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

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[Item 1.]
[2.] DE MAXIMIS, ET MINIMIS LIBRIDVO.
[3.] DE MAXIMIS, ET MINIMIS GEOMETRICA DIVINATIO In Qvintvm Conicorvm APOLLONII PERGÆI _ADHVC DESIDERATVM;_ AD SERENISSIMVM FERDINANDVM II. MAGNVMDVCEM ETRVRIÆ. LIBER PRIMVS. _AVCTORE_ VINCENTIO VIVIANI.
[4.] FLORENTIE MDCLIX Apud Ioſeph Cocchini, Typis Nouis, ſub Signo STELLÆ. SVPERIORVM PERMISSV.
[5.] SERENISSIMO FERDINANDO II. MAGNODVCI ETRVRIÆ.
[6.] IN DIVINATIONEM GEOMETRICAM DE MAXIMIS, ET MINIMIS PRÆFATIO. AMICE LECTOR.
[7.] Il Principe Leopoldo mano prop.
[8.] Il Principe Leopoldo mano prop.
[9.] Il Principe Leopoldo mano prop.
[10.] DE MAXIMIS, ET MINIMIS Geometrica diuinatio in V. conic. Apoll. Pergæi. LIBER PRIMVS. MONITVM.
[11.] THEOR. I. PROP. I.
[12.] Definitiones Primæ. I.
[13.] II.
[14.] III.
[15.] IV.
[16.] V.
[17.] VI.
[18.] VII.
[19.] VIII.
[20.] IX.
[21.] COROLL.
[22.] MONITVM.
[23.] PROBL. I. PROP. II.
[24.] ALITER.
[25.] ALITER.
[26.] MONITVM.
[27.] LEMMAI. PROP. III.
[28.] PROBL. II. PROP. IV.
[29.] MONITVM.
[30.] PROBL. III. PROP. V.
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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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