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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 57, page id 898203430:0085
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=85
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 46 lines, status machine
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VEL LMET. ORDIBAHOAEM CONC. LIB. L.
D Fpetita pERCCdeNEI AOUTA; CK CONFACF A Ad _ILIHCCLMIH R BI DIAMC.
aL cur A PLC quae cangenes BC, IBHue Putalelae O P. aequidittabic)
iansacurque lL. (quae itidem Sectionem concinget da L. pel primns
Conicorum, e producta ad O nunquam cum Sectione L D COnveNIEL:
Ex 33. Sec. Corundem) ac producatur D F ip(S IL, AL OccurrenS in O, P,
Cirque tandem quae libet alia ordinatim ducta RX Sectionem AB, TansCn
tes, de diametrum secans in.
5, V; in R, X, de in T. Di
co rectangulum OD F ad
R S X esse ve quadratum leg.
menei A F ex tangente AC L
ad quadracum scemenci AI
ex eadem AC F.
Nam cium sIE A P ad R F
Vt P I. ad L R, vel ve P P ad
KO, Lique permutando A P
requalis PL, erit quoque F R
aequalis KO, Sed est DK aequaliS R F (cum B K sIC diameteK) erSO d
reliqua DP aequalis reliquae FO; rectangulum igItUE ODF, aequale est
rectangulo F F. D: Sed rectangulum P F D ad quadratum tangentis BC
CstVe 2 quadratum F. A ad quadratum A C; quadratum vero BC ad re. 229. huius.
Atangulum VRS, Sive ad R SX est vED quadratum A C ad quadratum b 16. cercii
AR, ergo, ex aequali, rectangulum OD E, siuC F F. D ad rectangulum R S X Conic
est ve quacratum F. A ad quadratum AR. Ouod erat demonstrandum.
M.
I vero in Sectione F D Ruerit alia quacunque ordinatim ducta, cam
Pecans in V, _e Contingentes TL, AL in 9, Z; itidem ex demonstr-
tis octenditur rectangulum ODE ad OYZ esse ve quadratum tansentis
AE 2d AZ.
Habet enim rectangulum ODF ad RSZ rationem quadrati AF. ad
AR, ve in superiori conclusimus, de RS X ad OYZ CAt, ob candem 12-
cionem, vi quadratum AR ad AZ, ex aequo isitur rectangulum ODF.
ad OYZ est ve quadratum AF. ad AL.
PraterCA: Si concipiatur ex vertice 3. diametri BN ducta contingens
34. eric etiam quadeatum 3 4 ad quadratum BO, ve quadratum A 4 ad
AC; de ad rectangulum RSX ve quadratum A4 ad AR, ee ad ODF
ve quadratum A+ ad AF..
Nam ob cansentem AL, est 3L ad L. B, vel 34 2d BC vt c 3 P ad c 36. primi
PB, vel ve A 4 ad AC, ergo e quadratum 3 4 ad BC erit ve quadra- Conic.
tum A4 ad AC. Sed BC quacracum ad rectansulum RSX eA vE qua-
dratum C A ad AR, ergo ex aequali quadratum 3 4 ad R S X est vI
quadratum A4 ad AR. RCctangulum verO RSZ ad ODF. eAt vE qua.
dracum A R ad AL, er50 icerum ex aequali quadratm 3 4 ad rCCTAI.
culum ODF est ve quadratum A 4 ad AF..
PrOPO-