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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 116, page id 898203430:0144
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=144
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VINCENTIL VINLANt DE LOCIS SOLIDIS
ic
22C
CUIUS aXIS ETAHSVErSUS SIE MOduluS N L, guI de AIIL RECTuM L R SiE vi calt
suersus datae Fllipsis ad disferenciam lacerum ciuldem; ipsam Ayperbolam
esse Ellips circumleripeam, ejusque concauum esse Zimitem proxocum.
DuCaTUT ex A Cuper tansenem laceralem A P. perpendicularis AR.
23. lecun. Eric isitur OD ad D R ve 2 Ellipsis transuersum latus ad rectum, sed
noltrae Di
WIBAE. 1N
APOIL.
est quoque OP 2d PD ve idem transversum ad rectum, ergo cum tam
OP ad PD, quam OD ad D R Cu ve cransuersum ad rectum, crie per
convertionem rationis tam PO ad OD, quam DO ad OR, d quam
PD ad D R ve cransuersum idem ad lacerum differentiam, vel, ex con
Aructione, VENI. ad L B, sed PD ad DR, sumpea communi alticudine
B 19. huius DF, CA VE rectanGulUm PDF, vel NDL. ipsi aequale b ad rectangulum
ed num. 3. R D F, vel ad quadeatum semiordinata D A perpendicularis super balim
r9. huiu
E R in erianguIO rectanGUIO F AR, _ VE NE ad L B ita CA, ob FIypein
bolam, rectangulum idem N
DL ad quadratum semiordina.
Ex ex D in eadem Hyverbola,
er so reraque harum Secrionum
cransic per Ai ee ob caldem ra
tiOnes per C. Sed rectatien
ad cum, 2. IuI O PF xquale cA C quactra-
d ex conver
1037. Prim
COn16.
tO PL, CrBO LCCL F A, F C
concingune a Hyperbolam ad
A, C, Led iplae concingunt quo-
que Elliplim ad eadem punccak,
C ex constructione, ergo hu-
iulmodi Sectiones in ip(is tan
cum punCtis A, C, sC MIEIO
contingun e ideoque FIyper BO.
8E. primi la TA I. C est datae L Hlixs circumleripta. Secet itaque verticalem TAN
nottiae Vi
Winac. I
F 18. BuII5.
Sentem BG in O. Sicque altera verticalis K Tvique ad Fyperbolam, d
alius quicunque rnuS D5, AC per S Ordinetr V X.
Ouoniam isitur ex terminiS K, S, A, B, LAIMOLUM D K, DS, DA,
DB ac. ducta sune Ordinata ad aXCM B H datae FllipsIS, N L. vero est
Modulus ex verricali _c. erune quadraca rAIOrIM D H, DS, DB, DA,
vet rectangula NKL, NVL, NDL, NBL, vel, ob Hyperbolam TALC.
 Et DEmI VES Quadrata SemiOrdiNACAFIUIM R F, VZ, D A, BO, Sed quadratum r2-
Cont.
mi D A idem est ac quadeatum semiordinatae D A sibi homologx, ergo
de reliqua reliquis, et ipsi rami iplis lemiordinatis aequales crune singuli
singulis ec. Concauum erso deleripiae Hyperbolae est Limes propoliu
Ordinationis. Ouod erat _c.
Vum demonstracum sic OD ad DH, hoc est trantuertum
Elliplis ad rectum ese ve OL de PD, dividendo eric OR
ad
APOil.