By Marshall Clagett
Read Online or Download Archimedes in the Middle Ages, Vol. 4: A supplement on the Medieval Latin traditions of conic sections (1150-1566). Part i PDF
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Extra info for Archimedes in the Middle Ages, Vol. 4: A supplement on the Medieval Latin traditions of conic sections (1150-1566). Part i
Let there be a [right] cone whose apex [is] A [see Fig. 12], [whose] diameter of the base [is] BC , [whose] center of the base [is] D , and [whose] axis [is] AD, which [cone] is cut by a plane surface through the axis, according to triangle ABC, by the 90th [prop,] of this [book]. And let another [plane] surface u Ed. of Unguru, pp. 273-74: ‘‘[Propositio] 98. Omnis superficiei plane secantis pyrami dem rotundam non per verticem et superficiei conice pyramidis communem sectionem figuram triangularem esse impossibile.
Hence the straight line joining these points falls inside the cone [by Proposition 1]. Therefore, kel, being on the surface of the cone, is not ex tended in the straight line of any two points posited on kel. Hence kel is a curved line. And so let us posit point m on kel, drawing from it a perpendicular to triangle abg, and let it be the perpendicular mn. It is clear, therefore, that it falls upon the common section of plane deh and triangle abg, which is dz, and it falls upon the segment of this line inside the cone, because it falls be yond points, from which the tangent perpendicular eh is drawn.
To mg. scr. m. 1 sicut patet ex 6 elementorum et libello de proporcionibus thebith 43 post et1 dei. P et 4 4 - 45 supra ts2 . . similiter scr. m. I per 2 6‘ elementorum 4 5 - 46 de proporcio . . hn mg. scr. m. I Istud per 7am aut 9 aut 10 5“ patet 51 de Fig. 4 scr. mg. m. ) et cont. supra triangulus scindit piramidem per medium et inferius est alia figura (cum notis) in m. 3, que non est bona et eam hic omitto Prop. 5 1 sub 5 mg. scr. m. 1 disposicio 10 post dez mg. scr. m. 2 que est in superficie trianguli abg ita quod e est in puncto sectionis et z est diametro basis piramidis inter extremitates diametri et a puncto e protrahitur linea eh perpendicularis in puncto e in triangulo abg 59 60 ARCHIMEDES IN THE MIDDLE AGES 25 30 35 40 45 50 55 finitum.
Archimedes in the Middle Ages, Vol. 4: A supplement on the Medieval Latin traditions of conic sections (1150-1566). Part i by Marshall Clagett