Let them be candidly reviewed under a sense of the difficulty of combining in one system the various sentiments and interests of a continent divided into so many sovereign and independent communities, under a conviction of the absolute necessity of uniting all our councils and all our strength, to maintain and defend our common liberties ...

Let S ( fig. 5 ) be any optical system, rays proceeding from an axis point O under an angle u1 will unite in the axis point O ' 1 ; and those under an angle u2 in the axis point O ' 2.

Let x, y, z be a system of Cartesian coordinates in 3-dimensional Euclidean space, and let i, j, k be the corresponding basis of unit vectors.

Let ( X < sub > i </ sub >, f < sub > ij </ sub >) be an inverse system of objects and morphisms in a category C ( same definition as above ).

* Let the index set I of an inverse system ( X < sub > i </ sub >, f < sub > ij </ sub >) have a greatest element m. Then the natural projection π < sub > m </ sub >: X → X < sub > m </ sub > is an isomorphism.

Let ε ( n ) denote the energy of a particle in state n. As the particles do not interact, the total energy of the system is the sum of the single-particle energies.

Let the state of the composite system be

Let be the input to a general linear time-invariant system, and be the output, and the bilateral Laplace transform of and be

Let A be an observable of the system, and suppose the ensemble is in a mixed state such that each of the pure states occurs with probability p < sub > j </ sub >.

The study of suspension bridges formed for the last few years of my residence in Europe my favourite occupation ... Let but a single bridge of the kind be put up in Philadelphia, exhibiting all the beautiful forms of the system to full advantage, and it needs no prophecy to foretell the effect which the novel and useful features will produce upon the intelligent minds of the Americans.

Let N represent the common nine-point center and P be an arbitrary point in the plane of the orthocentric system.

Let A be an observable of a quantum mechanical system.

Let t represent time and let f ( t, •) be a function which specifies the dynamics of the system.

Let there be a system or piece of substance a of amount m < sub > a </ sub > and another piece of substance b of amount m < sub > b </ sub > which can be combined without interaction.

Let be a direct system of objects and morphisms in ( same definition as above ).

* Let I be any directed set with a greatest element m. The direct limit of any corresponding direct system is isomorphic to X < sub > m </ sub > and the canonical morphism φ < sub > m </ sub >: X < sub > m </ sub > → X is an isomorphism.

Let us now determine the physical state of the partial system A as completely as possible by measurements.

He believed that the only effective system of government necessitated prescribed relationships for each individual: " Let the ruler be a ruler and the subject a subject ".

Let us be more concrete and consider a magnetic system ( e. g.: the

Let denote the quantum state of the perturbed system at time t. It obeys the time-dependent Schrödinger equation,

Let us label with s ( s = 1, 2, 3, ...) the exact states ( microstates ) that the system can occupy, and denote the total energy of the system when it is in microstate s as E < sub > s </ sub >.

Let B be the base of the number system you are using, and n be the degree of the root to be extracted.

The Maoists announced a ‘ People's War ’ on February 13, 1996, under the slogan: " Let us march ahead on the path of struggle towards establishing the people's rule by wreaking the reactionary ruling system of state.

Let the open enemy to it be regarded as a Pandora with her box opened ; ;

Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.

`` Let him be now ''!!

Let us assume that it would be possible for an enemy to create an aerosol of the causative agent of epidemic typhus ( Rickettsia prowazwki ) over City A and that a large number of cases of typhus fever resulted therefrom.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.

Let Af be the null space of Af.

Let N be a linear operator on the vector space V.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.

Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.

Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.

Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.

Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.

Let this be denoted by Af.

Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.

Let not your heart be troubled, neither let it be afraid ''.

The same God who called this world into being when He said: `` Let there be light ''!!

For those who put their trust in Him He still says every day again: `` Let there be light ''!!

Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.

Let her out, let her out -- that would be the solution, wouldn't it??