By Marshall Clagett
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Additional info for Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv
Mp Ed3 I: L u Variant readings: om. ab et u omnes numeros P 12 . . C2: | A ^ ^ C ^ Ed3 add. M A ------ 1 DE I--------- 1 B et I----------- 1 D K ------------------------- 1 L I----------1 CHI I-------- 1 | A B |_____ A D |_____ C 1-------- K G ------E1 H I ____ 1 F F7 Variant readings: Q Q G 27 . . M 8 om. a i------- 1 i------- 1 bMp Ed3 K Η Μ N A 9 . . B 2: 6K4 H g i--------1 i------- 1 u C A i------- 1B a 9 om. M Ed3p 17 b 5 om. Mp Ed3 9 b IK N4 M4 4 R 2 H u 2 om. Mp Ed3 I------- 1---------- 1 I---------1 I---------- 1 2 D 2 C u 4: 60a 3 b 6p om.
Ergo quadratum eius, scilicet M N O (/ L N O ) quadruplum est ad quadratum A C E , ut patet ad sensum, et per consequens semi circulus L P Q N super dictam lineam descriptus quadruplus erit ad semicirculum A D C per dictam propositionem, sicut se habet quadratum alicuius linee ad quadratum alterius linee sic semicirculus ad semi circulum. Valet ergo semicirculus L P Q N tres semicirculos L P , P Q , Q N descriptos super tria latera medietatis figure exagone et alium semi circulum quartum, scilicet T, qui omnes sunt equales semicirculo A D C .
Alberti, O p e ra in e d ita (Florence, 1890), pp. 305-07. I have, however, come up with a quite different set of letters for the missing figure (see Text C, Fig. 9). As the text stands in the manuscript (which is obviously not the original version), the letters referring to the missing figure are mutually inconsistent and must be corrected in some fashion. If we adopt Mancini’s assumption that A B C F marks the smaller circle and A B E H the larger one, somewhat fewer corrections are necessary than in my scheme, but then we have the absurdity in the text that the smaller circle is to the larger one as 2 is to 1.