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From the presentation on Nirvana found in the Analysis of the Perfection of Wisdom, by Kedrup Tenpa Dargye (1493-1568):

Here secondly is the section in which we present our own position. The definition of nirvana is “A cessation which comes from the individual analysis, and which consists of having eliminated the mental-affliction obstacles in their entirety.”

In name only, nirvana can be divided into the following four types: natural nirvana, nirvana with something left over, nirvana with nothing left over, and nirvana which does not stay.

The following all refer to the same thing: natural nirvana, the natural Mother, the natural perfection of wisdom, the natural Dharma Body, and ultimate truth.

The definition of nirvana with something left over is: “A cessation which comes from the individual analysis, and which consists of having eliminated the mental-affliction obstacles in their entirety, but where one still has the suffering heaps that are a result of his past actions and bad thoughts.” A classical example of this would be the nirvana found in the mental stream of a listener who is a foe destroyer, and who has not yet shucked off the heaps he took on.

The definition of nirvana with nothing left over is: “A cessation which comes from the individual analysis, and which consists of having eliminated the mental-affliction obstacles in their entirety, and where one is free of the suffering heaps that are a result of his past actions and bad thoughts.” A classical example of this would be the nirvana found in the mental stream of a listener who is a foe destroyer, and who has shucked off the heaps he took on.

The definition of nirvana which does not stay is: “A cessation which comes from the individual analysis, and which consists of having eliminated both kinds of obstacles in their entirety.” A classical example of this would be the truth of cessation in the mental stream of a realized being who is a Buddha.

The nirvana we are describing here is not something that one can achieve by using any method at all. Rather, you must achieve it with the training of wisdom, which realizes that nothing has any self nature; this wisdom must be under the influence of the first two trainings, and with it you must habituate yourself to what you were already able to realize.

This fact is supported by the King of Concentration, which states:

Suppose you are able to analyze
One by one those things that have no self;
And after that you habituate
Yourself to what you analyzed individually.

This is what then leads you to
Achieve your freedom; nirvana beyond grief.
It is impossible for any other
Cause to bring this peace to you.

*****************

From the presentation on The Proofs for Emptiness [“The Emptiness of One or Many”] found in the Analysis of the Perfection of Wisdom, by Kedrup Tenpa Dargye (1493-1568):

Here secondly is our own position.

Consider the three: basic knowledge, path knowledge, and
the knowledge of all things.
They do not really exist;
For they exist neither as one thing which really exists, nor as many
things which really exist.
They are, for example, like the reflection of a figure in a mirror.

The Jewel of the Middle Way supports this when it says,

The things of self and other
Are free of being purely one
Or being purely many,
And so they have no nature:
Just like a reflection.

Consider these same things.
They do not exist as one thing which really exists;
For they are things with parts.

The one always implies the other, for if something existed as one thing which really exists, then it could never be a thing which appeared one way but actually existed in a different way.

They do not exist as many things which really exist, because they do not exist as one thing which really exists. The one always implies the other, for many things come from bringing together a group of things that are one.

The implication in the original statement is true, for if something really existed, it would have to exist either as one thing that really existed or as many things that really existed. This is always the case, for if something exists it must exist either as one or as many.

Here is the “Sliver of Diamond” reasoning, for denying that things can come from causes:

Consider all inner and outer things that perform a function.
They do not arise ultimately,
For they do not arise from themselves, and they do not arise
ultimately from something other than themselves, and they
do not arise from both, and they do not arise without a cause.

These things do not arise from themselves, because they do not arise from a cause which is such that, if something were the cause, it would have to be the thing it caused.

They do not arise ultimately from something which is other than themselves, for they neither arise ultimately from a cause which is other than themselves and which is unchanging, nor do they arise ultimately from a cause which is other from themselves and which is changing.

They do not arise ultimately from both the above, because they do not arise ultimately from either one of them individually.

They do not arise without a cause, because that would be utterly absurd.

The implication in the original statement is true, for if something were to arise ultimately, it would have to arise ultimately through one of the four possibilities mentioned.

Here is the reasoning called “The Denial that Things which Exist or Do Not Exist could Arise,” which we use for denying that things can come from results:

Consider results.
They do not arise ultimately,
For results which exist at the time of their cause do not arise ultimately, and results that do not exist at the time of their cause do not arise ultimately, and results that both exist and do not exist at the time of their cause do not arise ultimately, and results that neither exist nor do not exist at the time of their cause do not arise ultimately.

The implication is proven in the same way as above.

Here is the reasoning known as “The Denial that Things could Arise through Any of the Four Possibilities,” which we use for denying that things can come from both causes and results:

Consider the functional things of causes and results.
They do not arise ultimately,
For multiple results of multiple causes do not arise ultimately, and single results of multiple causes do not arise ultimately, and multiple results of single causes do not arise ultimately, and single results of single causes do not arise ultimately.