PASCAL: Treatise on the Arithmetical Triangle

Treatise on the Arithmetical Triangle by Pascal

Proportions and Consequences of the Arithmetical Triangle

• First Consequence: “In every arithmetical triangle all the cells of the first parallel row and of the first perpendicular row are the same as the generating cell.”

PASCAL: Pensées [Numbers 607-610, 613, 619-620, 631, 640, 644, 673, 675, 684, 692-693, 737, 760, 768, 792-793]

Pensées by Pascal

607 – Jews and Christians

• Carnal Jews believe that the Messiah would be a temporal prince. Carnal Christians believe that the Messiah gave us sacraments which will do everything without our help. These two sects are both mistaken. True Jews and true Christians believe that the Messiah makes them love God, and triumph over their enemies by their love of God.

PASCAL: Pensées [Numbers 416, 418, 425, 430, 434-435, 463, 491, 525-531, 538, 543, 547, 553, 556, 564, 571, 586, 598]

Pensées by Pascal

416 – Greatness and Wretchedness

• Wretchedness is deduced from greatness and vice versa. The more one proves the greatness of man, the more one proves the wretchedness of man.

PASCAL: Pensées [Numbers 194-195, 219, 229, 233-234, 242, 273, 277, 282, 289, 298, 303, 320, 323, 325, 330-331, 374, 385, 392, 395-397, 409, 412-413]

Pensées by Pascal

194 – Life After Death

• Christianity does not claim that men have a clear view of God. It claims that men are estranged from God and are in darkness. Thus, it is not discrediting to Christianity to assert that there is nothing in this world which demonstrates the existence of God. God has created visible signs of His existence to make Himself known to those who seek Him, and He also has disguised these visible signs from those who turn away from Him.

PASCAL: Pensées [Numbers 72, 82-83, 100, 128, 131, 139, 142-143, 171]

Pensées by Pascal

72 – Man’s Disproportion

• The earth is a point compared to the vastness of the sun; the sun is a point compared to other stars; the stars are points in an infinite universe. Nature surpasses our capacity of imagination; this is the greatest sensible mark of God – i.e. imagination loses itself in contemplation of nature.