In October, Leopold, much against his inclinations, asked him to form a ministry.
Her hatred of Germans showed itself likewise in her persistent struggle with Frederick the Great, which cost Russia 300,000 men and 30 millions of roubles - an enormous sum for those days - but in the choice of a successor she could not follow her natural inclinations, for among the few descendants of Michael Romanov there was no one, even in the female line, who could be called a genuine Russian.
Beton was arrested and the regency fell to the heir presumptive James, earl of Arran, whose inclinations were towards England and the Protestant party, and who hoped to secure the hand of the infant princess for his own son.
Marguerite herself, however, was protected by her brother, and her personal inclinations seem to have been rather towards a mystical pietism than towards dogmatic Protestant sentiments.
The light is supposed to descend vertically upon the country represented, and in a true scale of shade the intensity increases with the inclination from o° to 90°; but as such a scale does not sufficiently differentiate the lesser inclinations which are the most important, the author adopted a conventional scale, representing a slope of 45° or more, supposed to be inaccessible, as absolutely black, the level surfaces, which reflect all the light which falls upon them, as perfectly white, and the intervening slopes by a proportion between black and white, as in fig.
The long-sought cause of the "great inequality" of Jupiter and Saturn was found in the near approach to commensurability of their mean motions; it was demonstrated in two elegant theorems, independently of any except the most general considerations as to mass, that the mutual action of the planets could never largely affect the eccentricities and inclinations of their orbits; and the singular peculiarities detected by him in the Jovian system were expressed in the so-called "laws of Laplace."
He was several times a successful competitor for the prizes given by the Academy of Sciences of Paris; the subjects of his essays being: - the laws of motion (Discours sur les lois de la communication du mouvement, 1727), the elliptical orbits of the planets, and the inclinations of the planetary orbits (Essai d'une nouvelle physique celeste, 1735).
He displayed such radical and reforming inclinations that he laid the foundations of his popularity among the lower and middle classes, which lasted more than a quarter of a century, during which time the Progressists, Democrats and advanced Liberals ever looked to him as a leader and adviser.
The other treatises of Apollonius mentioned by Pappus are - 1st, Aayov alroropii, Cutting off a Ratio; 2nd, Xcopiov a7rorop, Cutting off an Area; 3rd, Ocwpui j Av i Tog, Determinate Section; 4th, 'Eiraci)aL, Tangencies; 5th, 11-€1,o-as, Inclinations; 6th, Tinrot bri ret50t, Plane Loci.
Mr Mackenzie and his chief followers, whose inclinations were towards free trade, pinned their political fortunes to the maintenance of a tariff for revenue only.
In the same preface is included (a) the famous problem known by Pappus's name, often enunciated thus: Having given a number of straight lines, to find the geometric locus of a point such that the lengths of the perpendiculars upon, or (more generally) the lines drawn from it obliquely at given inclinations to, the given lines satisfy the condition that the product of certain of them may bear a constant ratio to the product of the remaining ones; (Pappus does not express it in this form but by means of composition of ratios, saying that if the ratio is given which is compounded of the ratios of pairs - one of one set and one of another - of the lines so drawn, and of the ratio of the odd one, if any, to a given straight line, the point will lie on a curve given in position), (b) the theorems which were rediscovered by and named after Paul Guldin, but appear to have been discovered by Pappus himself.
Pursuing the investigations of Laplace, he demonstrated with greater rigour the stability of the solar system, and calculated the limits within which the eccentricities and inclinations of the planetary orbits vary.
Dr Abbott's liberal inclinations in theology were prominent both in his educational views and in his books.
But, regarded broadly, the Highland mountains are monuments of erosion, the relic of an old tableland, the upper surface and former inclinations of which are shown approximately by the summits of the existing masses and the direction of the chief water-flows.
The strict military discipline of the school lay heavily on Schiller, and intensified the spirit of rebellion, which, nurtured on Rousseau and the writers of the Sturm and Drang, burst out in the young poet's first tragedy; but such a school-life had for a poet of Schiller's temperament advantages which he might not have known had he followed his own inclinations; and it afforded him glimpses of court life invaluable for his later work as a dramatist.
As regards original sin they taught that the inclinations to evil inherited from Adam are not themselves blameworthy, and only consent to them involves real guilt.
Let a, $ be the inclinations of the planes, and 0 the angle which the bar makes with thE vertical.
If 0, 4, be the inclinations of the two strings to the vertical, we have, approximately, 2T=Ma1O2+~n(aO+b~)1, ~ 1
A condition equivalent to the above, and necessarily connected with it, is, that at each pair of points of contact the inclinations of the curves to their radii-vectores shall be equal and contrary; or, denoting by r1, rf the radii-vectores at any given pair of points of contact, and s the length of the equal arcs measured from a certain fixed pair of points of contact dri/ds= drm/ds; (18)
Of his amours and mistresses the same shrewd observer of human character, who was also well acquainted with the king, declares " that his inclinations to love were the effects of health and a good constitution with as little mixture of the seraphic part as ever man had..
His idea would have been a parliamentary republic on the American lines, with some traits of the Swiss constitution to keep in touch with the regionalist and provincialist inclinations of many parts of the peninsula.
It may well be believed that Canning followed his natural inclinations, and it can be asserted without the possibility of contradiction, if also without possibility of proof, that he had influenced the mind of Castlereagh.
He could trade upon Edwards precocious hatred of Marys religion, he could rely upon French fears of her Spanish inclinations, and the success which bad attended his schemes in England deluded him into a belief that he could supplant the Tudor with a Dudley dynasty.
This predisposed him to regard physical miracles as the solid criterion for distinguishing reasonable religious conviction from " inclinations, fancies and strong assurances."
So far the system would seem to suit the inclinations of the most thorough-going voluptuary.
Thus, in his view, not merely natural inclinations towards pleasures, or the desires for selfish happiness, require to be morally resisted; but even the prompting of the individual's conscience, the impulse to do what seems to him right, if it comes into conflict with the common sense of his community.
The result of these conditions is that all the quantities required admit of development in series proceeding according to the powers of the eccentricities and inclinations of the orbits, and the ratio of the masses of the several planets to the mass of the sun.
The proper share of each in bringing about this memorable result is not easy to apportion, since they freely imparted and profited by one another's advances and improvements; it need only be said that the fundamental proposition of the invariability of the planetary major axes laid down with restrictions by Laplace in 1773, was finally established by Lagrange in 1776; while Laplace in 1784 proved the subsistence of such a relation between the eccentricities of the planetary orbits on the one hand, and their inclinations on the other, that an increase of either element could, in any single case, proceed only to a very small extent.
Whether the entrance pupil be before or behind the object, in general its position is such that it lies not too near the object, so that the principal rays will have in the object space only trifling inclinations towards one another or are strictly parallel.
Her life had no external aims--only a need to exercise her various functions and inclinations was apparent.