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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 67, page id 898203430:0259
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VARIAR: DISPOSTTTONYM LIMIT. LIBFR III.
eL0lLL datal
Oeus subtensarum ex eodem termino datae rectae ter-
minatae usque ad normales ordinatas ad datam line-
am, sive ad productam ad partes sumpri termini, es
potentium summam duorum quadratorum, alterum ex
data, alterum ex huius parte assumpia inter propriam
ordinatam, (5 reliquum datae terminum, est ad conca-
num Parabola, cuius axis verrex sit hu idem termin
nus, rectum vero latus sit duplum datae.
O quod necestario constabic, dum ipsus conversum demonstrandum.
Preponaur ve sequicur.
N Parabola. Ouadratum rami ducti ab orreine sut
in termino semirecti lateris ab axis vertice super axem
extensi, aequatur quadrato seomenti axis inter ordinatam
per rami terminum, (5 verticem intercepti, ona cum
guadrato semirecti ejusdem.
SrO rarabola AB, cuius axis B C, vertex B, de lemirectum latuS
LBD, SIEquC ex D ramuS quicunque DA, vel D C ex terminis vero
A. C. sinc ordinatae ad axem AC, C7II. Dico quadrarum D A duobus (-
mul CB, BD, ec quadratum D C duobus siiuL HB, BD aequale cC.
Ponatur primo ramum D A cadere
intra ordinatam F D L. Fixit ergo qua-
dratum leiniordinatae A C aequale a
rectangulo Tub C B in latus rectum,
nempe in duplum iptus BD, hoc eA
duplo rectanculi (ub CB in BD, sed
duplum sub C B in BD aequacur du
plo sub CD in D B cum duplo qua
drari D B, ergo _ quadratum A C
dupso rectanguli sub C Id in D B cum
duplo guadrati DB xquale est, de ad
dico communi quadrato D C, crue duo simul quactad AC, CD, vel
rnicum quadratum rami D A aequale duplo rectansuli C. DB cum duplo
quadrati DB, Se cum quadrato CD, sed duplum rectanguli CDB cum
quddratis BD, DC xqualu nico quactraco C. B, sse0 qadracum 19.
odi vci