Viviani, Vincenzo - De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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5434 patet quomodo cuilibet horum trilineorum circumſcribi poſſit figura ex
æque-altis parallelogrammis, & c. quæ ſuperet proprium trilineum magni-
tudine, quæ minor ſit quacunque magnitudine propoſita.

Iam dico huiuſmodi trilinea inter ſe eſſe æqualia. Nam ſi ſint inæqualia,
alterum ipſorum, vt puta AHBCGA altero AHBE minus erit, & defectus ſit
ſpacium V; quo poſito circumſcribatur, vti nuper docuimus, trilineo AHB
CGA figura ex parallelogrammis SC, TN, VO, HP, & c. cuius exceſſus ſupra
trilineum ſit minor magnitudine V. quapropter talis figura adhuc minor erit
trilinco AEBHA, cui circumſcribatur, item per eaſdem lineas ipſi CB æqui-

31[Figure 31] diſtantes, figura ex totidem parallelogrammis EY, 1Z, 2& , 3I, & c. Patet nũc
talem circumſcriptam, alteri circumſcriptæ ABD 567, & c. ęqualem eſſe, cum
vtraq; ipſarum ex æqualibus numero, & magnitudine parallelogrammis cõ-
ſtet vtrunq; vtrique: (parallelogramma enim EY, BD, ſunt inter eaſdem pa-
rallelas, & ſuper æqualibus baſibus EB, BE; & parallelogrammum IZ æqua-
tur parallelogrãmo Q5, cum inter eaſdem ſint parallelas, & ſuper æqualibus
baſibus IQ, QN, & ſic de ſingulis) ſed circumſcripta ABD 567, & c. eſt 113. Co-
roll. 13. h. nor trilineo AEBHA, vt modò oſtendimus, ergo & circumſcripta AEBYZ
& I, & c. minor erit eodem trilineo AEBHA; totum parte, quod eſt abſurdũ.
Quare huiuſmodi trilinea inter ſe ſunt æqualia. Quod oſtendere propoſi-
tum fuit.

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Scan	Original
51	31
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53	33
54	34
55	35
56	36
57	37
58	38
59
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64	40
65	41
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