Then, by applying and maintaining sufficient pressure to prevent it from inhaling, the prey eventually succumbs due to asphyxiation.

Then, from the late 1960s onward, Stanford's goal became applying research and findings toward humanistic ends.

Then, applying transformation T to all the points on this sphere yields

Then, by applying and maintaining sufficient pressure to prevent it from inhaling, the prey eventually succumbs due to asphyxiation.

Then applying the Gram – Schmidt process to the three vectors ( A < sub > 2 </ sub >− A < sub > 1 </ sub >, A < sub > 3 </ sub >− A < sub > 1 </ sub >, V ) produces an orthonormal basis of space, the third vector of which will be normal to plane A.

Then ( the same result can be obtained by applying the current conservation principle ).

Then in early 1963, California guitar manufacturer Mosrite re-branded their uniquely styled, futuristic-looking Mark 1 electric guitar model for the Ventures by applying decals that stated " The Ventures Model " on the headstock.

Then one computes the next iteration of P by applying F < sub > j </ sub > on ( P. x, P. y ).

To see why this is true, suppose x ∈ X is the state at time s. Then by the definition of F, F < sub > t, s </ sub >( x ) is the state of the system at time t and consequently applying the definition once more, F < sub > u, t </ sub >( F < sub > t, s </ sub >( x )) is the state at time u.

Then, by applying the Phragmén – Lindelöf principle ( a kind of maximum principle for infinite domains ) one gets that

Then the basic EPS number is diluted one by one by applying each one, skipping any instruments that have an antidilutive effect.

Then, applying the differential pointwise to X yields the pushforward φ < sub >*</ sub > X, which is a vector field along φ, i. e., a section of φ < sup >*</ sup > TN over M.

Then applying different sampling methods will lead to different sets of individuals being observed for the same area of interest, and the species richness of each set may be different.

Then applying this to yields the probabilities:

Then applying ν < sub > 2 </ sub > to the equation yields

Then, for the class of scores which are discrete convolutions, configurations related to each other by translation of one protein by an exact lattice vector can all be scored almost simultaneously by applying the convolution theorem.

Let t and s ( t > s ) be the sides of the two inscribed squares in a right triangle with hypotenuse c. Then s < sup > 2 </ sup > equals half the harmonic mean of c < sup > 2 </ sup > and t < sup > 2 </ sup >.

Then we can apply Gauss – Bonnet to the surface T formed by the inside of that triangle and the piecewise boundary given by the triangle itself.

Denote the orthocenter of triangle ABC as H, denote the sidelengths as a, b, and c, and denote the circumradius of the triangle as R. Then

Then f + g is in L < sup > p </ sup >( S ), and we have the triangle inequality

Then the point O, by the second fact above, is equidistant from A, B, and C. And so O is center of the circumscribing circle, and the hypotenuse of the triangle AC is a diameter of the circle.

Then the sum of the signed distances from the circumcenter D to the sides of triangle ABC is

Then it can be scaled down to give a primitive ( i. e., with no common factors ) Pythagorean triangle with the same property.

Then there exists a triangle from T, whose vertices are colored with the three different colors.

Then this player performs the last two moves of Opening A: taking the string which runs on the inside of the left arm onto the first finger of their right hand, then, reaching through the triangle created, the loop on the inside of the right hand is taken onto the first finger of the left hand ).

Then G requires at least three colors in any coloring, but has no triangle, so it is not perfect.

Then Richard and Julia get married, prompting a bitter love triangle between the three.

Call the point closer to the perpendicular B, and the farther point C. Draw the line m connecting P to C. Then the distance from B to m is smaller than the distance from P to l, contradicting the original definition of P and l. One way to see this is to notice that the right triangle with hypotenuse BC is similar to and contained in the right triangle with hypotenuse PC.

Then, the isometry group of the set of three vertices of this triangle is the trivial group.

Then any point on any of the edges of the triangle is within a distance of δ from one of the other two sides.

Then the three lines AD, BE, and CF meet in a single triangle center known as the first Ajima – Malfatti point after the contributions of Ajima and Malfatti to the circle problem.

Let B < sub > 1 </ sub > be the base of altitude in the triangle ABD through B and let C < sub > 1 </ sub > be the base of altitude in the triangle ACD through C. Then,

Then by the triangle inequality the polygon perimeter > AB + AX + XB = AB + AC + CX + XB ≥ AB + AC + BC.

Then the triangle ABP is a 60 ° rotation of the triangle AFQ about A so these two triangles are congruent and it follows that d ( P )

Then the triangle formed by joining the vertex of the square distant from both triangles and the vertices of the triangles distant from the square is equilateral.

Then Jensen's inequality can be applied to get

Then Bernstein's inequality states that for M non-zero,

Then f is called weak if there exists a constant C such that the distribution of f satisfies the following inequality for all t > 0:

Then the following interpolation inequality holds for all r between p and q and all f ∈ L < sup > r </ sup >:

Then the inequality above needs to be replaced with

Suppose that r < R. Then, we have the following inequality:

Then the Ky Fan inequality can be written as

Then the inequality