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

Table of contents

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[221.] THEOR. I. PROP. III.
Page: 184 (2)
[222.] LEMMA III. PROP. IV.
Page: 185 (3)
[223.] THEOR. II. PROP. V.
Page: 186 (4)
[224.] THEOR. III. PROP. VI.
Page: 188 (6)
[225.] LEMMA IV. PROP. VII.
Page: 189 (7)
[226.] THEOR. IV. PROP. VIII.
Page: 191 (9)
[227.] THEOR. V. PROP. IX.
Page: 193 (11)
[228.] SCHOLIVM.
Page: 194 (12)
[229.] THEOR. VI. PROP. X.
Page: 195 (13)
[230.] THEOR. VII. PROP. XI.
Page: 195 (13)
[231.] THEOR. VIII. PROP. XII.
Page: 197 (15)
[232.] THEOR. IX. PROP. XIII.
Page: 198 (16)
[233.] THEOR. X. PROP. XIV.
Page: 199 (17)
[234.] THEOR. XI. PROP. XV.
Page: 200 (18)
[235.] LEMMA V. PROP. XVI.
Page: 201 (19)
[236.] COROLL.
Page: 202 (20)
[237.] THEOR. XII. PROP. XVII.
Page: 202 (20)
[238.] THEOR. XIII. PROP. XVIII.
Page: 203 (21)
[239.] THEOR. XIV. PROP. XIX.
Page: 204 (22)
[240.] PROBL. I. PROP. XX.
Page: 205 (23)
[241.] MONITVM.
Page: 206 (24)
[242.] THEOR. XV. PROP. XXI.
Page: 207 (25)
[243.] PROBL. II. PROP. XXII.
Page: 208 (26)
[244.] PROBL. III. PROP. XXIII.
Page: 212 (30)
[245.] MONITVM.
Page: 215 (33)
[246.] THEOR. XVI. PROP. XXIV.
Page: 216 (34)
[247.] THEOR. XVII. PROP. XXV.
Page: 217 (35)
[248.] COROLL.
Page: 217 (35)
[249.] THEOR. XIIX. PROP. XXVI.
Page: 217 (35)
[250.] COROLL. I.
Page: 218 (36)
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22442
Iam ducatur per D quælibet alia F D G.
186[Figure 186] Et cum in triangulo D G C ſit externus
angulus D C L maior interno D G C, fiat
angulus D G H ipſi D C L, ſiue D A F æ-
qualis, eſtque angulus G D C æqualis an-
gulo A D F, & duo ſimul D A F, A D F
minores ſunt duobus rectis, ergo & duo
D G H, G D C erunt duobus rectis mino-
res, ſiue G H cum D C producta conue-
niet, vt in H, eritque reliquus angulus H
in triangulo D H G æqualis reliquo F in
triangulo D F A: quare huiuſmodi trian-
gula ſimilia erunt, & circùm æquales an-
gulos ad D habebunt latera proportio-
nalia, ſiue vt A D ad D F, ita G D ad D
H, vnde rectangulum A D H æquale erit
rectangulo F D G, ideoque rectangulum
A D C minus erit rectangulo F D G, & hoc ſemper vbicunque applicata
ſit per D, recta F D G præter A D C. Quare rectangulum ſub ſegmentis
A D, D C eſt _MINIMV M_ quæſitum. Quod erat faciendum.
PROBL. V. PROP. XXXIV.
A puncto intra coni-ſectionem dato rectam applicare, cuius
rectangulum ſegmentorum ſit MINIMVM. In Ellipſi verò, &
MAXIMVM rectangulum reperire.
ESto primùm A B C Parabole, vel Hyperbole, vt in prima figura, cu-
ius axis B D, & datum intra ipſam punctum ſit E. Oportet per E re-
ctam ſectioni applicare, ita vt rectangulum ſub eius ſegmentis ſit _MINI-_
_MVM_.
Applicetur per E recta A E D C axi ordinatim ducta. Dico hanc ip-
ſam quæſitum ſoluere: ſiue rectangulum A E C eſſe _MINIMVM_.
Nam applicata per E qualibet alia inclinata F E G: non abſimili mo-
do, ac in 26. ſecundi conicorum, demonſtrabitur applicatas A C, F G in-
tra ſectionem ſe mutuò ſecantes in E, in ipſo E nunquam bifariam ſimul
ſecari, ex quo ipſarum applicatarum diametri diſiunctæ erunt inter ſe,
ideoque B vertex portionis A B C non erit vertex portionis F H G: is er-
go ſit H; ducaturque ex B ſectionem contingens B I, ſiue applicatę A C
æquidiſtans; itemque ex H recta contingens H I, ſiue F G parallela, que
contingentes ſimul conuenient in I. Erit ergo rectangulum A E C, 1158. pri-
mih. rectangulum G E C, vt quadratum B I ad quadratum H I; ſed eſt 2216. tertij
conic. tingens B I, ad axis verticem, minor contingente H I, ergo & quadra- tum quadrato minus erit, ſiue rectangulum A E C minus rectangulo F E
3387. primi
huius. G, & hoc ſemper quæcunque ſit quæ per E applicatur diuerſa ab appli-
cata A C, ergo rectangulum A E C eſt _MINIMVM_ quæſitum.

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