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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 157, page id 898203430:0185
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ORDINATIONNM CONIC. LIMIMBVS LIB. I.
SHIX cransi per C. Ex quum rectangula sub I. O, OF, _ sub his aequa-
libus MO, OE quadratis aequalium OC, OH aequalia Cint, ve lupra.
demonstrauimus, recta A L, C L Iyperbolas COHTINBCHE 2 in pUIeTIS 2 exconver
A, C.
(037. Primi
Amplius, sit quicunque alius ramiis DV ad latus BA ductus, et alius Conien
guilibet DK ad idem lacus AB produccm, de ex V, B, K. tinc ordi-
natae Z X, 23, T5.
Ouum itaque sit quadratum OC aequale quadrato D F, vel duobus
DO, OE; dempro communi OF, eric rectangulum HIF. C aequale qua
drato DO.
InSUPer, qLU ReCt ABK, C BX OppOsitaS Sectiones contingane ad
R. C. Timuilque conveniant in B, halque, d Hrpeibolas secene rectae
CH, ZX, 23, TS ipsI AC cactus iunsenti parallelae, crune inter se
reccangula HIE. C, YVZ, 3B2, S R T ve sune b quadrata seGMCNIO 2 20. certii
rum tangentis, hoc est ve quadeata AF, AV, AB, A K, vel ve qua- Conic.
draca his proportionalia DO, D4, DB, DR, sed rectangulum HFC
aequale nuper octensum fuit quadrato DO, ergo, e rectangulum YV L
quadrato D4, _ rectangulum 3 B 2 quadrato DB, _ rectangulum SRY
guadrato DR aequale eric: Si primis igitur commune addatur quadratum
4. cerriis vero commune quadratum I R, erune ibi rectangulum
YVZ, cum quadrato V 4. sive vnicum quadratum Z 4 aequale quadia-
to D4 cum quadrato 4 V, Sive rnico quadrato D V; hic vero rectangu
lum S H. T cum quadrato K R, Sive rnicum quadracum SR, vel R V
aquale quadrato D R CII quadraLO RK, sive vnico quadrato D K: ac
demum quadrarum DB rectangulo 3 B 2, Siue quadrato B2 aequale: qua-
DTOPTEE CaI raMI DV, DA, DF, DB ducti ad latus A B dati anguli
rectilinei, quam ramus DK, aliique sic ducti ad productum latus BK in
angulo ad verticem RB Z, aequales sine luis lemiordinaris +Z, DA, OC,
B2, R T vique ad converum IIyperbolae ZGT. Et Sc de lingulis ramis,
atque semiordinatis ad aliam Fyperbolam oppolitam Y HIS. OuarC_C.
Ouod incerim circa Ordinationes cantum ramorum noux cuidam doctri-
nae destinatas supererac demonstrandum.
FitUdInCI FAMIL MIMIII. DIItat enIm per B, quae est disterentia inter ver
ticalem ramum DB, _ DO alcicudinem minimi eami DF..
dinatis ex origine, ee ex termino rami minimi. Ostensum est enim qua-
deatum OC aequale rectansulo I. OF, vel sub AD ex origine, de sub
PO ex termino minimi rami ordinata, quod aequatur quoque rectanoulo
Tub eamo verticali DB, ∞x sub minimi alticudine D O: nam ob similitu-
dinem crIanSUIOTUIM BD A, E. OD latus BD ad DA eA vE F. O ad OD,
idco.
Ducendum se praebet ex dictis, centrum O distare a verrice
LBdaci anguli per differentiam inter ramum verricalem, de 2l.
2. Praeterea lemiaxem Limitum OC posse rectangulum sub semior-