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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 163, page id 898203430:0191
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ORDINATTONVM COMTO. LIMITIBVS LIB. L.
163
Nam ducta quacunque laterali FanSentC AH verticalem L F secante in
HI, axem vero in C, X per A applicata A DI secante FIyperbolam DL
in L. DicO DL. ipsi AHI aequalem esse.
Per verticem B datae Parabolae adscribatur FTyperbola BL, quae sIE LI
mes Ordinationis concingentium Parabolam, guarum vna est A C erit
ergo a BE huius rectum lacus, d F.B cranluersum, quum sc subquadeu- 2 ex Br. hu-
plum ipsius BF; ergo e rectangulum F DB, SiC quacrat DL in FAV- IuS.
Perbola aequilatera, erir lubquadruplum quadrati DI, hoc estlinca DL. di-
midium erit ipsuS DI, Sed etiam A FI dimidium CA FOTUS A GG, FOEX VerO
DI, A C sune aequales, erso de dimidiae ipsarum, nempe DL, AHI
aquales etUnE. OuaprOpter concauum huiulmodi Fyperbolae BL. est Limes
Parabolam cansercium, quarum vna est AFL. Ouod erat _C.
PROPOSTTIO LAXXNI.
X Porabola. Limes Ordinationis normalium super
Sectionem ductarum. C5 ad tancentem ex vertice or
dinatarum; est ad Locum conuexum FIyperbola in
vertice Parabola centrum habentis, (5 aequalium la-
terum, vtrunque recto Parabola aequale.
OVT Parabola A B, cuius axis B C, vertex B, de semirectum latus
B D, Factoque centro B per verricem D sic circa cundem azem BDR
Hyperbola aequilatera D F, de a quocunque Parabolae puncto A ducta
normali AF super Sectionem A B, _ per A recta G AF axi B C paral-
lela, quae producta, Hyperbolae occurrat in F. Dico normalem AF ip (I
CF. ad cansentem BC Ordinatim ductae aequalem esse.
Applicetur, in Parabola, ordinata
AC, _e F R in TIyperbola, iungatue
GD, de Tumatur BH in directum, ee
aequalis ipA BD, iea ve HID sic erans
versum Elyperbola DF.
Tam, in ParabOla, GuU SIE A F nOFI
malis ad punctum A, e AC ad axem
Ordinata, eric C F aequalis B ips BD
recti laceris dimidio: eltque AC equa
lis G B, ergo in criangulis rectangulis
A C F, G B D lubtenla A F, C
aequales etunE.
Praeterea, quum Eyperbola DF. (
requilatera, erie quadratu F. IL, sive
GB aequale reCtanguIO FLK D, e communi addito quadrato BD, crune
quactrara simul CB, BD, line rnicum GD, vel AF aequale rectansulo
HKD cum quadrato DB, hoc est vnico quadrato BH (nam HD secta
B Prop. dc
libri prii
itiarE. 
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