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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 172, page id 175905688X:0194
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172
FR AN CESOF A SCHOOFEN
Ximus; hoc est, angulus D F A aequalis sic angulo C R B. Produ-
Catur autem BC, ut seCeE D F in I; _ PEFD aGatUT rCCta D FI
parallela ipsi AF, occurrens cum BC in FI. Ouoniam igitur si
milia (UnE erianOuIa DFTT _E R L NF crianGUIO F AD, CrunEe
ipla inter se similia. EIndeerie uEK P ad L N, hoc est, ut b adc,
ita D HI Seu AB, hoc Cst, X, ad FII, qua ideocrit ? Deinde
subducta FIT ex HB Ccu D A, hoc ett,  ex a. F6, relinqueeur
TB, a Lc - =. F qua SI anteratuT B C SCuy, remanebit TC,
a 6 C -y. Ouia rero in FIyperbola rectansulum ICB
aquatur rectangulo DP A, Per 2O proP. 2 di libri Conicorum
Apollonii; ideo simulciplicetur IC per C B, hoc eA, a Lc-
 -y pery, tiec rectansulum ICB, ay + cy -  3 -yy
aequale rectangulo DF. A Scu ac, hoc est, ei quod Hc ex ductu
ip(IuS D F seu C A in P A. Ouare ordinata aquarione, Factaque
cranspolitione, uc ry unam obtineat aequationis partem, inve-
HICTUF Y y ∞ Cp. CY  ay - ac. Ouae aequatio eadem est,
qua supra ex motu regula OP _ rectae linex C. R fuit inventa.
Adeduc aftirmare liceat, delcripeam lincam curram C P I Iy per-
bolam esse, cujus AIympEoti AF, FD; quemadmodum sup
poluimus. Duorum pleniorem demonstrationem qui deliderat,
contulat capur sum cractatus nostri de Organica Conicaru Se-
ctionum in plano descriptione, ubi casus omnes prosecuri luimus.
Sed utile fuerit unum aut alterum Problema simile adijun-
BeIC.
In plano quocunque concipiatur moveri AB regula, mobilis
circa punctum fxum A, atque huic regulae affixa alia aequalisrc.
sula BD, in puncto B, ut limilicer circa punctum B in eodem
plano moreri pollic. Allumpeo aurem in B D inter B e D quo-
vis puncto F, e commoro puncto D per rectam lineaim AD;
Duxritur cujus generis suc curra linea, quam punctum F. motu
illo describied
Duoniam isitur ad hanc quaeCtionem oportet cognoscerere.
lationem, quam hujus currae puncta habent ad puncta linea rectae
AD, in qua punctum A eAt datum; CuxpOnO ex PunCtO F, 2d
quod
1
D
e
e
aGu
ab algr
H H X