Thus while among his own colleagues he seemed merely a hypocritical and arrogant priest, in his relations with his brother humanists, such as Cosimo de ' Medici, he appeared as the student of classical antiquities and especially of Greek theological authors ".

Thus in the classical tradition of later Western art and literature, the mythology of the two figures becomes virtually indistinguishable.

Thus if we reason from the statement " Pegasus flies " to the statement " Pegasus exists ", we are not asserting that Pegasus is made up of atoms, but rather that Pegasus exists in a particular worldview, the worldview of classical myth.

Thus, he challenged the arguments of clerical intellectuals who wanted to limit access to classical sources to prevent any moral harm to Christian readers.

Thus the connectives " and " and " or " of intuitionistic logic do not satisfy de Morgan's laws as they do in classical logic.

Thus, measuring a quantum state described by complex coefficients ( a, b ,..., h ) gives the classical probability distribution and we say that the quantum state " collapses " to a classical state as a result of making the measurement.

Thus the republicanism developed during the Renaissance is known as ' classical republicanism ' because it relied on classical models.

Thus it was Pythagoras who gave the word " theory " the specific meaning which leads to the classical and modern concept of a distinction between theory as uninvolved, neutral thinking, and practice.

Thus, for example, formal notions of causality do not appear in standard texts in classical mechanics.

Thus the Dirac Hamiltonian is fundamentally distinguished from its classical counterpart, and we must take great care to correctly identify what is an observable in this theory.

Thus, quantum physics casts reasonable doubt on the traditional determinism of classical, Newtonian physics in so far as reality does not seem to be absolutely determined.

Thus locally compact spaces are as useful in p-adic analysis as in classical analysis.

Thus, the ontology of pilot wave theory contains as the trajectory we know from classical mechanics, as the wave function of quantum theory.

Thus West Greek is the most accurate name for the classical dialects.

Thus knowledge of Tages comes mainly from what is said about him by the classical authors, which is a legendary and quasi-mythical view ; Lydus suggests that Tages is only a parable.

Thus, both pre-20th century disciplines were labelled " classical " and modern movements in art which saw themselves as aligned with light, space, sparseness of texture, and formal coherence.

Thus the enforced introspection and reflection of camp life bore fruit in one of 20th-century European classical music's acknowledged masterpieces.

This happens because a magnetic field is produced by an electric current, J, which reverses sign under T. Thus, the motion of classical charged particles in electromagnetic fields is also time reversal invariant.

Thus, in classical ( Newtonian ) mechanics a cause may be represented by a force acting on a body, and an effect by the acceleration which follows as quantitatively explained by Newton's second law.

Thus, in classical physics, it was assumed that all events are caused by earlier ones according to the known laws of nature, culminating in Pierre-Simon Laplace's claim that if the current state of the world were known with precision, it could be computed for any time in the future or the past ( see Laplace's demon ).

Thus, any cooperation of modern ethical reformers and those seeking guidance from classical Islam would be doomed from the start.

Thus, by expressing quantum mechanics in phase space ( the same ambit as for classical mechanics ), the Weyl map facilitates recognition of quantum mechanics as a deformation ( generalization ) of classical mechanics, with deformation parameter ħ / S, where S is the action of the relevant process.

Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

Thus three major themes in 19th century mathematics were combined by Lie in creating his new theory: the idea of symmetry, as exemplified by Galois through the algebraic notion of a group ; geometric theory and the explicit solutions of differential equations of mechanics, worked out by Poisson and Jacobi ; and the new understanding of geometry that emerged in the works of Plücker, Möbius, Grassmann and others, and culminated in Riemann's revolutionary vision of the subject.

Thus, id's decision to protect Quake IIIs code inadvertently caused machinima creators to use more general solutions and thus widen their audience.

Thus, nowadays, we speak of Diophantine equations when we speak of polynomial equations to which rational or integer solutions must be found.

Thus, concentrated solutions of polymers are far rarer than those of small molecules.

Thus a developer gravitates toward solutions that reside at the intersection of the capabilities of UML and the implementation language.

Thus, the differential equation solutions can be classified into homotopy classes.

Thus, the difference of any two solutions to the equation Ax = b lies in the null space of A.

Thus, treatment of concentrated solutions of ammonium salts with strong base gives ammonia.

Thus in most " natural " settings, if a complex number provides a solution to a problem, so does its conjugate, such as is the case for complex solutions of the quadratic formula with real coefficients.

Thus, world conscience is a concept that overlaps with the Gaia hypothesis in advocating a balance of moral, legal, scientific and economic solutions to modern transnational problems such as global poverty and climate change, through strategies such as environmental ethics, climate ethics, natural conservation, ecology, cosmopolitanism, sustainability and sustainable development, biosequestration and legal protection of the biosphere and biodiversity.

Thus, many pyrophoric solids are sold as solutions, or dispersions in mineral oil or lighter hydrocarbon solvents.

Thus, the salt bridge or porous membrane serves both to keep the solutions apart and to allow the flow of anions in the direction opposite to the flow of electrons in the wire connecting the electrodes.

Thus the closed-loop poles ( roots of the characteristic equation ) of the transfer function are the solutions to the equation 1 + KC ( s ) P ( s )

Thus, general solutions can be specified by convolving the ( periodic ) boundary condition at t

Thus though Dirichlet flows ( potential solutions ) and other steady flows are mathematically possible, there is no reason to suppose that any steady flow is stable.

Thus, iodine tincture solutions are characterized by the presence of alcohol, and about the same amount ( weight % content ) of elemental iodine as iodide.

) Thus, the solutions above are all singular solutions, in the sense that solution fails to be unique in a neighbourhood of one or more points.

Thus, a program that is able to reduce this number of candidate solutions through the process of hypothesis formation is essential.

Thus, when pCr = 2, the chromium concentration is 10 < sup >- 2 </ sup > mol dm < sup >- 3 </ sup ></ ref > The chromate ion is the predominant species in alkaline solutions, but dichromate can become the predominant ion in acidic solutions.

Thus, in the example of the Travelling salesman problem, it is not necessary that an ant actually travels the shortest route: the shortest route can be built from the strongest segments of the best solutions.