Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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F G recta G H ęqualis dimidio re-
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cti B E, & </
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xml:space
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">ex H agatur H I paral-
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conic.</
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lela ad G F, & </
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">in angulo I H D per
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punctum F deſcribatur Hyperbo- le F A, quæ Parabolæ periphe-
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riam in vno tantùm puncto A ſe-
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cabit, & </
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<
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xml:space
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">iungatur F A. </
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<
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xml:space
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">Dico hãc eſſe _MINIMAM_ quæſitam.</
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<
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<
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xml:space
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">Applicetur A L, & </
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">ex A duca-
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tur contingens A M, axi occur-
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xlink:label
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">8. ſecũ-
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di conic.</
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rens in M, producaturque F A ad
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vtranque partem, quæ cum aſym-
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ptotis conueniet in I, D, eruntq;</
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<
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xml:space
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"> in vtraque figura, interceptę A I,
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F D inter ſe ęquales, ac ideo H L,
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G D ęquales erunt, ob ęquidiſtan-
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tes lineas I H, A L, F G, in trian-
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gulo I H D; </
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<
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">ſi ergo, in tertia figu-
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ra, dematur communis L G, & </
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in quarta, addatur, fient H G,
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L D inter ſe æquales; </
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H dimidia B E, quare, & </
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ipſius B E dimidia erit. </
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<
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niam quadratum A L æquatur re-
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primæ 1.
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huius.</
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ctangulo L B E, & </
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">rectangulum L B E, æquale eſt rectangulo ſub
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mi conic.</
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dupla L B, ſiue ſub M L, & </
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<
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">ſub dimidia B E, hoc eſt ſub L D, ergo qua- dratum A L æquale erit rectangulo M L D, ac ideo angulus M A D re-
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pt. Pappi.</
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ctus erit, ſiue F A erit ex contactu A contingenti A M
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11. h. ad
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num. 1.</
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laris: </
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">quare F A, in vtraque figura, erit _MINIMA_ quæſita. </
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">NOn te pigeat hoc loco, Lector humaniſsime, à ſuſcepta MA-
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XIMARVM, MINIMARV MQVE linearum inueſti-
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gatione circa reliquas coni- ſectiones, aliquantisper recedere,
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dum elegantiſsimam quandam, ac vere admirabilem affe-
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ctionem exhibere tibi decernimus, circa MINIMAS lineas, ad peri-
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pherias infinitarum Parabolarum, per eundem verticem ſimul adſcripta-
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rum, ex eodem communis axis puncto ducibiles, quarum veſtigia, dum
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hoc ipſam
<
unsure
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propoſitio prælo ſubijcitur, neſcio qua parùm morata cura inſe-
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qui voluimus. </
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">Huius itaque itineris delineatio, eſt quæ conſequitur.</
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