In The Last Two Months I Have

You Know That I Write Slowly. This Is Chiefly Because I Am Never Satisfied Until I Have Said As Much As Possible In A Few Words, And Writing Briefly Takes Far More Time Than Writing At Length.

Sin2 φ Is Odious To Me, Even Though Laplace Made Use Of It; Should It Be Feared That Sin2 φ Might Become Ambiguous, Which Would Perhaps Never Occur, Or At Most Very Rarely When Speaking Of Sin(φ2), Well Then, Let Us Write (sin φ)2, But Not Sin2 φ, Which By Analogy Should Signify Sin (sin φ)

The Enchanting Charms Of This Sublime Science Reveal Only To Those Who Have The Courage To Go Deeply Into It.

The Problem Of Distinguishing Prime Numbers From Composite Numbers And Of Resolving The Latter Into Their Prime Factors Is Known To Be One Of The Most Important And Useful In Arithmetic. It Has Engaged The Industry And Wisdom Of Ancient And Modern Geometers To Such An Extent That It Would Be Superfluous To Discuss The Problem At Length. ... Further, The Dignity Of The Science Itself Seems To Require That Every Possible Means Be Explored For The Solution Of A Problem So Elegant And So Celebrated.

Mathematics Is The Queen Of Sciences And Number Theory Is The Queen Of Mathematics. She Often Condescends To Render Service To Astronomy And Other Natural Sciences, But In All Relations She Is Entitled To The First Rank.