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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 58, page id 898203430:0086
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=86
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VINCEN LH VIVANT PROLOCIS.
R O POS ITIO XXXI
N Sectionibus Oppositis. Si vnius Fyperbolae recata
ad alteram partem intra oppositam Sectionem produca
tur, in qua sit quaecunque semiordinata reculatricem;
secans; ibsius quadratum aequale est rectanculo sub sui
sermento inter regulatricem ac diametrum interposito.
C9 sermentum diametri inter ipsam semiordinatam; (5
Flyperbolam, cuius data est reculatrix.
(InE OpPOsiX Sectiones A B C, DFP,
aquarum communis transuer la diamer
ter L B, _ ip(IBSA B C SIE VerTCX B, TC.
ctum latus BC ad B continsenter posicum,
e regulatris P. C, quae ad partem oppoluta
DEF producatur donec conveniae in I cum
qualibet in ipsa semiordinata D IS, quae
diaetro occurrat in R. Dico quadratum.
iplius DR rectangulo BRI requale esse.
Ducatur ex vertice F. continsens F. HI, et
aequalis Aac ipA BC, iunsaturque BH, 8
Producatur donec protractum DR lecet in L. Frit el BMIL LCGaI
Sectionis D F F: quare quadratum D K rectangulO F KL aequale est 
F. primi EF quoniam BIE ad RI. eAt ve BF ad F HL, vel ve EB ad BC, vel ve LR
2d KI, eric reccangulum sub mediis F. K L. Ciuc quadratum semiordinatue
D K, aequale rectansulo sub extremis B K L. Quod Cxac, ec.
P R O P OSTYIO
Lltata
N Sectionibus Oppositis. Ouadrata ramorum ad vnam
Sectionum ab orisine in vertice reliquae oppositarum. sunt
inter se et rectansula sermentorum axis inter ordinatas
ex ramorum terminis, Co terminos Moduli ex semire.
cto eiusdem Oppositae interceptorum.
E TNE OppOsita Sectiones ABC, DEF, quarum axis EraNIUEKUS L B,
 licque ABC rectum latus BC concingenter applicatum ad B, d FC
rCsULatrIX; BL vero sI ipsiuS A BC Modulus ex semirecto, inVentIS Per
lemirc Ccum angulum EBI, vE in PFOP. F3. X DeFin. 2g. huius; X ex B ad aliam
OPDOSITaM D F F Sic quicunque FamUS A F, C cuius termino F SIC ad diame-
nrum BF H or dinaca FH. Dico quctraeum rami B F. a quadracum rami
On6.