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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21836
Erigatur ex A contingenti A G perpendicularis A L, quæ axi 1188. pri-
mi huius. ret in L, cui applicata A H, erit intercepta L H æqualis dimidio 2290. pri-
mi huius. B I, hoc eſt dupla interuallo D B, (cum punctum D diſtet à vertice B
per quartam recti lateris partem ex hypoteſi) & H G dupla eſt quoq; 3335. pri-
mi conic. G B, quare, & tota L G dupla eſt tota G D, ſiue L D æqualis D G, eſt-
que angulus L A G rectus, quare ſi
cum centro D, interuallo G, vel L
179[Figure 179] circulus deſcribatur, ipſe omnino
tranſibit per A; vnde D A item æ-
qualis erit ipſis D G, D L, ſiue L G
erit dupla D A. Et cum rectum axis
B D, ad rectum diametri A E, ſit vt
quadratum A H ad A G, vel 44Coroll.
24. huius. triangulorum ſimilitudinem, vt qua-
dratum A L ad L G, vel vt recta
H L ad rectam L G (cum L A ſit
media proportionalis inter G L, L H)
ſumptis harum ſubduplis, erit rectũ
axis ad rectum diametri A E, vt D
B dimidium H L ad D A dimidium L G. Quod erat demonſtrandum.
Vocatur autem punctum D, focus Parabolæ.
COROLL. I.
HInc cõſtat, omnes eductas à foco ad Parabolę peripheriam, ęqua-
ri quartæ parti rectorum, earum diametrorum, quarum vertices
ſint termini, quibus ipſæ eductæ ſectioni occurrunt: rectum enim axis
B D ad rectum diametri A E, eſt vt D B ad D A, eſtque D B quarta pars
recti B I, quare, & D A erit quarta pars recti lateris diametri A E, & D F
quadrans recti, diametri F R. Vnde quò diametri ab axe remotiores
fuerint, eò ipſarum recta maiora erunt. nam eſt D F maior D A, & c.
COROLL. II.
PAtet etiam, quamlibet eductam ex foco, ęquari aggregato ex inter-
uallo foci ab axis vertice, & ſegmento axis inter verticem, & ap-
plicatam ex occurſu eductæ cum ſectione. Oſtenſa eſt enim D A æqua-
lis D G, quæ æqualis eſt aggregato G B, cum B D, vel H B cum B D.
SCHOLIVM.
CVm demonſtratum ſit D G æqualem eſſe D A, erit angulus D G A,
vel parallelarum externus E A M, æqualis angulo D A G, ſed M
A G Parabolen contingit in A, quare ex Opticæ legibus, ſi E A fuerit
radius incidens ad concauam peripheriam A B C, ipſe A D erit 55Breuiùs,
& clariùs
quàm à
Vitellione
in 41. 9. xus, atque omnes radij axi Parabolę æquidiſtantes in punctum D coi-
bunt; vnde ſi ipſi fuerint ſonori, aut lucidi, ſimulque calidi, ibi

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