By Marshall Clagett
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Additional info for Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv
P Prop. 2: A I------ 1 C I------ 1 E__ B Prop. 4: (occurs only in a, p and M ): The diagrams do not go with any of the fragments proposed to fill the lacuna at Prop. 4, and they contain extra letters (V, T, X) not required in the text for any of the 8 proofs of the De ponderibus Archimendis. The large number of letters appearing here that are common to the incomplete proof of Prop. 8 suggest the possibility of the original existence of some proof similar to that of the eighth proposition. P L I Variant readings: A .
Quare per 27 et 28 primi D I , F E sunt equidistantes et equales, et ideo E I, D F equales. / Similiter et E I , I P , quia a centro. Ergo I P , D F equales. 70 Igitur additur equalibus, scilicet F O addita ipsi DE, et D I addita/E; que quidem F O , D I sunt equales, quia F O equalis EE cum a centro, et F E , D I equales, ut visum est. Ergo exeunt D P ,D O equales; a quibus equalibus amotis, scilicet D N , D A , quia utraque semidyameter, restant Q P , N O equales. Cadit ergo maxima cathetus lunule hexagone intra trigonam.
P / enim G: NB E d d l-2 157 B: H pM / E in C: E et C b CE E d d l-2 / L: AL u / C2: E b E d d l-2 / post C2 add. Ed3 Et quia quod fit ex E in C et ex D in C est tanquam quod fit ex F in E, ergo quod fit ex F in E aequum est ei quod fit ex C in A cum eo quod fit ex D in B. 158-65 Si . . mixti om. p 158 8 mg. I 2, om. abpM Ed3 propositio 8a mg. E ddl-2 1 mg. 0 2 / post equalia add. b magnitudine / duorum I 159 mixtum om. E ddl-2 160 utrisque E d d l-2 I genere . . simplicium om. I / genere: grave M Ed3 1305 1306 DE PONDERIBUS ARCHIMENIDIS ARCHIMEDES IN THE MIDDLE AGES 165 170 175 180 UNUM GRAVIUS RELIQUO ERIT PARTIS MIXTI QUE IN IPSO EST DE GENERE GRAVIORIS AD PARTEM QUE IN IPSO EST DE GENERE LEVIORIS PROPORTIO TANQUAM PROPORTIO DIFFERENTIE PONDERIS MIXTI AD PONDUS LEVIORIS AD DIFFERENTIAM PONDERIS GRAVIORIS AD PONDUS MIXTI.