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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 82, page id 898203430:0110
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NINCENTIL NIVLAHL DLE L. OCIS SOLR
Ec quoniam ratio quadrati BL. ad reclangulum lBe componitilles
ratione linca FB ad BC, sive adt C L,  ex ratione BF ad B , lille
CL. ad C. D; ratio autem BE ad C D ex iildem componitur rationibus,
ereo rario quadraci B F. ad rectangulum D BC eadem est ac lincae BF
ad GD; Sed BL: est rectum Frperbolae C7FI, _ C D est ipsius crantuer.
sum, ex constructione, ergo quadeatum B F. ad rectansulum D B CY est
21. primi ve rectum F B ad crantuertum GD, vel ve 2 quadracum B HI ad idem
rectangulum DBC. Ouadrata igitur B F, B FI sunc aequalia. Ideoque
delcripca Hyperbola HC.
tran(ir necettario Pet P,
Quae produCtaOCCUEFALOF.
dina ae TC in M, iplaque
TC regulatricem secet inF.
Inluper, quoniam IIY.
perbolae HICF, AB SINE
Per diverlos vertices .
B simul adlcripeae, idem
que est earum lupremus
terminus D cransuerlorum
lateru D C, D B, at-
que iplarum recta latera
Donun ur requalia, eric re-
8. huius. Ctangulum ETBF ad TAM ve B quadratum D B ad D C, Vel ve qua
dratum BP ad C F, Sed permutando rectangulum II B F aGuaLUE quI.
drato BF, ergo de rectangulum I A M quadrato C F aequale exit, seu
quadrato C R C qua quum sic alticudo normalis A K super ramum BI
43. huius ductae, aequalis elt E iph C F vlque ad regulatricem D F ordinatae) lis
isitur communi addico quadrato C A, eric rectangulum PA M cum qui
drato AC, vel vnicum quadracum PC aequale duobus simuI CA, CH,
vel vnicO AK: id eoque Lemiordinata C L aequalis normali A K; Ex hC
de linsulis. Ouare concauum Fyperbolx C L est Limes PFOPOlituS. Ouoi
erat _C.
8
MIS OctauO Theoremate huius, ac per consequens Lemmate iplius.
bremus demonstrabitur semiordinata PC aequalis normali AK.
tam. quum primo loco supectus ostentum sic L. C sequalem este ipsi
CB, eric d CH asta CB.
Ex quoniam ratio rectanguli NF C ad quadratum B F componitur ex
ratione lineae C F ad BF, sive linea C D ad D B, d ex ratione linea
NF ad BF, vel NL ad L B, seu C C ad G B, et ex his componitur
quoque ratio rectanguli D CC ad D BC, sive (ob FIyperbolam) racio
quadrati PC ad quadratum HB, erso rectangulum NFC ad quadratm
BF est ve quadraium LC ad guacratum HB. sed consequentia quadrata
HB,
Conic.
lunsatur L B, quae producta secet CI in N.