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Si ad Sphæricæ superficiei puncta singula tendant vires æquales centripetæ decrescentes in duplicata ratione distantiarum a punctis: dico quod corpusculum intra superficiem constitutum his viribus nul...

Descendat corpus aliquod ab A per D , E , ad centrum C , moveatur corpus aliud a V in linea curva VIKk . Centro C intervallis quibusvis describantur circuli concentrici DI , EK rectæ AC in D E , curvæ...

Lemma XV. Si ab Ellipseos vel Hyperbolæ cujusvis umbilicis duobus S , H , ad punctum quodvis tertium V inflectantur rectæ duæ SV , HV , quarum una HV æqualis sit axi transverso figuræ, altera SV a per...

The Project Gutenberg eBook of Philosophiae Naturalis Principia Mathematica This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almo...

*** END OF THE PROJECT GUTENBERG EBOOK FLATLAND: A ROMANCE OF MANY DIMENSIONS *** Updated editions will replace the previous one—the old editions will be renamed. Creating the works from print edition...

PREFACE TO THE SECOND AND REVISED EDITION, 1884. BY THE EDITOR If my poor Flatland friend retained the vigour of mind which he enjoyed when he began to compose these Memoirs, I should not now need to ...

§ 22 How I then tried to diffuse the Theory of Three Dimensions by other means, and of the result My failure with my Grandson did not encourage me to communicate my secret to others of my household; y...

§ 21 How I tried to teach the Theory of Three Dimensions to my Grandson, and with what success I awoke rejoicing, and began to reflect on the glorious career before me. I would go forth, methought, at...

§ 20 How the Sphere encouraged me in a Vision. Although I had less than a minute for reflection, I felt, by a kind of instinct, that I must conceal my experiences from my Wife. Not that I apprehended,...

§ 19 How, though the Sphere shewed me other mysteries of Spaceland, I still desire more; and what came of it When I saw my poor brother led away to imprisonment, I attempted to leap down into the Coun...

§ 18 How I came to Spaceland, and what I saw there An unspeakable horror seized me. There was a darkness; then a dizzy, sickening sensation of sight that was not like seeing; I saw a Line that was no ...

§ 17 How the Sphere, having in vain tried words, resorted to deeds It was in vain. I brought my hardest right angle into violent collision with the Stranger, pressing on him with a force sufficient to...

§ 16 How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland As soon as the sound of the Peace-cry of my departing Wife had died away, I began to approach the Stranger ...

§ 15 Concerning a Stranger from Spaceland From dreams I proceed to facts. It was the last day of our 1999th year of our era. The patterning of the rain had long ago announced nightfall; and I was sitt...

§ 14 How I vainly tried to explain the nature of Flatland Thinking that it was time to bring down the Monarch from his raptures to the level of common sense, I determined to endeavour to open up to hi...

PART II OTHER WORLDS “O brave new worlds, That have such people in them!” § 13 How I had a Vision of Lineland It was the last day but one of the 1999th year of our era, and the first day of the Long V...

§ 12 Of the Doctrine of our Priests As to the doctrine of the Circles it may briefly be summed up in a single maxim, “Attend to your Configuration.” Whether political, ecclesiastical, or moral, all th...

§ 11 Concerning our Priests It is high time that I should pass from these brief and discursive notes about things in Flatland to the central event of this book, my initiation into the mysteries of Spa...

§ 10 Of the Suppression of the Chromatic Sedition The agitation for the Universal Colour Bill continued for three years; and up to the last moment of that period it seemed as though Anarchy were desti...