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

Table of contents

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[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)
[41.] THEOR. IV. PROP. XI.
Page: 43 (23)
[42.] COROLL.
Page: 44 (24)
[43.] MONITVM.
Page: 45 (25)
[44.] LEMMA III. PROP. XII.
Page: 45 (25)
[45.] ALITER idem breuiùs.
Page: 46 (26)
[46.] ITER VM aliter breuiùs, ſed negatiuè.
Page: 47 (27)
[47.] COROLL.
Page: 47 (27)
[48.] THEOR. V. PROP. XIII.
Page: 47 (27)
[49.] COROLL. I.
Page: 49 (29)
[50.] COROLL. II.
Page: 49 (29)
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255
Ducatur enim per N linea RNS parallela ad BC, eſt autem & MN ipſi DE
æquidiſtans, quare angulus RNM æqualis erit angulo BGD, nempe 1110. Vn-
dec Elem.& planum tranſiens per MN, RS æquidiſtabit plano per BCDE, hoc 2215. Vn-
dec. Elem. baſi coni; ſi igitur planum per MNRS producatur ſectio circulus erit, 334. primi
conic. diameter RNS, atque eſt ad ipſam perpendicularis MN, ergo rectangulum
RNS æquale eſt quadrato MN, vti rectangulum BGC æquale eſt quadra-
to DG.
Iam cum ſit NX parallela ad GV, & NS ad GC, erit in prima figura GV
ad NX, vt GC ad NS, ob æqualitatem; in reliquis verò erit GV ad NX, vt
GH ad HN, vel GC ad NS, ob triangulorum ſimilitudinem; quare permu-
tando in omnibus, GV ad GC, erit vt NX ad NS.
Amplius cum in prima figura factum ſit vt quadratum FG ad rectãgulum
BGC, ſiue ad quadratum GD, ita recta HF ad FL, vel ad GV ei æqualis, ob
parallelogrammum FV, erit FG ad GV, vt GV ad GD; quare rectangulum
FGV æquatur quadrato DG, ſiue rectangulo BGC. Item in reliquis figuris,
cum factum ſit vt rectangulum HGF, ad rectangulum BGC, ita recta HF ad
FL, vel HG ad GV, & idem rectangulum HGF ad rectangulum FGV ſit vt
eadem HG ad GV, erit rectangulum BGC æquale rectangulo FGV: cum
ergo in ſingulis figuris rectangulum BGC æquale ſit rectangulo FGV, erit
BG ad GF, ſiue RN ad NF, vt VG ad GC, ſiue vt XN ad NS: rectangulum
ergo RNS, ſiue quadratum MN æquatur rectangulo XNF. Linea igitur MN
poteſt rectangulum ſub ON, & NF, quod adiacet lineæ FL, latitudinem
habens FN, in prima figura, ſed in ſecunda ipſum rectangulum excedit, &
in tertia & quarta ab eodem deficit, rectangulo ſub LO, & OX, ſimili ei,
quod ſub HF, & FL continetur. Quod erat demonſtrandum.
Definitiones Primæ.
I.
Sectio DFE, cuius diameter FG in prima figura æquidiſtat AC vni laterum
trianguli per axem, vocatur PARABOLE.
II.
Et cuius diameter in ſecunda figura occrrrit vtrique lateri trianguli per axẽ,
dicitur HYPERBOLE.
III.
Et cuius diameter, in tertia, & quarta conuenit cum vtroque latere infra
verticem trianguli per axem, ELLIPSIS nuncupatur.
IV.
Segmentum verò HF diametri ſectionis inter latera trianguli per axem in-
terceptum, in ſecunda, tertia, & quarta, dicitur LATVS TRANSVER-
SVM Hyperbolæ, vel Ellipſis, quod in ſequentibus intelligatur ſemper
extra Hyperbolen ex ipſius vertice in directum poſitum cum diametro,
licet in conſtructionibus expreſsè non dicatur.
V.
In omnibus autem figuris linea FL, quarto loco inuenta, dicitur LATVS
RECTVM ſectionis, quod deinceps concipiatur ſemper contingenter
applicari ex ſectionis vertice, ſiue ordinatim ductis æquidiſtans.

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