Lao Tzu's quote

Saw a post by Salad Boy on Fb today. He's reading the book 'How to Win Friends and Influence People' by Dale Carnegie. He shared a quote originally from Lao Tzu in the book.

English translation in 'How to Win Friends and Influence People':
"The reason why rivers and seas receive the homage of a hundred mountain streams is that they keep below them. Thus they are able to reign over all the mountain streams. So the sage wishing to be above men, putteth himself below them;wishing to be before them, he putteth himself behind them. Thus, though his place be above men, they do not feel his weight; though his place be before them, they do not count it an injury"

The supposed original Chinese quote from 'Tao Te Ching' that Salad Boy gave me was:
http://blog.xuite.net/chun.hung693/twblog/155961170-%E8%80%81%E5%AD%90%E9%81%93%E5%BE%B7%E7%B6%93%E7%99%BD%E8%A9%B1%E8%A7%A3+(%E7%AC%AC%E5%85%AD%E5%8D%81%E4%B8%80%E7%AB%A0+%E5%A4%A7%E5%9C%8B%E8%80%85%E4%B8%8B%E6%B5%81)

老子道德經白話解 (第六十一章 大國者下流) 《請先默誦原文》
大國者下流。天下之交，天下之牝。
牝常以靜勝牡，以靜爲下。
故大國以下小國，則取小國；小國以下大國，則取大國。
故或下以取，或下而取。
大國不過欲兼畜人，小國不過欲入事人。
夫兩者各得其所欲，大者宜爲下。

Explanation:

《白話解》
大國者下流。天下之交，天下之牝。
「執大象，天下往」的大國要像位處低下的大海一般才能匯聚百川，它是天下的會歸、天下的母親。
牝常以靜勝牡，以靜爲下。
雌性常藉由靜而勝過雄性，因為「靜為躁君」而又處下才能有容乃大。
故大國以下小國，則取小國；小國以下大國，則取大國。
所以，大國能放下身段去照顧小國，小國就願意依附。小國能識時務去服侍大國，大國就會保護他。
故或下以取，或下而取。
同樣用謙下的態度，而取得對方的依附和保護。
大國不過欲兼畜人，小國不過欲入事人。
大國不過是想教化小國；小國不過是想藉大國謀生。
夫兩者各得其所欲，大者宜爲下。
想做到大國小國各取所需，還是要大國先主動放下身段才得以完成。

But I found this webpage, so I think this is the correct quote.

http://www.yellowbridge.com/onlinelit/daodejing66.php

道德經第六十六章

後巳 Putting One's Self Last

Putting Oneself Behind / To Subordinate Self

江海之所以能為百谷王者，以其善下之，故能為百谷王。
是以聖人欲上民 ，必以言下之﹔欲先民，必以身后之。
是以聖人處上而民不重，處前而民不害。
是以天下樂推而不厭。以其不爭，故天下莫能與之爭。