1
PROPOSITIO X. PROBLEMA. V.
Sunto CA, CBſemiaxes Ellipſeos; GP, DKdiametri conju
gatæ; PF, Qtperpendicula ad diametros; Qvordinatim appli
cata ad diametrum
20[Figure 20]
GP; & ſi compleatur
parallelogrammum
QvPR,erit (ex CoNI
cis) PvGad Qv quad.
ut PC quad.ad CD
quad.& (ob ſimilia
triangula Qvt, PCF)
Qv quad.eſt ad Qt
quad.ut PC quad.ad
PF quad.& conjun
ctis rationibus, PvG
ad Qt quad.ut PC
quad.ad CD quad.
& PC quad.ad PF
quad.id eſt, vGad
(Qt quad./Pv) ut PC quad.
ad (CDqXPFq/PCq). Scribe QRpro Pv,& (per Lemma XII.) BCXCA
pro CDXPF,nec non, punctis P& Qcoeuntibus, 2PCpro
vG,& ductis extremis & mediis in ſe mutuo, fiet (Qt quad.XPCq/QR)
æquale (2BCqXCAq/PC). Eſt ergo (per Corol. 5 Prop. VI.) vis centri
peta reciproce ut (2BCqXGAq;/PC) id eſt (ob datum 2BCqXCAq)
reciproce ut (1/PC); hoc eſt, directe ut diſtantia PC. que E. I.
gatæ; PF, Qtperpendicula ad diametros; Qvordinatim appli
cata ad diametrum
20[Figure 20]GP; & ſi compleatur
parallelogrammum
QvPR,erit (ex CoNI
cis) PvGad Qv quad.
ut PC quad.ad CD
quad.& (ob ſimilia
triangula Qvt, PCF)
Qv quad.eſt ad Qt
quad.ut PC quad.ad
PF quad.& conjun
ctis rationibus, PvG
ad Qt quad.ut PC
quad.ad CD quad.
& PC quad.ad PF
quad.id eſt, vGad
(Qt quad./Pv) ut PC quad.
ad (CDqXPFq/PCq). Scribe QRpro Pv,& (per Lemma XII.) BCXCA
pro CDXPF,nec non, punctis P& Qcoeuntibus, 2PCpro
vG,& ductis extremis & mediis in ſe mutuo, fiet (Qt quad.XPCq/QR)
æquale (2BCqXCAq/PC). Eſt ergo (per Corol. 5 Prop. VI.) vis centri
peta reciproce ut (2BCqXGAq;/PC) id eſt (ob datum 2BCqXCAq)
reciproce ut (1/PC); hoc eſt, directe ut diſtantia PC. que E. I.