( «4» ) 
in prsecedetitis Prop, conftruflione , fluxio ordinatz B F 
= --f — . Quare hsec conflrudlio eodem redit cum con* 
(Irudlione Prop, prsecedentis^ & confequenter pun£lum F eft 
ad Catenariam. q. e. d. 
Corottarium> 
Sicut in Prop, priced. Catenaria deicribitur ex data lonei- 
tudine Curvae parabolics, ita in hac, illius deicriptio pendec 
^ quadratura fpatii in quo x' = a* — i a x y*. Nam y (five 
BK) = -^. 
Txax +X2 
Trop. 4,. Theorema. 
Fig. I. CPatium AGF fub Catenaria AF & redis 
^ FG, AG ad AB, BF parallelis compre- 
henfiim, aequale eft re<Stangulo fiib femi-axe A C, & 
D H intervallo applicatarum in Hyperbola 2c Ca- 
tenaria. 
• » 
ax X X 
Nam D H = (BH — B D =, ex Prop. 2. hujus, — 
V r a X + x2 
ax XX 
— =) s ' Quare fluxio re<ftanguli fub da- 
Vxax+x^ Viax-x2 
ta AC&DH = ( 7-^— = xx— i-— =:fsxFG=) 
Va.ax+x2 V»ax+x2 
fluxioni fpatii AGF. Cumque figurae hae fimul nafcaniur, fe- 
quitur re6langulum fub AC & DH sequari fpatio AGF. 
q. e. d. 
CoroUarium* 
Hinc fequitur fpatium FAD, fub Catena F A D & refta Ho- 
rizontali F D comprehenfiim, aequari redlangulo fub F D & B A, 
dempto redlangulo fob Hyperbolae A H axe alterutro, & D H 
cxceflii re£tae B yel Curyae A fupra ordinatam B D. 
Trop. 
