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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 107, page id 898203430:0299
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=299
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# Lines: 42 recognised, mean confidence 0.91
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ADDEHDA LIBRO SECONVO.
P R OBH.
Ata quavis Fyperbola ABC, eusas ht centrum . se-
midiamerer transversa DB, ac semidiamerri secundae
conjucarae sint DP, D E quantum libet utrinque productae
versus C, F: si inter convexum curvae ABC, e rectam
EP, ductae fuerint quorcumque rectae TA, LC aequidistan-
res ipsi semidiametro transversae DB. Dico, harum ordi-
natarum quadrata ad assrecata quadratorum partium se-
cundae diametri P F, inter hujus terminos, e ipsas ordina-
tas contentarum, semper illam eamdemque rationem habe-
re, quam habet datae Flyperbola diameter transversa, Cud
ordinatae aequidistant, adt duplum sui recti lateris.
Cal enim hajus EIyperbolae ABC semidiamerer traniverla D B P0-
ceric duplum DL, vel D F Temiconjugata; jam per decimamno-
nam Propolitionem Libri Sccundi hujus, constabit provolicum:
Ouoniam in figura, quae ibi ad p28. 12. Libri Secundi, quadracum
C. D ad duo liniul equalia quadraca C. A, C B, est ue semitransver-
sum C D a duo simul lemirecta latera FIyperbola CFDF, vel uc la-
cus eranlverlum ad duo simul recta lacera.
Acli in hac Fyperbola
ABC quadratum D BFueriE
vel majus, vel minus duplo
quadraei lacundae diametri
D F. (manence haC D H)
Donatur hoc loco, quod
quadratum DO, SEPExCISC
duplum quadrari D F; ec
concipiatur alia IIy perbola
MON concentrica dats
ABC, e cujus eadem sIE
secunda diamerer, conjugara eidem eransvetse DB; quaeq; iplasl A,
LC secet in MI, N. Jam constat, ex secunda Propolicione Libri Pri-
mi hujus, omnes ordinaeas ab his FIrperbolis proportionalicer di-
vidi; ac ideo, e quadrata iplarum esse proportionalia; sed rario
quadratorum IMI, DO, L N crea summas quadracorum P. L, IF 3
HD, DF; E L, LF, est semper eadem aequalicatis, ut in ProPOlIE.
XIX. Secundi hujus ostensum fuic; ergo ratio quoque quadratorum
LA, DB, L. C. ersa eaIdem summas quadratorum, erie semiper ca-
dem, sed ejuldem inaequalitaris.
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d