Recognized as one of the world´s first constitutions, the Magna Carta Libertatum, signed by King John of England in 1215, had major influence in the US Constitution, and of many other countries.
The article 39 of the Magna Carta states:
"No free man shall be seized or imprisoned, or stripped of his rights or possessions,  or outlawed or exiled, or deprived of his standing in any other way, nor will we proceed with force against him, or send others to do so, except by the lawful  judgement of his equals or by the law of the land"
From this excerpt we can find a very similar text to the Fifith Amendment to the US Constitution:
"No person shall be held to answer for a capital, or otherwise infamous crime, unless on a  presentment or indictment of a Grand Jury, except in cases arising in the land or naval  forces, or in the Militia, when in actual service in time of War or public danger; nor shall  any person be subject for the same offense to be twice put in jeopardy of life or limb; nor  shall be compelled in any criminal case to be a witness against himself, nor be deprived  of life, liberty, or property, without due process of law; nor shall private property be  taken for public use, without just compensation."
This idea of right to life, liberty and property, free from authoritarian attacks (without due process), derives from the Magna Carta.
The second main idea is more subjective: The US Constitution has a stance of untrust on the government and all centralized power, delegating it to the states or to the people. This also comes from the Magna Carta, the liberal constitution.
Other european constitutions, such as the french, that influenced most Latin American Countries, demonstrate a relation of trust and participation of the people in the government.
In other words, while Magna Carta is about protection from power, constitutions nowadays are about organization of power.
