10 In 1629 he asks Mersenne to take care of himself " till I find out if there is any means of getting a medical theory based on infallible demonstrations, which is what I am now inquiring."
Fermat, Roberval and Desargues took exception in their various ways to the methods employed in the geometry, and to the demonstrations of the laws of refraction given in the Dioptrics and Meteors.
He was educated there and at Madrid University, where his Radicalism soon got him into trouble, and he narrowly escaped being expelled for his share in student riots and other demonstrations against the governments of Queen Isabella.
In October 1900 Dr Manuel Campos Salles, president of Brazil, paid a visit to Buenos Aires, and was received with great demonstrations of friendliness.
Many of the propositions contained in his dissertation are general; but the demonstrations are not supplied for the case of seven squares.
In 1896 he came to England and gave demonstrations to the British postal telegraph department and other officials.
Marconi's successes and the demonstrations he had given of the thoroughly practical character of this system of electric wave telegraphy stimulated other inventors to enter the same field of labour, whilst theorists began to study carefully the nature of the physical operations involved.
Every fresh reform edict was greeted with demonstrations of enthusiasm, but the ominous cry Viva Pio Nono solo!
These occurrences provoked anti-French demonstrations in many parts of Italy, and revived the chronic Italian rancour against France.
This was seized upon as a pretext for violent anti-clerical demonstrations all over Italy and for brutal and unprovoked attacks on unoffending priests; at Spezia a church was set on fire and another dismantled, at Marino Cardinal Merry del Val was attacked by a gang of hooligans, and at Rome the violence of the teppisti reached such a pitch as to provoke reaction on the part of all respectable people, and some of the aggressors were very roughly handled.
Further acts of violence were committed by the Germans in 1903, which led to antiAustrian demonstrations in Italy.
Anti-Italian demonstrations occurred periodically also at Vienna, while in Dalmatia and Croatia Italian fishermen and workmen (Italian citizens, not natives) were subject to attacks by gangs of half-savage Croats, which led to frequent diplomatic incidents.
He added, however, that if France waged a successful war, he would remain in the East, and do more damage to England there than by mere demonstrations in the English Channel.
He was still in office when the final rising of the Cubans began in February 1895, and he had to resign in March because he could not find superior officers in the army willing to help him to put down the turbulent and disgraceful demonstrations of the subalterns of Madrid garrison against newspapers which had given offence to the military.
Three days later the latter town surrendered, amid demonstrations of joy on the part of the inhabitants.
Rouelle, while in England Humphry Davy expounded the same idea in the experimental demonstrations which gave his lectures their brilliant charm.
The second work of Leonardo, his Practica geometriae (1220) requires readers already acquainted with Euclid's planimetry, who are able to follow rigorous demonstrations and feel the necessity for them.
His lucid style and the perfection of his experimental demonstrations drew to his lectures a crowd of enthusiastic scholars, on whom he impressed the importance of applied science by conducting them round the factories and workshops of the city; and he further found time to hold weekly "colloquies" on physical questions at his house with a small circle of young students.
The second includes definitions of technical terms in common use, together with so much of the elementary theory as is necessary for understanding the experimental work described in subsequent portions of the article; a number of formulae and results are given for purposes of reference, but the mathematical reasoning by which they are obtained is not generally detailed, authorities being cited whenever the demonstrations are not likely to be found in ordinary textbooks.
Anselm had made an elaborate employment of reason in the interest of faith, but the spirit of pious subordination which had marked the demonstrations of Anselm seemed wanting in the argumentations of this bolder and more restless spirit; and the church, or at least an influential section of it, took alarm at the encroachments of Rationalism.
But beside these public demonstrations he sought and found access in private to many of the leading statesmen, in the various countries he visited, with a view to indoctrinate them with the same principles.
Biot, who assisted in the correction of its proof sheets, remarked that it would have extended, had the demonstrations been fully developed, to eight or ten instead of five volumes; and he saw at times the author himself obliged to devote an hour's labour to recovering the dropped links in the chain of reasoning covered by the recurring formula.
Pascal and P. de Fermat had initiated he brought very nearly to perfection; but the demonstrations are so involved, and the omissions in the chain of reasoning so frequent, that the Theorie analytique (1812) is to the best mathematicians a work requiring most arduous study.
The first signs of reviving solidarity came in 1903, when Khucn's rigorous suppression of rioting in Zagreb and several country districts of Croatia, led to demonstrations of protest throughout Dalmatia and Istria.
This gave rise to sympathetic demonstrations in many Dalmatian and Bosnian towns, and to a series of interpellations and speeches by the Yugoslav and Czech deputies in the Parliament of Vienna.
The Austrian Government committed the grave blunder of answering these demonstrations by press confiscations and by the dissolution of the town councils of Spalato and Sebenico.
Under the influence of the touchstone of strict inquiry set on foot by the Royal Society, the marvels of witchcraft, sympathetic powders and other relics of medieval superstition disappeared like a mist before the sun, whilst accurate observations and demonstrations of a host of new wonders accumulated, amongst which were numerous contributions to the anatomy of animals, and none perhaps more noteworthy than the observations, made by the aid of microscopes constructed by himself, of Leeuwenhoek, the Dutch naturalist (1683), some of whose instruments were presented by him to the society.
The demonstrations of the unity and the attributes of God, with which the treatise De Melisso, Xenophane et Gorgia (now no longer ascribed to Aristotle or Theophrastus) accredits Xenophanes, are plainly framed on the model of Eleatic proofs of the unity and the attributes of the Ent, and must therefore be set aside.
Anatomy was as little regarded as it was in the later ancient schools, the empiric and methodic, but demonstrations of the parts of the body were given on swine.
In the 17th and 18th centuries it was a favourite duellingground, and in the present day it is not infrequently the scene of political and other popular demonstrations (as is also Trafalgar Square), while the neighbourhood of Marble Arch is the constant resort of orators on social and religious topics.
Made his descent into Italy in 1494, and came to Sarzana on his way to Tuscany, he was welcomed by the Pisans with the greatest demonstrations of joy.
This, which was carried out by the united armies and by reinforcements from France, while Turenne's cavalry screened them by bold demonstrations on the Tauber, led to nothing less than the conquest of the Rhine Valley from Basel to Coblenz, a task which was achieved so rapidly that the Army of France and its victorious young leader were free to return to France in two months from the time of their appearance in Turenne's quarters at Breisach.
It may be said to have begun with the visit of the Association of British Chambers of Commerce to Paris in 1900, at a time when France was still smarting from the humiliation of the Fashoda affair, and the Boer War was exciting hostile demonstrations against Great Britain throughout the continent of Europe.
18 amid great demonstrations of popular enthusiasm.
In various systems of triangular co-ordinates the equations to circles specially related to the triangle of reference assume comparatively simple forms; consequently they provide elegant algebraical demonstrations of properties concerning a triangle and the circles intimately associated with its geometry.
The theory of centres of similitude and coaxal circles affords elegant demonstrations of the famous problem: To describe a circle to touch three given circles.
John Casey, professor of mathematics at the Catholic university of Dublin, has given elementary demonstrations founded on the theory of similitude and coaxal circles which are reproduced in his Sequel to Euclid; an analytical solution by Gergonne is given in Salmon's Conic Sections.
Negotiations for peace accompanied these demonstrations, which showed that Saladin was master of the situation.
While Gage is to be credited with advising his government that not less than 20,000 men would be necessary for the work in hand, he proceeded at once to suppress demonstrations around Boston.
Demonstrations against Canada were soon discontinued, Arnold drawing off the remnant of his army in May 1776.
Two naval demonstrations were made by France during the reign of Louis XIV., one by Abraham Duquesne in 1682, and the other by Marshal Jean d'Estrees in 1688, but these repressive measures were too intermittent to produce a durable effect.
Nevertheless the naval demonstrations made by Lord Exmouth in 1816, and by a combined English and French squadron in 1819, remained equally fruitless.