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Geometry Has Two Great Treasures; One Is The Theorem Of Pythagoras; The Other, The Division Of A Line Into Extreme And Mean Ratio. The First We May Compare To A Measure Of Gold; The Second We May Name A Precious Jewel.

-Johannes Kepler

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Geometry Has Two Great

Johannes Kepler

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Geometry Has Two Great Treasures; One Is The Theorem Of Pythagoras; The Other, The Division Of A Line Into Extreme And Mean Ratio. The First We May Compare To A Measure Of Gold; The Second We May Name A Precious Jewel.

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After The Birth Of Printing Books Became Widespread. Hence Everyone Throughout Europe Devoted Himself To The Study Of Literature... Every Year, Especially Since 1563, The Number Of Writings Published In Every Field Is Greater Than All Those Produced In The Past Thousand Years. Through Them There Has Today Been Created A New Theology And A New Jurisprudence; The Paracelsians Have Created Medicine Anew And The Copernicans Have Created Astronomy Anew. I Really Believe That At Last The World Is Alive, Indeed Seething, And That The Stimuli Of These Remarkable Conjunctions Did Not Act In Vain.

Thus God Himself Was Too Kind To Remain Idle And Began To Play The Game Of Signatures Signing His Likeness Unto The World: Therefore I Chance To Think That All Nature And The Graceful Sky Are Symbolized In The Art Of Geometria.

Wherever There Are Qualities There Are Likewise Quantities, But Not Always Vice Versa.

Now, As God The Maker Play'd He Taught The Game To Nature Whom He Created In His Image; Taught Her The Selfsame Game Which He Played To Her.

I Am Stealing The Golden Vessels Of The Egyptians To Build A Tabernacle To My God From Them, Far Far Away From The Boundaries Of Egypt. If You Forgive Me, I Shall Rejoice; If You Are Enraged With Me, I Shall Bear It. See, I Cast The Die, And I Write The Book. Whether It Is To Be Read By The People Of The Present Or Of The Future Makes No Difference: Let It Await Its Reader For A Hundred Years, If God Himself Has Stood Ready For Six Thousand Years For One To Study Him.

A Most Unfailing Experience... Of The Excitement Of Sublunary (that Is, Human) Natures By The Conjunctions And Aspects Of The Planets Has Instructed And Compelled My Unwilling Belief.

I Am Much Occupied With The Investigation Of The Physical Causes [of Motions In The Solar System]. My Aim In This Is To Show That The Celestial Machine Is To Be Likened Not To A Divine Organism But Rather To A Clockwork ... Insofar As Nearly All The Manifold Movements Are Carried Out By Means Of A Single, Quite Simple Magnetic Force. This Physical Conception Is To Be Presented Through Calculation And Geometry.

But Although The Attractive Virtue Of The Earth Extends Upwards, As Has Been Said, So Very Far, Yet If Any Stone Should Be At A Distance Great Enough To Become Sensible Compared With The Earth's Diameter, It Is True That On The Motion Of The Earth Such A Stone Would Not Follow Altogether; Its Own Force Of Resistance Would Be Combined With The Attractive Force Of The Earth, And Thus It Would Extricate Itself In Some Degree From The Motion Of The Earth.

Yet In This My Stars Were Not Mercury As Morning Star In The Angle Of The Seventh House, In Quartile With Mars, But They Were Copernicus, They Were Tycho Brahe, Without Whose Books Of Observations Everything Which Has Now Been Brought By Me Into The Brightest Daylight Would Lie Buried In Darkness.

Eyesight Should Learn From Reason.

The Diversity Of The Phenomena Of Nature Is So Great, And The Treasures Hidden In The Heavens So Rich, Precisely In Order That The Human Mind Shall Never Be Lacking In Fresh Nourishment.

I Had The Intention Of Becoming A Theologian...but Now I See How God Is, By My Endeavors, Also Glorified In Astronomy, For 'the Heavens Declare The Glory Of God.'

Nothing Which Consists Of Corporeal Matter Is Absolutely Light, But That Is Comparatively Lighter Which Is Rarer, Either By Its Own Nature, Or By Accidental Heat. And It Is Not To Be Thought That Light Bodies Are Escaping To The Surface Of The Universe While They Are Carried Upwards, Or That They Are Not Attracted By The Earth. They Are Attracted, But In A Less Degree, And So Are Driven Outwards By The Heavy Bodies; Which Being Done, They Stop, And Are Kept By The Earth In Their Own Place.

Science Is The Process Of Thinking God's Thoughts After Him.

Geometry Has Two Great Treasures; One Is The Theorem Of Pythagoras; The Other, The Division Of A Line Into Extreme And Mean Ratio. The First We May Compare To A Measure Of Gold; The Second We May Name A Precious Jewel.

[god] Is The Kind Creator Who Brought Forth Nature Out Of Nothing.

The Wisdom Of The Lord Is Infinite As Are Also His Glory And His Power. Ye Heavens, Sing His Praises; Sun, Moon, And Planets, Glorify Him In Your Ineffable Language! Praise Him, Celestial Harmonies, And All Ye Who Can Comprehend Them! And Thou, My Soul, Praise Thy Creator! It Is By Him And In Him That All Exist.

I Also Ask You My Friends Not To Condemn Me Entirely To The Mill Of Mathematical Calculations, And Allow Me Time For Philosophical Speculations, My Only Pleasures.

Where There Is Matter, There Is Geometry.

Since We Astronomers Are Priests Of The Highest God In Regard To The Book Of Nature, It Befits Us To Be Thoughtful, Not Of The Glory Of Our Minds, But Rather, Above All Else, Of The Glory Of God.

...those Laws Are Within The Grasp Of The Human Mind. God Wanted Us To Recognize Them By Creating Us After His Own Image So That We Could Share In His Own Thoughts... And If Piety Allow Us To Say So, Our Understanding Is In This Respect Of The Same Kind As The Divine, At Least As Far As We Are Able To Grasp Something Of It In Our Mortal Life.

Repudiating The Sensible World, Which He Neither Sees Himself Nor Believes From Those Who Have, The Peripatetic Joins Combat By Childish Quibbling In A World On Paper, And Denies The Sun Shines Because He Himself Is Blind.

I Used To Measure The Heavens, Now I Measure The Shadows Of Earth. The Mind Belonged To Heaven, The Body's Shadow Lies Here.

When Things Are In Order, If The Cause Of The Orderliness Cannot Be Deduced From The Motion Of The Elements Or From The Composition Of Matter, It Is Quite Possibly A Cause Possessing A Mind.

I Myself, A Professional Mathematician, On Re-reading My Own Work Find It Strains My Mental Powers To Recall To Mind From The Figures The Meanings Of The Demonstrations, Meanings Which I Myself Originally Put Into The Figures And The Text From My Mind. But When I Attempt To Remedy The Obscurity Of The Material By Putting In Extra Words, I See Myself Falling Into The Opposite Fault Of Becoming Chatty In Something Mathematical.

As Soon As Somebody Demonstrates The Art Of Flying, Settlers From Our Species Of Man Will Not Be Lacking On The Moon And Jupiter. Who Would Have Believed That A Huge Ocean Could Be Crossed More Peacefully And Safely Than The The Narrow Expanse Of The Adriatic, The Baltic Sea Or The English Channel? Given Ships Or Sails Adapted To The Breezes Of Heaven, There Will Be Those Who Will Not Shrink From Even That Vast Expanse.

As Soon As Somebody Demonstrates The Art Of Flying, Settlers From Our Species Of Man Will Not Be Lacking On The Moon And Jupiter... Given Ships Or Sails Adapted To The Breezes Of Heaven, There Will Be Those Who Will Not Shrink From Even That Vast Expanse.

Once Miracles Are Admitted, Every Scientific Explanation Is Out Of The Question.

The Squares Of The Periodic Times Are Proportional To The Cubes Of The Mean Distances From The Sun.

Since Geometry Is Co-eternal With The Divine Mind Before The Birth Of Things, God Himself Served As His Own Model In Creating The World (for What Is There In God Which Is Not God?), And He With His Own Image Reached Down To Humanity.

Great Is God Our Lord, Great Is His Power And There Is No End To His Wisdom. Praise Him You Heavens, Glorify Him, Sun And Moon And You Planets. For Out Of Him And Through Him, And In Him Are All Things..... We Know, Oh, So Little. To Him Be The Praise, The Honor And The Glory From Eternity To Eternity.

It May Be Well To Wait A Century For A Reader, As God Has Waited Six Thousand Years For An Observer.

Geometry Is One And Eternal Shining In The Mind Of God. That Share In It Accorded To Men Is One Of The Reasons That Man Is The Image Of God.

Why Are Things As They Are And Not Otherwise?

Either... The Moving Intelligences Of The Planets Are Weakest In Those That Are Farthest From The Sun, Or... There Is One Moving Intelligence In The Sun, The Common Center, Forcing Them All Round, But Those Most Violently Which Are Nearest, And That It Languishes In Some Sort And Grows Weaker At The Most Distant, Because Of The Remoteness And The Attenuation Of The Virtue.

Truth Is The Daughter Of Time, And I Feel No Shame In Being Her Midwife.

The Moon... Is A Mass, Akin To The Mass Of The Earth, Attracts The Waters By A Magnetic Force, Not Because They Are Liquid, But Because They Possess Earthy Substance, And So Share In The Movements Of A Heavy Body.

I Am A Lutheran Astrologer, I Throw Away The Nonsense And Keep The Hard Kernel.

I Believe The Geometric Proportion Served The Creator As An Idea When He Introduced The Continuous Generation Of Similar Objects From Similar Objects.

We Do Not Ask What Hope Of Gain Makes A Little Bird Warble, Since We Know That It Takes Delight In Singing Because It Is For That Very Singing That The Bird Was Made, So There Is No Need To Ask Why The Human Mind Undertakes Such Toil In Seeking Out These Secrets Of The Heavens. ... And Just As Other Animals, And The Human Body, Are Sustained By Food And Drink, So The Very Spirit Of Man, Which Is Something Distinct From Man, Is Nourished, Is Increased, And In A Sense Grows Up On This Diet Of Knowledge, And Is More Like The Dead Than The Living If It Is Touched By No Desire For These Things.

He Who Will Please The Crowd And For The Sake Of The Most Ephemeral Renown Will Either Proclaim Those Things Which Nature Does Not Display Or Even Will Publish Genuine Miracles Of Nature Without Regard To Deeper Causes Is A Spiritually Corrupt Person... With The Best Of Intentions I Publicly Speak To The Crowd (which Is Eager For Things New) On The Subject Of What Is To Come.

If God Himself Has Waited Six Thousand Years For Someone To Contemplate His Works, My Book Can Wait For A Hundred.

Geometry Existed Before The Creation. It Is Co-eternal With The Mind Of God...geometry Provided God With A Model For The Creation.

My Aim Is To Say That The Machinery Of The Heavens Is Not Like A Divine Animal But Like A Clock (and Anyone Who Believes A Clock Has A Soul Gives The Work The Honour Due To Its Maker) And That In It Almost All The Variety Of Motions Is From One Very Simple Magnetic Force Acting On Bodies, As In The Clock All Motions Are From A Very Simple Weight.

We Do Not Ask For What Useful Purpose The Birds Do Sing, For Song Is Their Pleasure Since They Were Created For Singing. Similarly, We Ought Not To Ask Why The Human Mind Troubles To Fathom The Secrets Of The Heavens.

If Two Stones Were Placed... Near Each Other, And Beyond The Sphere Of Influence Of A Third Cognate Body, These Stones, Like Two Magnetic Needles, Would Come Together In The Intermediate Point, Each Approaching The Other By A Space Proportional To The Comparative Mass Of The Other.

In Theology We Must Consider The Predominance Of Authority; In Philosophy The Predominance Of Reason.

The Radius Vector Describes Equal Areas In Equal Times.

The Roads By Which Men Arrive At Their Insights Into Celestial Matters Seem To Me Almost As Worthy Of Wonder As Those Matters In Themselves.

There Will Certainly Be No Lack Of Human Pioneers When We Have Mastered The Art Of Flight....let Us Create Vessels And Sails Justed To The Heavenly Ether, And There Will Be Plenty Of People Unafraid Of The Empty Wastes. In The Meantime We Shall Prepare, For The Brave Sky-travelers, Maps Of The Celestial Bodies.

Do We Ask What Profit The Little Bird Hopes For In Singing?

Geometry Is One And Eternal Shining In The Mind Of God

Astronomy Would Not Provide Me With Bread If Men Did Not Entertain Hopes Of Reading The Future In The Heavens.

I Much Prefer The Sharpest Criticism Of A Single Intelligent Man To The Thoughtless Approval Of The Masses.

The Cause Of The Six-sided Shape Of A Snowflake Is None Other Than That Of The Ordered Shapes Of Plants And Of Numerical Constants; And Since In Them Nothing Occurs Without Supreme Reason-not, To Be Sure, Such As Discursive Reasoning Discovers, But Such As Existed From The First In The Creators's Design And Is Preserved From That Origin To This Day In The Wonderful Nature Of Animal Faculties, I Do Not Believe That Even In A Snowflake This Ordered Pattern Exists At Random.

On How The Motion Of A Planet Defines Its Sphere: ... And Thus It Comes About Gradually By The Linking And Accumulation Of A Great Many Revolutions That A Kind Of Concave Sphere Is Displayed, Having The Same Center As The Sun, Just As By A Great Many Circles Of Silken Thread, Linked With Each Other And Wound Together, The Dwelling Of A Silkworm Is Made.

Nature Uses As Little As Possible Of Anything.

When Ships To Sail The Void Between The Stars Have Been Built, There Will Step Forth Men To Sail These Ships.

My Greatest Desire Is That I May Perceive The God Whom I Find Everywhere In The External World, In Like Manner Also Within And Inside Myself.

Without Proper Experiments I Conclude Nothing.

[quantity Is The Fundamental Feature Of Things,] The 'primarium Accidens Substantiae,' ...prior To The Other Categories.

The Heavenly Motions... Are Nothing But A Continuous Song For Several Voices, Perceived Not By The Ear But By The Intellect, A Figured Music Which Sets Landmarks In The Immeasurable Flow Of Time.

If The Moon And Earth Were Not Retained In Their Orbits By Their Animal Force Or Some Other Equivalent, The Earth Would Mount To The Moon By A Fifty-fourth Part Of Their Distance, And The Moon Fall Towards The Earth Through The Other Fifty-three Parts, And They Would There Meet, Assuming, However, That The Substance Of Both Is Of The Same Density.

It Is A Right, Yes A Duty, To Search In Cautious Manner For The Numbers, Sizes, And Weights, The Norms For Everything [god] Has Created. For He Himself Has Let Man Take Part In The Knowledge Of These Things ... For These Secrets Are Not Of The Kind Whose Research Should Be Forbidden; Rather They Are Set Before Our Eyes Like A Mirror So That By Examining Them We Observe To Some Extent The Goodness And Wisdom Of The Creator.

A Mind Is Accustomed To Mathematical Deduction, When Confronted With The Faulty Foundations Of Astrology, Resists A Long, Long Time, Like An Obstinate Mule, Until Compelled By Beating And Curses To Put Its Foot Into That Dirty Puddle.

The Sun Alone Appears, By Virtue Of His Dignity And Power, Suited For This Motive Duty (of Moving The Planets) And Worthy To Become The Home Of God Himself.

If The Earth Were Not Round, Heavy Bodies Would Not Tend From Every Side In A Straight Line Towards The Center Of The Earth, But To Different Points From Different Sides.

The Sphere Of The Attractive Virtue Which Is In The Moon Extends As Far As The Earth, And Entices Up The Waters; But As The Moon Flies Rapidly Across The Zenith, And The Waters Cannot Follow So Quickly, A Flow Of The Ocean Is Occasioned In The Torrid Zone Towards The Westward.

The Creator, The Fountain Of All Wisdom, The Approver Of Perpetual Order, The Eternal And Superessential Spring Of Geometry And Harmonics.

The Soul Of The Newly Born Baby Is Marked For Life By The Pattern Of The Stars At The Moment It Comes Into The World, Unconsciously Remembers It, And Remains Sensitive To The Return Of Configurations Of A Similar Kind.

O Telescope, Instrument Of Much Knowledge, More Precious Than Any Sceptre!

If My False Figures Came Near To The Facts, This Happened Merely By Chance ... These Comments Are Not Worth Printing. Yet It Gives Me Pleasure To Remember How Many Detours I Had To Make, Along How Many Walls I Had To Grope In The Darkness Of My Ignorance Until I Found The Door Which Lets In The Light Of The Truth ... In Such Manner Did I Dream Of The Truth.

We Find, Therefore, Under This Orderly Arrangement, A Wonderful Symmetry In The Universe, And A Definite Relation Of Harmony In The Motion And Magnitude Of The Orbs, Of A Kind That Is Not Possible To Obtain In Any Other Way.

Gravity Is A Mutual Affection Between Cognate Bodies Towards Union Or Conjunction (similar In Kind To The Magnetic Virtue), So That The Earth Attracts A Stone Much Rather Than The Stone Seeks The Earth.

I Believe Only And Alone In The Service Of Jesus Christ. In Him Is All Refuge And Solace.

If The Earth Should Cease To Attract Its Waters To Itself All The Waters Of The Sea Would Be Raised And Would Flow To The Body Of The Moon.

The Earth Is Round, And Is Inhabited On All Sides, Is Insignificantly Small, And Is Borne Through The Stars.

I Measured The Skies, Now The Shadows I Measure, Sky-bound Was The Mind, Earth-bound The Body Rests. [kepler's Epitaph]

So Long As The Mother, Ignorance, Lives, It Is Not Safe For Science The Offspring, To Divulge The Hidden Causes Of Things.

Geometry, Which Before The Origin Of Things Was Coeternal With The Divine Mind And Is God Himself (for What Could There Be In God Which Would Not Be God Himself?), Supplied God With Patterns For The Creation Of The World, And Passed Over To Man Along With The Image Of God; And Was Not In Fact Taken In Through The Eyes.

Just As The Eye Was Made To See Colours, And The Ear To Hear Sounds, So The Human Mind Was Made To Understand, Not Whatever You Please, But Quantity.

Nature Loves Simplicity And Unity.

...for A Long Time I Wanted To Become A Theologian... Now, However, Behold How Through My Efforts God Is Being Debated In Astronomy.

Every Corporeal Substance, So Far Forth As It Is Corporeal, Has A Natural Fitness For Resting In Every Place Where It May Be Situated By Itself Beyond The Sphere Of Influence Of A Body Cognate With It.

Sphere Of Influence

God Gives Every Animal The Means Of Saving Its Life-why Object If He Gives Astrology To The Astronomer?

Discover The Force Of The Skies O Men: Once Recognised It Can Be Put To Use.

Some Of What These Pamphlets [of Astrological Forecasts] Say Will Turn Out To Be True, But Most Of It Time And Experience Will Expose As Empty And Worthless. The Latter Part Will Be Forgotten Literally: Written On The Winds While The Former Will Be Carefully Entered In People's Memories, As Is Usual With The Crowd.

Planets Move In Ellipses With The Sun At One Focus.

So, Fabricius, I Already Have This: That The Most True Path Of The Planet [mars] Is An Ellipse, Which Dürer Also Calls An Oval, Or Certainly So Close To An Ellipse That The Difference Is Insensible.

Ships And Sails Proper For The Heavenly Air Should Be Fashioned. Then There Will Also Be People, Who Do Not Shrink From The Dreary Vastness Of Space.

Why Waste Words? Geometry Existed Before The Creation, Is Co-eternal With The Mind Of God, Is God Himself (what Exists In God That Is Not God Himself?): Geometry Provided God With A Model For The Creation And Was Implanted Into Man, Together With God's Own Likeness - And Not Merely Conveyed To His Mind Through The Eyes.

The Chief Aim Of All Investigations Of The External World Should Be To Discover The Rational Order And Harmony Which Has Been Imposed On It By God And Which He Revealed To Us In The Language Of Mathematics.

The Heavenly Bodies Are Nothing But A Continuous Song For Several Voices (perceived By The Intellect, Not By The Ear); A Music Which... Sets Landmarks In The Immeasurable Flow Of Time. It Is Therefore, No Longer Surprising That Man, In Imitation Of His Creator, Has At Last Discovered The Art Of Figured Song, Which Was Unknown To The Ancients. Man Wanted To Reproduce The Continuity Of Cosmic Time... To Obtain A Sample Test Of The Delight Of The Divine Creator In His Works, And To Partake Of His Joy By Making Music In The Imitation Of God.

Geometry Is The Archetype Of The Beauty Of The World.

If There Is Anything That Can Bind The Heavenly Mind Of Man To This Dreary Exile Of Our Earthly Home And Can Reconcile Us With Our Fate So That One Can Enjoy Living,-then It Is Verily The Enjoyment Of The Mathematical Sciences And Astronomy.

If This [the Mysterium Cosmographicum] Is Published, Others Will Perhaps Make Discoveries I Might Have Reserved For Myself. But We Are All Ephemeral Creatures (and None More So Than I). I Have, Therefore, For The Glory Of God, Who Wants To Be Recognized From The Book Of Nature, That These Things May Be Published As Quickly As Possible. The More Others Build On My Work The Happier I Shall Be.

Wheresoever The Earth May Be Placed, Or Whithersoever It May Be Carried By Its Animal Faculty, Heavy Bodies Will Always Be Carried Towards It.

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