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

Table of contents

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[11.] THEOR. I. PROP. I.
Page: 22 (2)
[12.] Definitiones Primæ. I.
Page: 25 (5)
[13.] II.
Page: 25 (5)
[14.] III.
Page: 25 (5)
[15.] IV.
Page: 25 (5)
[16.] V.
Page: 25 (5)
[17.] VI.
Page: 26 (6)
[18.] VII.
Page: 26 (6)
[19.] VIII.
Page: 26 (6)
[20.] IX.
Page: 26 (6)
[21.] COROLL.
Page: 26 (6)
[22.] MONITVM.
Page: 26 (6)
[23.] PROBL. I. PROP. II.
Page: 30 (10)
[24.] ALITER.
Page: 30 (10)
[25.] ALITER.
Page: 31 (11)
[26.] MONITVM.
Page: 32 (12)
[27.] LEMMAI. PROP. III.
Page: 32 (12)
[28.] PROBL. II. PROP. IV.
Page: 33 (13)
[29.] MONITVM.
Page: 35 (15)
[30.] PROBL. III. PROP. V.
Page: 35 (15)
[31.] PROBL. IV. PROP. VI.
Page: 37 (17)
[32.] PROBL. V. PROP. VII.
Page: 38 (18)
[33.] MONITVM.
Page: 39 (19)
[34.] THEOR. II. PROP. VIII.
Page: 40 (20)
[35.] MONITVM.
Page: 41 (21)
[36.] LEMMA II. PROP. IX.
Page: 41 (21)
[37.] THEOR. III. PROP. X.
Page: 41 (21)
[38.] COROLL. I.
Page: 43 (23)
[39.] COROLL. II.
Page: 43 (23)
[40.] MONITVM.
Page: 43 (23)
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3616 tranſeunte, & horum communis ſe-
12[Figure 12] ctio ſitrecta E F, cui in plano GEH
perpendicularis ducatur recta G B H
ad vtramque partem plani A E F pro-
ducta, in qua ſumpto quocunq; pun-
cto G, fiat, vt G B ad B E, ita B E ad
BH; (& erit rectangulum BGH æqua-
le quadrato BE, vel BF) iungaturque
BA, & per H in plano per HG, & GA
ducto agatur recta HI ipſi BA paral-
lela.
Itaque cum GH, EF in vno ſint pla-
no, ac inter ſe perpendiculares, ſitque
rectangulum GBH æquale quadrato
vtriuſque EB, BF, ſi circa G H, tan-
quam diametrum deſcribatur circulus
GEHF, ipſe tranſibit per E, & F. Si
ergo intelligatur recta IAG circa pe-
ripheriam circuli GE, H F conuerti,
manente eius extremo puncto I, deſcribetur conus IGH cuius vertex I, ba-
ſis circulus GH, & communis ſectio conicæ ſuperficiei cum ſubiecto plano
erit linea EMANF, quam dico eſſe Parabolen quæſitam.
Conus enim IGH, cuius vertex I, & baſis diameter GH ſecatur plano per
axem deſcribens triãgulum GIH; ſecatur autem, & altero plano EAF (quod
eſt datum ſubiectum planum) baſi coni non æquidiſtante, cum eam ſecet,
ſecante baſim coniſecundum rectam lineam EF, quæ ad GH baſim triangu-
li per axem eſt perpendicularis, atque eſt AB diameter ſectionis EAF vni
laterum H I trianguli per axem æquidiſtans, talis ſectio E A F per primam
huius erit Parabolæ, cuius diameter A B, vertex A, & ordinatim ducta EF,
quæ ipſi diametro ad angulum ABF, dato angulo D æqualem, ap-
plicata eſt, ex ipſa conſtructione. Et cum factum ſit vt AB,
ad BE, ita BE ad A C, erit quadratum AB ad qua-
dratum BE, vel ad rectangulum GBH, vt
AB ad AC. Quare AC erit rectum
latus Parabolæ EMANF,
deſcriptæ vti quære-
batur: Quod erat
faciendum.
13[Figure 13]

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