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

Table of contents

< >
[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.
[31.] PROBL. IV. PROP. VI.
[32.] PROBL. V. PROP. VII.
[33.] MONITVM.
[34.] THEOR. II. PROP. VIII.
[35.] MONITVM.
[36.] LEMMA II. PROP. IX.
[37.] THEOR. III. PROP. X.
[38.] COROLL. I.
[39.] COROLL. II.
[40.] MONITVM.
[41.] THEOR. IV. PROP. XI.
[42.] COROLL.
[43.] MONITVM.
[44.] LEMMA III. PROP. XII.
[45.] ALITER idem breuiùs.
[46.] ITER VM aliter breuiùs, ſed negatiuè.
[47.] COROLL.
[48.] THEOR. V. PROP. XIII.
[49.] COROLL. I.
[50.] COROLL. II.
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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.

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