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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 45, page id 898203430:0237
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=237
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ORDINATAEVM LOTCHLETM LMIL. LLb. 
COPOSITTO LMVII
Deus Ordinataram pocentium differentiam inter re-
ctangulum sub data, quae secta sit secundum extre-
mam, (s mediam rationem, in partem, quae minoris se
omenti sit minor, (5 quadratum reliqua partis ex 1ota,
est ad concauum FEyperbola aequilatera, cuus vertex fit
punctum datam secans in praedicta ratione, semiaxis
vero transuersus aequalis sit aepresato ex dimidio da
tae cum maiori seementorum ejusdem secundum extre-
mam, e5 mediam rationem sectae.
Cdata AB secta fuerit in C secundum extremam de mediam ratio
anem, ita ve BC sic legmencum minus. Constat rectangulum A B C
aequale esse quadrato C A, adeoque s BC vicunque leCCTUT In O, rC,
etineulum ABO, quod minus est A B C, minus quoque esse quadrato
AC, et co minus quadrato AO. Dico itaque, si in producta C A Lumatur
AF dimidio torius datae AB aequalis, _ cum centro F. cum semiaxe crans.
verlo FC delcribatur Eyperbola aequilatera PC9, hanc ese Locum PFO
Dolicum: hoc est ordinatam OR posse disserentium inter rectangulum
ABO, e quadracum reliqua partis OR.
11
Producatur semiaxis CF in H vsque ad semicireuli CFH peripheriam.
Ex eric C H avis deseripea Hy perbolae P C9.
Jam, quoniam AB secta est in C secundum extremam, de mediam r2.
tionem, ee legmenci maiori A C in directum est A HI aequalis agoregatO
ex AE CUM EH, vel CUM F C, vel agoregaTO ex duabUS AF CUM AC,
8 dux A F aQuaNIUE data AB, ex ConsructiONC, CFOO AHI RGUATUE
REGFeSATO ex data A B, _ CZ MLiOTi seGIeNIO A C, LCGMIENELI VerO
MInUS BC sectum est vecunque in O: ergo (per Lemma praecedens) re-
clansulum ABO cum HIO C, vel cum sibi aequali quadrato semiordinatae
OR, in Hyperbola, aequale est quadrato reliqui sesmenti OA: OUAPIO
PCeF