving the conic sections were also given by Adrianus Romanus, Vieta, Newton and others.
- The next to advance the calculation was Francisco Vieta.
- The theorem for angle-bisection which Vieta used was not that of Archimedes, but that which would now appear in the form I - cos 0 = 2 sin e 20.
- With Vieta, by reason of the advance in arithmetic, the style of treatment becomes more strictly trigonometrical; indeed, the Universales Inspectiones, in which the calculation occurs, would now be called plane and spherical trigonometry, and the accompanying Canon mathematicus a table of sines, tangents and secants.'
- Further, in comparing the labours of Archimedes and Vieta, the effect of increased power of symbolical expression is very noticeable.Advertisement
- Accordingly, we find in Vieta a formula for the ratio of diameter to circumference, viz.
- Van Ceulen's process was essentially identical with that of Vieta.
- This problem, which is sometimes known as the Apollonian Problem, was proposed by Vieta in the 16th century to Adrianus Romanus, who gave a solution by means of a hyperbola.
- Vieta thereupon proposed a simpler construction, and restored the whole treatise of Apollonius in a small work, which he entitled Apollonius Gallus (Paris, 1600).
- For the time, however, he tranquilly pursued his studies, writing those notes on Vieta which establish his proficiency in mathematics, and a metaphysical treatise now lost, which, if Foscarini's account of it may be relied upon, anticipated the sensationalism of Locke.Advertisement
- In a small commonplace book, bearing on the seventh page the date of January 1663/1664, there are several articles on angular sections, and the squaring of curves and " crooked lines that may be squared," several calculations about musical notes, geometrical propositions from Francis Vieta and Frans van Schooten, annotations out of Wallis's Arithmetic of Infinities, together with observations on refraction, on the grinding of " spherical optic glasses," on the errors of lenses and the method of rectifying them, and on the extraction of all kinds of roots, particularly those " in affected powers."
- The arithmetical half of mathematics, which had been gradually growing into algebra, and had decidedly established itself as such in the Ad logisticen speciosam notae priores of Francois Vieta (1540-1603), supplied to some extent the means of generalizing geometry.
- Vieta, who does not avail himself of the discoveries of his predecessors - the negative roots of Cardan, the revised notation of Stifel and Stevin, &c. - introduced or popularized many new terms and symbols, some of which are still in use.
- Girard is inconsistent in his notation, sometimes following Vieta, sometimes Stevin; he introduced the new symbols ff for greater than and Ã¯¿½ for less than; he follows Vieta in using the plus (+) for addition, he denotes subtraction by Recorde's symbol for equality (=), and he had no sign for equality but wrote the word out.
- In that year Adriaan van Roomen gave out as a problem to all mathematicians an equation of the 45 th degree, which, being recognized by Vieta as depending on the equation between sin 4 and sin 43/45, was resolved by him at once, all the twenty-three positive roots of which the said equation was capable being given at the same time (see Trigonometry).Advertisement