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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 267, page id 1066518432:0295
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DE VERTDOS ET MIOTTBOS COREOROM. LIB. II. 267
rectam IEC in a, _ OK in puncto h interlecans; junsaturque Ke
e producatur in a, per quod punctum alia de ducta lic priori DC
aequidistans: aGANEUE Pariter dL _ OC, item Cn parallela Od, et
rs parallela OK, hyperbolae ordinata P B continuetur usque in B,
et CD usque in d; quibus factis per quadrantis puncta  ScR du-
cta sint tangentes CTe RI, quae aequalescrunt; quibus pexeparatis
I. Liquet Fore aL. Parallelam cansenti los-micae in puncto C,
quandoquidem hujus log. micxe subtangens (secundum hiypothelin)
aequalis est OL; atque adco dd Parallela et sequalis erit particulx
L0g-mica CC, ac etiam cn = Dd.
II. Priangula similia OFB, OAF prXbeNt OR~: FB. =OA:
AF2. Vel, quia in hrperbola quadratum OF. aequatur binis quadra-
eis OA_ FB collectire sumtis, crit etiam OA L E B: EB =OC2:
OTT; e diridendo ON: F B =GTT: OTI vel AF, vel inver-
tendo ac permutando EB: AF2 =OG: OTP. AEqui EB. AF: -
OB: OF: = 2. triang. BOB ad 2. triang. FOf, id cst, ad rec lum FHI.
HIh, ergo 2. triangulum BOB: FHI. IIB = OC.: 6II.
TIT. Trianoula similia Cea ex OIK exhibent 6g: ca = OT: IK,
unde, quia tangentes IK et Cil aequantur, etiam (8 et sa requales
CeUnE.
TV. Propter parallelas Od de B, crit Od: Dd = he vel IIC: a8
vel (nUM. TFT.) C2. X invertendo ac permutando Vd: C =Od:
OHL, at Do: Dd = OL. vel O6: Od, ergO Cx aquo Dd: (18 =O6:
GHL, ex proptextriangula similia OCFL et Ger, Hc 68: r8 vel Ff.-
OO: CFI erso ex xequo ex per rationum compositionem, Dd: lif =
OA. D d: FTI. Ff = OG: GTI (HM. TF.) = 2. triangulum BOB: FFI.
Ffrel FHI. IIB. Adeoque 2. FrianS. AOB =O A. DD (nuM. L.) =OA.
cn. ergo omnia 2. BOB id est duplus scetor BAO = omnibus cn in AO,
id est rec. 10DC in AO. Ouod crat demonstrandum.
Miter.
464. Per hsperbolae punctum B ducta luetansens B l, ac per pun-
ctum P recta TV parallela OR rectae OB occurrens in puncto V,
ac denique asatur Bd Parallela AD.
I. Ostendam, quod PV producta transibit per punctum C, adeo
ut TO =GTI. Nam in hyperbola lincxe OTI, OA ec OF Tunc in
continua ratione, atqui propter tansentem BT, etiam OI, OA
ec OE sunc in continua ratione, ergo OT =6II.
II. ElC.