Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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recta AE vtranque ſectionem contingat. </
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<
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tex D eſt infra alterius verticem B, totam cadere intra ſectionem ABC, hoc
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eſt ei eſſe inſcriptam, & </
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<
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<
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<
s
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">Nam producta AE vſque ad occurſum cum diametro in E (ſi tamen ap-
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plicata AC non fuerit diameter circuli, vel Ellipſis, vt ſecunda figura, quo
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<
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">27. ſec.
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conic. &
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6. eiuſd.</
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in caſu contingentes AE, CE ſibi ipſis, & </
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<
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">coniugatæ diametro BT æquidi- ſtabunt) iungatur ECO, quæ item vtranque ſectionem continget in C: </
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<
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applicetur quæcunque L O. </
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<
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">_lo_ eaſdem ſectiones ſecans in I, N, G, M. </
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<
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_g, m_, contingentes verò in L, O. </
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<
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<
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">ducanturque ex verticibus tangentes
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BQ, DP, quę ordinatim ductis æquidiſtabunt, & </
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">iungatur AB, ſecans DP
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in S.</
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<
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<
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">Iam cum ſit AH æqualis H C, erit LF. </
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æqualis FN. </
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xml:space
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">_fm_ (ſunt enim ſectionum ſemi-appli-
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catæ) quare reliquæ LI. </
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</
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<
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">_o m_ inter ſe æquales, ideoque rectangulum OIL. </
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NLI. </
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">rectangulum OGL. </
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conic.</
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ctione ABC ſit quadratum BQ ad quadratum QA, hoc eſt quadratum SP ad PA, vt rectangulum NLI. </
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<
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<
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">ibidem.</
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ADC quadratum DP ad idem PA ſit vt rectangulum MLG. </
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<
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">_l_A, habeatque quadratum SP ad PA minorem rationem
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quàm DP quadratum, ad idem quadratum PA, habebit quoque rectangu-
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lum NLI. </
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<
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<
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MLG. </
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<
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<
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<
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<
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eſt OIL. </
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<
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60. h.</
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vnde punctum I remotius eſt ab ipſo F quàm pũctum G. </
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<
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">_g_ ſectionis ADC cadet intra ABC, & </
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<
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de quolibet alio puncto ſectionis SADCT, præter A, C: </
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ſcripta erit ſectioni ABC, & </
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plicatæ ſe mutuò contingent. </
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nonſtrandum.</
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<
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ctionis, vel circuli, ad vtranque diametri partem rectis lineis iun-
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gantur, ipſæ ſimul, & </
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<
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">in eodem diametri puncto conuenient, à
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quo, ſi ad terminos ordinatim ductæ per interſectionem diagona-
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lis cum diametro, ducantur aliæ rectæ lineæ, hæ omnino ſectionem
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contingent.</
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<
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">SIt menſalis coni-ſectionis, vel circuli ABCD, cuius baſis, AD maior,
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BC minor, diameter E F. </
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<
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">Dico ſi iungantur AB, DC, ipſas cum dia-
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metro, & </
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<
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metrum in G, & </
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<
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occurſum ducantur rectæ, ipſas ſectionem contingere.</
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<
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">ipſi parallela, occurret AB cum FE ad par-
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<
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mi conic.</
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tes B, E, vt in H; </
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<
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