████████████

███████ ████████████

An ██████'s ███████ ████████████ ${\displaystyle \overline{\mathbf{a}}}$ over a ██████ of ████ is ███ ██████ in ████████, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ███████ by the ████████ of the ██████, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. ██████████████, $${\displaystyle \overline{\mathbf{a}}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$The ███████ ████████████ is the ████████ ███ to ███████ ████████████, █████████ ████ █████████ of the ██████ in ████████ and the ██████ in ████. In a ██████ █████, the ███████ ████████████ is the ████ ████ ████████████ ███ is ████ to ████████ ███████ without █████████ to an █████████ ███, ███████ that it is the ████ ███████████ ████ of ████████████ ███████████.

The ███████ ████████████ is ████ █████ used to ███████████ the ██████████ of an ██████ by ████████ that the ████████ ███████ ████████ with ████. Over █████ ████ █████████, ██ can █████ ██████ that the ████████████ is ███████, ███████ ████████████ ${\displaystyle \mathbf{a}}$ of the ██████ will be ███████ █████ to the ███████ ████████████ ${\displaystyle \overline{\mathbf{a}}}$ (███ ██████████ ███████ ████████████ for ███████.)

By ██████'s ██████ ███ of ██████, the ███████ ████████████ is ███████ to the ███████ █████ ${\displaystyle \overline{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ on a ████████ of ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ by, $${\displaystyle \overline{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\overline{\mathbf{a}}.}$$This █████ that a ███████████ of the ███████ ████████████ is ████ a ███████████ of the ███████ █████ (████ █████ as ███████ ${\displaystyle \mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}=\overline{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$.)

█████████████ ████████████

█████████████ ████████████ is the █████ of the ███████ ████████████ over an █████████████ ████████ of ████. In the █████ of ████████, █████████████ ████████████ is the ██████████ of the ████████ ██████ with ███████ to ████: $${\displaystyle \mathbf{a}=\underset{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{<span\; word-length="3"\; class="word\; redacted">███</span>}\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\dot{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$ As ████████████ is ███████ as the ██████████ of ████████, █, with ███████ to ████ █ and ████████ is ███████ as the ██████████ of ████████, █, with ███████ to ████, ████████████ can be ███████ of as the ██████ ██████████ of █ with ███████ to █: $${\displaystyle \mathbf{a}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}=\ddot{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$(████ and █████████, if ██████ is in a ████████ ████, ██████ ██████████ can be ███████████ by ███████ in the █████████.)

By the ███████████ ███████ of ████████, it can be ████ that the ████████ of the ████████████ ████████ a(█) is the ████████ ████████ █(█); that is, the ████ under the █████ of an ████████████ ██. ████ (a ██. █) █████ ███████████ to the ██████ of ████████. $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}=\int \mathbf{a}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}.}$$

████████, the ████████ of the ████ ████████ █(█), the ██████████ of the ████████████ ████████, can be used to ████ the ██████ of ████████████ at a ███████ ████: $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{a}=\int \mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}.}$$

█████

████████████ has the ██████████ of ████████ (█/█) ███████ by ████, █.█. █ █^−█. The ██ ████ of ████████████ is the █████ per ██████ ███████ (█ █^−█); or "█████ per ██████ per ██████", as the ████████ in ██████ per ██████ ███████ by the ████████████ █████, █████ ██████.

█████ █████

An ██████ ██████ in a ████████ ██████—████ as a █████████ ████████ the █████—is ████████████ ███ to the ██████ of █████████ of ██████, ████████ ███ █████ ███ be ████████. In this ████ it is ████ to be ██████████ ███████████ (████████ ███████ the ██████) ████████████.

██████ ████████████, the ████████████ of a ████ ████████ to a ████-████ █████████, is ████████ by an ██████████ ██████ an █████████████. ██████'s ██████ ███ is ████████ ███████ in an ████████ █████████ █████. In a █████████ █████ ████████████ with ████████████ ${\displaystyle a}$ (in ███ █████████), ██████'s ████ can █████ be used by ███████████ an ████████ █████ (██████████ █████) ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}a}$ on a ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, opposite the ████████████ of the █████. This ████████ for the ████████ of the ████ to ████████ ███ ████████ ██████—to ████ "as is," at ████ or ██████ at ████████ ████████—█████ the █████ ███████████. ███ ███████ is that a ██████ in an ████████ █████ ███████ or ███████ as the ████████ ███████████ or ███████████. If ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is █████, ███████████ of the ██████████ █████ on the ████ can be used to █████ the ████████████; this is the █████████ of a ██████████ █████████████. In ███████ ██████████, ███████ and ████████ ████████████ ███ be ███████ █████████████████ (███ ███████ ██████████).

In █████████ █████████, for a ████ with ████████ ████, the (██████) ████████████ of the ████'s ██████ of ████ is ████████████ to the ███ █████ ██████ (█.█. ███ of ███ ██████) ██████ on it (██████'s ██████ ███): $${\displaystyle \mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{a}⟹\mathbf{a}=\frac{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},}$$ █████ █ is the ███ █████ ██████ on the ████, █ is the ████ of the ████, and a is the ██████-of-████ ████████████. As ██████ ████████ the █████ of █████, ████████████ ███████ ██████ ████████████ █████.

███████ ████████████

███████ or ████████ ████████████ is a ████ of ██████ in which the ████████ of an ██████ ███████ by an █████ ██████ in █████ █████ ████ ██████.

A ██████████ █████ ███████ of ███████ ████████████ is that of an ██████ in ████ ████ in a ███████ █████████████ █████. The ████████████ of a ███████ ████ in the ███████ of ███████████ to ██████ is █████████ ████ on the █████████████ █████ ████████ █ (████ ██████ ████████████ ███ to ███████). By ██████'s ██████ ███ the █████ ${\displaystyle {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ██████ on a ████ is █████ by: $${\displaystyle {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}.}$$

Because of the ██████ ████████ ██████████ of the ████ of ████████ ████████████, there are ██████ ████████ ████████ the ████████████, ███████ and ████-█████████ ██████████, and ████████████ to the ████ ███████: █████

• ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the ███████ ████,
• ${\displaystyle {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is the ███████ ████████████ from the ██████,
• ${\displaystyle \mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ is the ████████████ from the ██████ at ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$,
• ${\displaystyle {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is the ███████ ████████,
• ${\displaystyle \mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ is the ████████ at ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, and
• ${\displaystyle \mathbf{a}}$ is the ███████ ████ of ████████████.

In ██████████, the ██████ can be ████████ into ███ ██████████ █████, ███ of ████████ ████████ and the █████ █████████ to the above █████████. As ███████ ██████, the ███ ██████ is █████████ ██████, which █████████, █.█., the ██████████ of a ██████████ in ██████ near the ███████ of █████.

████████ ██████

In ███████ ████████ ██████, that is ██████ with ████████ █████ along a ████████ ████, a ████████ ███████████ an ████████████ █████████ from the ██████ of the █████████ of the ████████ ██████, █████ ███ █████████ ███████ ████████. The ██████████ of the ████████ of a █████ on a █████ with ███████ to ████, █.█. ███ ████████, █████ out to be ██████ ███████ ██████████ to the █████, ████████████ ██████████ to the ██████ in this █████. Since in ███████ ██████ the ████████ in the ██████████ █████████ ████ not ██████, the ████████████ ████ be in ██████ █████████, ████████ to the ██████ of the ██████. This ████████████ ██████████ ███████ the █████████ of the ████████ to be ███████ in the ████████████ █████, ███████ ████████ the ████████ ██████ along the ██████.

• For a █████ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, the █████████ of this █████████████ ██████ ████████████ (███████████ ████████████) is █████████ ████████████ to the ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ of the ██████, and █████████ as the ██████ of this █████: $${\displaystyle a_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$
• For a █████ ███████ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, the ███████████ ████████████ is ████████ ████████████ to ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. This is ███ to the ██████████ of ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ on the ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}.}$$

██████████ ███████████ ████████████ ██████ in █████ ██████████, █████ ${\displaystyle \mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a ██████ from the ██████ of the ██████ to the ████████ with █████████ █████ to this ████████, and considering the ███████████ of the ████████████ ███████ the ██████, ██████ $${\displaystyle {\mathbf{a}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=-\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{|\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}|}\cdot \frac{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}{|\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}|}.}$$As █████ in █████████, the █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ of a ████████ ███ be █████████ as an ███████ █████ with ███████ to a █████ at the ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ as $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$████ ${\displaystyle {\mathbf{a}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}.}$

This ████████████ and the ████ of the ████████ █████████ the █████████ ███████████ █████, ████████ toward the ██████ of the ██████, as the ███ █████ ██████ on this ████████ to ████ it in this ███████ ████████ ██████. The ██-██████ '███████████ █████', █████████ to ███ ███████ on the ████, is a ██-██████ ██████ █████ ███████████ in the █████ of █████████ of the ████ in ████████ ██████, ███ to the ████'s ██████ ████████, a ██████ ███████ to the ██████ of ██████.

In a ██████████ ████████ ██████, █.█., the █████ along the ██████ ████ is ████████, the ████████████ has a ███-████ █████████ ██████████ to the █████, and is not ████████ to the █████████ ██████, which ███████ to the ██████ of the ██████████ ██████, that ██████████ the ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ for the ███████████ ████████████. The ██████████ █████████ is █████ by the ███████ ████████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, █.█., the ████ of ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\dot{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ of the ███████ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ the ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. That is, $${\displaystyle a_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}.}$$

The ████ of the ██████████ █████████ of the ████████████ is ██████████ by the ████ of the ███████ ████████████ (${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$), and the ███████ is ██████ ████████ at █████ ██████ to the ██████ ██████.

███████ ██████████

The ███████ ██████ of ██████████ █████████ the █████████ of ███████ ██████████ ████████ to █████ ███████ at ██████ ███████████ that of █████ in ██████. █████████ █████████ is ███████ ████████ to be an █████████████ to ███████, █████ to █████ ████████ at █████ ██████. As the ████████ ██████ ████████ toward the █████ of █████, ████████████ ██ ██████ ███████ █████████ █████████.

As ██████ ████████ that of █████, the ████████████ ████████ by a █████ █████ █████████, ████████ ███████████████ █████ as █████ █████ is ██████████; an ██████ with ████ can ████████ this █████ ██████████████, but █████ █████ it.

███████ ██████████

██████ the █████ of ██████ of an ██████ is █████, it is ██████████ to ███████████ ███████ an ████████ █████ is ███ to ███████ or to ████████████—███████ and ████████ ████████████ have █████████ ███████. ██████ ████████ ██████ this the ███████████ █████████, and ████ that ████ █████████ ███ ████ ██ █████ at ███—█████████ the █████ of ███████—are █████████ in ██████████ that they are not ████████████.