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Sed \/ 1 a X TTT, ex Corol. 2. Prop, a, = A F. Unde A C . A 8 
:;AF.KV. 
6. Redla K I diipla eft ipfius A B. Cum enim B I = (B C 
=)CA + AB, ent AI = CA + iAB; At AK = AC, 
per Corol. 4. hujus ; Igiuir K 1 = 2 A B. 
7. Redangulum fiib A C & B R eft aequale dnplo fpatio 
hyperbolico B A H. Nam F R x A C = (a + xxVaax + x' 
a 
X a = a + X X V lax +x2 = X X V Hx + x2 + ^ ^ V IIx + xz 
= ABxBH + ACxBH:=)ABxBH + ACxBD-{-AC 
X D H. Qiiare F R x A C — B D x A Q hoc eR B R x A C 
= ABxBH + ACxDH. Sed, per Prop. 4. hujus, A C x D H 
= A G F fpatio. Et igitur BRxAC=(ABHL + AGF = 
per Corol. i. Prop, jr.) 2- B A H. 
Prop. 7. Theorema. 
SI in Curva Logarithmica LAG cujus data 
fiibtangens HS asqualis redtae a, Corol. 2, 
Prop. 2. hujus definitse, fiimatur pundum A cuju^ 
dift^ntia ab H P afymptoto, nempe A C, aequalis fit 
fiibtangenti H S, & ex pundtis H & P utcunque in 
afymptpto fumptis a puncSto C sequaliter diftanti- 
bus, erigantur H P G ordinate ad Logarithmi- 
cam, quarum femifummas ponatur sequalis H D vel 
P F, erunt D & F ad Catenariam reitse A C eor- 
refpondentem. 
Vocetur A B x, adeoque C B vel D H femifurama ordina- 
tatum H L, P G erit a+x ; femidifferentia earundem vocetur y. 
Unde H L = a-j-x + y,^ & PG = a + x — y. Cumq[ue ex 
natura LogarithmicsKj C A fit inter has media proportionalis, 
erit a^ -|- 2 ax -j- x'' — y"" == a^ Unde y = VHTTlz. Ad- 
eoque H L = a 4" X + a X + x2 & P G = a -f X — V^ax 
n a ' ' r x:iT r ri n ax+XX+X\/x ax +x2 
Quare fiuxio ipfius H L,five ipla 1 m elt . 
^ - y zax +x2 
C c c c c z Et 
