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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 28, page id 898203430:0056
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VINCENTM VIVLAM PRO LOCIS.
Nam lateralis tangens C, A maior est a verricali CB; quare L. C ad
uio. Sc MaL. A, vel F B ad BD est in minori ratione qua F. C7 ad CB, vel (his
cum aequalibus perMUIEAEIS) quam F. O ad D I: erGO DIEI producta COn
venit b cum C F. ad parres F sectioni contrarias, ve in M.
C87. DEMI I FllipE au em prolatai lateralis tansens C A, minor est c verticali
BC; quare F C ad CFA, vel F B ad BD maiorem habet rationem quam
EC ad C B, vel (his cum aequalibus permutatis) quam FO ad DI:
ergO HTD producta convenit cum P. C intra D C ad partes centri .
VE in NI.
Dico amplius, in Fyperbola; Occursum M cadere inter verricales
XR, BC cangentes ad opposicas lectiones. In Fllipsi vero prolata cade
re intra verricalem tangentem R R priori BD oppOlicam.
Si enim producatur CF doncc cum R R conveniat in R, iungaTuKquC
a 1b. hujus diagonalis DC: constas d iam iptam DC in eodem puncto l convenire,
(ed DI secac angulum E DC, quare producta D B in Frperbola, secabie
ER IICEF FaNSENCES RR, e CB, _ in prolata, ad partes centri intra R R.
Praterea, in lingulis fxuris, prima excepta, ex occursibus HI, M cum
lateralibus A F, C L ordinentur rectX HIL, MN, ecaxis scgmentum L. N
Disecetur in P. Dico primum punctum P, in Parabola, Hyperbola, de
Ellipsi oblonga, cadere inter N, _ F.
Producatur FIL ad S. Et erit TIL aequalis ipsi L S, eritque NM ad
L. S, Vel NE ad F L VE N M adHIL, SIVC vE N D ad DL, sed ND
maior eAt DL., ergo ee NVF maior eAt F. L: hoc est punctum P bilecans
NVL. cadic inter N, _ F.
In EExperbola vero dico punctum P cadere inter sectionis centrum 
_e ordinatam FTL verrici B propiorem.
Ac S ordinata MI N ceciderit in centrum C, vel intea vexsus F: iam
latis constat propolicum.
Si vero M N ceciderit inter R e O: prOdUICANEUE D M, NM donec
illa Cum R R, haec aurem cum iuncta diasonali D C3 R conveniant in
Y, V, _ agatUE ex V ipSi OHI aequidistans V X. FE quum (I AD aequa
lis DC, ee in criangulo DRC, sIE CR ad RM, vel DY ad Y M, vi
D C ad V M, erit quoque D Y ad YM VE AD ad VM: qUarC A Y
transir per V, ideoque, in triangulo AVHI, quae ex V ducitur basi AII
aequidistans secat Y II inter puucta X, M, vE in Z: Cunque sIE _E V M
Paralela ad OI  laterA XMI, FII ad eandem rectam D X applicata, crune
triangula VXM, GTII aequiangula, d circa aequales angulos V MX.
CTTI CFIE V M ad MX vE CT ad TFT, Sed permutando est V M maior
CTC in criangulo V D M) ergO _ M Z maior YFI, _ CO magis MY
maior FII: quare ( ob paraItelaS RK, MH, TTL, GB) CriE _ RN ma-
ior L. B; Sed K  Donicur aequalis QB, ergo reliqua NO minor est relir
qua OL; ideoque punctum P Bilecans totam N L. cadit infra FTyperbo
lxe centrum vertus ordinatam HII. vertici B propiorem.
Insuper in prolata Ellipli: dico punctum P bilecans lesmentum HL. Ca.
dere incer Sectionis centrum Q. de ordinatam N M vertici B remotio
rem.
2 87. PrimI
nOMrX VI.
_ et In
b 15. RuIU
ad v. 2.
nolla DI
at. A~ MaX
de Min.