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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 80, page id 898203430:0108
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=108
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VINCENTII VIVTANT DE LOCIS SCLN
eROPOSTELOIXXXXVI
NV Ellips prolata. Limes Ordinationis normalium su
per ramos ex vertice ductos erectarum, est ad Locum
concauum Eyperbolae per oppositum verticem sibi cir-
cumscripiae, cuijus rectum latus recto Ellipsis datae est
aequale, transuersum vero est tertia proportionalis post
differentiam laterum datae Fllipsis (5 ejusdem transuer-
sum latus.
FT FIIiOiS prolata A B, CUIUS VeTECX B, EANIHCUS LAIS HIIHOTBD.
Dde rectum BF ad B CONFINGCNECT OEdINAtM; SIEque D C ip( BD in
elirectum, ac tertia proportionalis post differentiam laterum BF, B D, 8
latus BD, d cum transuerlo axC CD, per verricem D, d cum recto la
terc aequali ipsi BF descripca sic FIyperbola D PF. Dico hanc esse Li-
mitem Ordinationis propolita; videlicet, duco per verricem B ad FIlipsim
quolibet ramo BA, iplique erecta normali AK, et per A d ca int
Hyperbola recta C L hanc ipli AK aequalem esse
lunsatur regulatrix F D, quae
producta, cum C. L. a puncto C ipB
B F. aequidistanter ducta, conveniae
in L, _ TC, F B producanur ad
F, M, H, Sumacur que BO iph BD
requalis.
Et quum siC, ex suppolicione, dit.
ferenria inter FB, BD, sive inter
EB, BO, nempe EO, ad BD, E
uc ad OB ita BD ad DC, ex
componendo L B ad B O, vel ad
BD, ve B G ad GD, _ Coner-
cendo DB ad BF, vel DC ad C. L, ve eadem DC ad GB, ergo 6l.
C B lunc aequales.
Praecerea quadratum B F ad rectanoulum D B C habet rationem com
POsitam ex ratione BP ad BC, sive ad GL, d ex ratione B F ad BD,
sive ET ad E D. e ratio BF ad C=D, ex jisdem rationibus BF ad CL.
_ GL, ad C D COmpOsica es, ergO quadeatum BF ad rectangulum DBC
2 primi est ve linea BF ad C D, hoc CA ve Polimr rectum latus FIy perbolX DH
ad latus cransuertum ciuldem (ex Fy pothe(i) vel ve 2 quadeatum semiora
dinatae IIB ad rectangulum DBC; quadratum ergo B F ad reCtaVOU
lum DBC est ve quadratum B HI ad idem rectanoulum D BC; ideoque
Tunc aequalia quadrata BF, B HI, ac propterea delcripea Fyperbola
EID nECeISariO TxanSIE per P terminum recti laceris BF data FllipsIS.
Amplius, quum Sectiones HDE, BAD sinc per cundem vericem
DA.
COnic.