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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 98, page id 898203430:0290
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VINCEHLII VIVIAMI DE LOCIS SOLIDIS
PROBL. XI.
PROP. ZXRXV.
Utam rectam terminatam AB se dividere, ut quadra-
rum sermenii majoris, sit medium arichmerieum, inter
quadratum minoris, es quadratum torius: vel secare da-
tam AB secundum mediam, e extremam rationem arith.
meticam quadratorum.
per Lem. Y Tridatur data AB in C sic  ue rectangulum (vD
AB in BC quadrari segmenri reliqui A C sic
subduplum; ec punctum C Problema POIVeE.
Jam patet, et Facile octendieur ex his duobus leg.
meneis ese majus AC, _ C B minuS.
Insuper summa quadracorum datae AB, Sc segmenLI BC eQUAEUE
b7. Lib. 2. Quadraro segmenti reliqui AC cum duplo rectanguli lub AB, in
BC, vel, ob constructionem, cum quadeaco AC; quare eadem lum-
ma quadrarorum, datx AB, ee segmenei minoris BC aequatUT du-
plo quadraci AC. leomenci majoris ejuldem date; ac ideo heec erin
quadrata AB, AC, C B lunc in concinva ratione arichmetica 3, 2, 1,
sive quadratum A C. legmenti majoris est medium arichmericum,
incer quadrarum AB corius, ec quadrarum C. B legmenci minoris;
sive secta est data AB in C secundum mediam, e extremam eatio.
nem arichmeticam quadracorum. Ouod crat ec.
PROBL. XII.
PROP. XXXXVI.
Aram rectam terminatam AB, sic in duo sermenta inae-
qualia dividere, ut sermentum majus sit medium har-
monicum inter datam, e sermentum minus. Ouod iden est,
ac secare datam secundum mediam, es extremam rationei
harmonisam.
Nempe secare datam sic, ut si ipsa sumatur pro primo termi-
no, sermentum majus pro secundo, e sermentum minus pro
tertio; primus terminus sit ad terrium  sive data recta ad
sermentum minus) ut primus excessus ad secundum exces-
sum; sive sit ut excessus, quo data recta superat majus sec.
mentum, ad excessum, quo majus sesmentum superat ses.
mentum minus.
ma praeced.
EteM.