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# Title: Optica Promota, Seu Abdita radiorum reflexorum & refractorum Mysteria, Geometrice Enucleata (shelfmark Leibn. Marg. 94)
# Folio 17, page id 727094130:0029
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coD. 8. Lemma.
Conoide, vel Sphaeroide, secta plano ad auem perpendiculari; sectione
fit Circulus. Centrum habens in axe.
Tridacur Conois, vel Sphaerois, plano ad axem A C perpen-
diculari, occurrente in puncto R, _ sic sectio (L. FI I, quom
dicoesse circulum: Fcenim per axem A H C planum agACUF Fa-
ciens sectionem PAFC, occurrentem secanci plano perpendiculari
ad axem, in punetis I, M, ad quae a puncto R ducaneur linea, III, KMI,
Qui ad aXeM AHC Cunc perpendiculares; ex proinde ordinacim ap-
plicarae: cum enim ex revolurione sectionis BAC. D, in consticurione
tigura, FaCtuS SIE. CIrCUIUS P ED F, cujus radii TunE CB, CB, C D.
CF, ad axem recti, et proinde ordinacim quoque applicaci;
joitur unusquisque erium Radiorum aequalium CB, C L, C D,
habee ad quamtiber sibi parallelam lineam e cribus HG, K Y AP. I. 2T.
K II, eandem rarionem, unde pAteE (cum C B, C F, C D
FDE aequales) _C KG, KI, K H esse aequales; igitur circulus eA
GMHILI, cujus, cencrum I, in axe conoidis vel sphaeroidis; quod
demonstrandum erat.
3. 95
lFOP. 9. Lemma.
Si Conoidem, vel Sphaeroidem, tancat planum, es per punctum con-
tactus, es arem, ducarur aliud planum; Dico haec duo plana se
invicem normaliter secare.
IcConois, vel Sphaerois ABD, quam cangac planum HIOF
in puncto F, perque punctum F, e axem figurae producacue
planum BE ALD, donec secec planum HIOF inrecta TF. Dico
plana HTCE, BEALD, se invicem normalicer secare. Pet DUn-
ctum F ducatur planum F M L. N, perpendiculare ad oxem A C,
de producacur, donec secec planum HIIOF in recta GH; SC
quoniam EI C esnoir circulum F M L. N, eric ad ipsius diame.
ETum FL perpendicularis; SC quia PlaNA B AD, FML, SC
invicem secan normalicer, _ HC in plano P. M L N, est Per-
pendicularis
B RujIS.
3. 18.