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Only the final bold section is connected to Laozi (see Ch. 17 of Tao Te Ching above). The origin of the added first section is unclear.
Misattributed
Variant: A leader is best when people barely know he exists, when his work is done, his aim fulfilled, they will say: we did it ourselves.
Context: "Go to the people. Live with them. Learn from them. Love them. Start with what they know. Build with what they have. With the best leaders when the work is done, the task accomplished, the people will say, "We have done this ourselves."

Variant: The Tao that can be told is not the eternal Tao;
The name that can be named is not the eternal name.
The nameless is the beginning of heaven and earth.
Source: Tao Te Ching, Ch. 1, as translated by Ch'u Ta-Kao (1904)
Also as Tao called Tao is not Tao.
Context: The Tao that can be expressed is not the eternal Tao; The name that can be defined is not the unchanging name.
Non-existence is called the antecedent of heaven and earth; Existence is the mother of all things.
From eternal non-existence, therefore, we serenely observe the mysterious beginning of the Universe; From eternal existence we clearly see the apparent distinctions.
These two are the same in source and become different when manifested.
This sameness is called profundity. Infinite profundity is the gate whence comes the beginning of all parts of the Universe.

From Lu Tong (also spelled as Lu Tung)
Misattributed

This quotation has been misattributed to Laozi; its origin is actually unknown (see "give a man a fish and you feed him for a day; teach a man to fish and you feed him for a lifetime" on Wiktionary). This quotation has also been misattributed to Confucius and Guan Zhong.
Misattributed

Source: Tao Te Ching, Ch. 1, as interpreted by Ursula K. LeGuin (1998)
Context: The way you can go
isn't the real way.
The name you can say
isn't the real name.
Heaven and earth
begin in the unnamed:
name's the mother
of the ten thousand things.
So the unwanting soul
sees what's hidden,
and the ever-wanting soul
sees only what it wants.
Two things, one origin,
but different in name,
whose identity is mystery.
Mystery of all mysteries!
The door to the hidden.

Source: Tao Te Ching, Ch. 1, as interpreted by Ursula K. LeGuin (1998)
Context: The way you can go
isn't the real way.
The name you can say
isn't the real name.
Heaven and earth
begin in the unnamed:
name's the mother
of the ten thousand things.
So the unwanting soul
sees what's hidden,
and the ever-wanting soul
sees only what it wants.
Two things, one origin,
but different in name,
whose identity is mystery.
Mystery of all mysteries!
The door to the hidden.

Source: Tao Te Ching, Ch. 41
Context: Scholars of the highest class, when they hear about the Tao, take it and practice it earnestly.
Scholars of the middle class, when they hear of it, take it half earnestly.
Scholars of the lowest class, when they hear of it, laugh at it.
Without the laughter, there would be no Tao.

Source: Tao Te Ching, Ch. 21, as interpreted by Stephen Mitchell (1992)
Context: Since before time and space were,
the Tao is.
It is beyond is and is not.
How do I know this is true?
I look inside myself and see.

Source: Tao Te Ching, Ch. 4, as interpreted by Stephen Mitchell (1992)

This quotation's origin is actually unknown, however it is not found in the Dao De Jing.
生命是一连串的自发的自然变化。逆流而动只会徒增伤悲。接受现实，万物自然循着规律发展。
Misattributed
Variant: Life is a series of natural and spontaneous changes. Don't resist them — that only creates sorrow. Let reality be reality. Let things flow naturally forward in whatever way they like.

Source: Tao Te Ching, Ch. 81 as interpreted by Stephen Mitchell (1992)

Source: Tao Te Ching, Ch. 46

Attributed to &quot;Jimmy R.&quot; in Days of Healing, Days of Joy (1987) <br class="br">Misattributed <br class="br">Source: link https://books.google.com/books?id=7QNk4eNvS44C&amp;pg=PA175&amp;lpg=PA175&amp;dq=%22days+of+healing+days+of+joy%22+%22jimmy+r%22&amp;source=bl&amp;ots=C-jAUVg8y8&amp;sig=fB9m-eQ1IvtjJV6Ncz8mZ30RRHo&amp;hl=en&amp;sa=X&amp;ved=0CB4Q6AEwAGoVChMIrYnZyNDlyAIVV_5jCh07uQOs#v=onepage&amp;q=%22days%20of%20healing%20days%20of%20joy%22%20%22jimmy%20r%22&amp;f=false

Source: Tao Te Ching, Ch. 5, as interpreted by Stephen Mitchell (1992)
Context: The Tao is like a bellows:
it is empty yet infinitely capable.
The more you use it, the more it produces;
the more you talk of it, the less you understand.

Source: Tao Te Ching, Ch. 59 as interpreted by Stephen Mitchell (1992)
Context: The mark of a moderate man
is freedom from his own ideas.
Tolerant like the sky,
all-pervading like sunlight,
firm like a mountain,
supple like a tree in the wind,
he has no destination in view
and makes use of anything
life happens to bring his way.

Source: Tao Te Ching, Ch. 48, as translated by Raymond B. Blakney (1955)