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Magic circle

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- Title: Facsimile of a Letter from Benjamin Franklin at Craven Street London to Mr Canton in the possession of R Canton Esq at 22 and 23 Aldersgate Street
- Creator: Benjamin Franklin (1706-1790)
- Date Created: 1765-05-29
- Transcript: Cravenstreet, May 29. 1765|Dear Sir|As you seem'd desirous of seeing the magic Circle I mention'd to you, I have revis'd the one I made many Years since, and with some Improvements, send it you.|I have made it as distinct as I could, by using Inks of different Colours for the several Sets of interwoven Circles; and yet the whole makes so perplext an Appearance, that I doubted whether the Eye could in all Cases easily trace the Circle of Numbers one would examine, through all the Maze of Circles intersected by it: I have therefore, in the middle Circle, mark'd the Centers of the Green, Red, Yellow, and Blue Sets; & so that when you would cast up the Numbers in any Circle of either of those Colours, if you fix one Foot of the Compasses in the Center of the same Colour, and extend the other to any Number in that Circle, it will pass round over all the rest successively.|This magic Circle has more Properties than are mention'd in the Description of it, some of them curious and even surprizing; but I could not mark them all without occasioning more Confusion in the Figure, nor easily describe them without too much Writing. When I have next the Pleasure of seeing you, I will point them out. I am, Dear Sir, Your most obedient humble Servant|B. Franklin|p.s. You have my curious Square of 8, and the great perfect one of 16; I enclose one of 6, and one of 4, which I assure you I found more difficult to make, (particularly that of 6) tho nothing near so good.|Mr Canton | A Magical circle of circles. | ByB:F. |It is compos'd of a Series of Numbers from 12 to 75 inclusive, divided in 8 concentric Circles of Numbers, and rang'd in 8 Radii of Numbers, with the Number 12 in the Center, which Number, like the Center, is common to all the Circles and to all the Radii.|The Numbers are so dispos'd, as that all the Numbers in any one of the Circles, added together, make, with the central Number, just 360, the Number of Degrees in a Circle.|The Numbers in each Radius also, with the central Number, make just 360.|There are moreover included 4 other Sets of concentric Circles, 5 in each Set, the several Sets distinguish'd by Green, Yellow, Red, and Blue Ink, and each Set drawn round a Center of the same Colour. These Sets of Circles intersect the first 8 and each other; and the Numbers contain'd in each of these 20 Circles, do also, with the Central Number, make 360. Their Halves also, taken above or under the horizontal Line, do, with half the central Number make 180.|Observe, That there is no one of the Numbers but what belongs to at least two different Circles, some to three, some to four, and some to five; and yet all so plac'd (with the central Number which belongs to all) as never to break the requir'd Number 360 in any one of the 28 Circles.|The Diagonals are to be reckon'd by Halves, not crossing but turning at right Angles from the Center, by which 4 Varieties are made instead of two.|
- Rights: Copyright The Royal Society, 2018
- External Link: See a full transcription of this letter and other on Founders Online
- Medium: paper, ink
- Scientist: Benjamin Franklin (1706-1790)
- Field: Mathematics
- Discovery: Magic circles
- Catalogue Reference: MS/597/2/21x