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

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[251.] COROLL. II.
Page: 218 (36)
[252.] SCHOLIVM.
Page: 218 (36)
[253.] LEMMA VI. PROP. XXVII.
Page: 219 (37)
[254.] LEMMA VII. PROP. XXVIII.
Page: 219 (37)
[255.] LEMMA VIII. PROP. XXIX.
Page: 220 (38)
[256.] THEOR. XIX. PROP. XXX.
Page: 220 (38)
[257.] SCHOLIVM.
Page: 222 (40)
[258.] COROLL.
Page: 222 (40)
[259.] LEMMA IX. PROP. XXXI.
Page: 222 (40)
[260.] THEOR. XX. PROP. XXXII
Page: 223 (41)
[261.] PROBL. IV. PROP. XXXIII.
Page: 223 (41)
[262.] PROBL. V. PROP. XXXIV.
Page: 224 (42)
[263.] DEFINITIONES. I.
Page: 225 (43)
[264.] II.
Page: 226 (44)
[265.] LEMMA X. PROP. XXXV.
Page: 227 (45)
[266.] THEOR. XXI. PROP. XXXVI.
Page: 227 (45)
[267.] THEOR. XXII. PROP. XXXVII.
Page: 229 (47)
[268.] SCHOLIVM.
Page: 230 (48)
[269.] LEMMA XI. PROP. XXXVIII.
Page: 230 (48)
[270.] LEMMA XII. PROP. XXXIX.
Page: 232 (50)
[271.] THEOR. XXIII. PROP. XXXX.
Page: 235 (51)
[272.] COROLL. I.
Page: 237 (53)
[273.] COROLL. II.
Page: 237 (53)
[274.] COROLL. III.
Page: 237 (53)
[275.] PROBL. VI. PROP. XXXXI.
Page: 238 (54)
[276.] PROBL. VII. PROP. XXXXII.
Page: 238 (54)
[277.] COROLL.
Page: 239 (55)
[278.] THEOR. XXIV. PROP. XXXXIII.
Page: 240 (56)
[279.] THEOR. XXV. PROP. XXXXIV.
Page: 240 (56)
[280.] SCHOLIVM.
Page: 242 (58)
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page |< < (36) of 347 > >|
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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