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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 83, page id 898203430:0111
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GRDIHATIONNM CONTO. LIMITTBVS LIB. I.
83
FTB, BF aequalia sunE C ob octentam lacerum xequalitarem) eroo ee an-
cecedentia, hoc est rectanoulum NF C quadeaco TC aequale eric; rectan
Gulu verO N F. C aequatur rectangulo B KE C (quum tam BC, C N
quam C K; CF 2 _ quam ideo BK, NF sinc aequales) sve OUadratO
medix proportionalis A HL inter BK, KC (in triangulo rectanouio BAK,
in quo AC super B R eAt perpendicularis) ergo de quadracum AH
aequale est quadrato PC: ideoque normalis AK semiordinatae IC est aequa
lis, e sic de lingulis sec. Ouare concauum Hyperb. Cl est Limes propolicus,
MI O N I Y V M.
acione huic simili, aliaque breniori methodo ostendi possent, plurima
praecedentium, ex consequentium Theorematum, nullo muliorum auxiu
lio, quae in prima parte Libri huius demonstrantur; sed quum haec nostris
alis Geomeiricis opem ferant; hanc ideo viam, licet lonziorem, ad amaenam
viique eruditionem nos ducentem, eligere statuimus. Quod secunda
hac vice maxime interest animaduertisse.
PROPOSITIO LMNM
N Oppositis Sectionibus. Limes Ordinationis norma
lium super ramos ex unius vertico ad sectionem Op.
positam ductos erectarum, est ad Locum concauum al
terius Eyperbolae per verticem ipsius oppositae circumseri-
ptae, (9 cuius idem est rectum latus, transuersum vero
est tertia proporcionalium post summam laterum datae
Eyperbolae co transuersum ejusdem.
Ine Sectiones oppolin
aD ta AB, RD, quan
rum axis tranluerus DB.
rectum lacus BF. Ordin-
cim applicatum ad B. d Frac
Ve SUmMa laterUM D B,
BF ad DB, ita DB ad
BC, de per verricem B
cum erantuerso (B, reu
etoque B E delcribatur
FEyperbola LB; quae Ca-
dec extra AB, guum
GEHTregulatrix ipsius IB,
infra tansentem B F. 10-
ta Cadac extrA regulatricem D F F alteriuS A B (ex prop. 29. prim. Lib.
de MaX. _t Mir.). Edis poluis: Dico si ex verrice D, data oppolicarm.
243. uius.
duCcUS