Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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xml:space
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">Nam ſit quæcunque recta DBE ſectionem contingens in B: </
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<
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</
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<
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<
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">conic. </
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<
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xml:space
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">ipſam DE cum vtraque aſymptoto conuenire, & </
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>
<
s
xml:id
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xml:space
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">ad tactum B ſe-
<
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cari bifariam, & </
s
>
<
s
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xml:space
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">quadratum vtriuſque portionis DB, BE æquale eſſe quarte
<
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parti figuræ, quæ ad diametrum CB per tactum ducta conſtituitur; </
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>
<
s
xml:id
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xml:space
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">quare ſi
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fiat CA æqualis CB, appliceturque quælibet GIH ipſi DB æquidiſtans,
<
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aſymptoton, ſectionem, ac diametrum ſecans in G, I, H, & </
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>
<
s
xml:id
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xml:space
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">per I ducatur
<
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IP parallela ad CD, ſecans diametrum in P infra C (nam punctum I eſt intra
<
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/>
angulum GCH) erit vt in præcedenti oſtenſum fuit rectangulum AHB ad
<
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/>
quadratum HI vt quadratum CB ad quadratum BD, vel vt quadratum PH
<
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/>
ad quadratum HI; </
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<
s
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xml:space
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">vnde rectangulum AHB æquale erit quadrato HP, ſiue
<
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recta HP erit media proportionalis inter AH & </
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<
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xml:space
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">HB; </
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<
s
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">hoc eſt punctum P ca-
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det inter C & </
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<
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">B; </
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<
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">quare IP, quæ ipſi GC æquidiſtat contingentem BD ſeca-
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bit in Q, eritque BD maior DQ, ſiue maior intercepta GI.</
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<
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<
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18
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<
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<
s
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">Iam applicata infra G qualibet alia RN diametro occurrent in O, ex N du-
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cta ſit NS parallela ad RC, quæ contingentem BD, ac diametrum ſecabit vt
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ſupra in T & </
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<
s
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">S. </
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<
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xml:space
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">Cumque rectangulum AHB ſit æquale quadrato HP, vt mo-
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dò oſtendimus, ſitque in directum ipſi AH addita quædam HO, erit, per
<
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præcedens Lemma, rectangulum AOB maius quadrato OP, ſed rectangu-
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lum AOB eadem ratione, vt ſupra, oſtenditur æquale quadrato OS; </
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<
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xml:space
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">quare
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quadratum OS maius eſt quadrato OP, hoc eſt punctum S cadit inter C, & </
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P, ſiue CP eſt maior CS, vel DQ maior DT, hoc eſt GI maior RN. </
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">Quare
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aſymptoton
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CD, & </
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">ſectio BIN quæ in infinitum productæ, nunquam ſimul
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conueniunt, ad ſe propiùs accedunt; </
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<
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">idemque de aſymptoto CE. </
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<
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primò &</
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">c.</
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<
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<
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<
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tur STN parallela ad CD diametro occurrens in S, ſeceturq; </
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