C S144 ) 
St quid forte fit QhfcHritatis in Regula,^//^^/^?^ exempli s illuftrahitfir: 
Data jit h£c ^quatie h y - y y =: v v V ^« EB fit b ^ BA , y , 
D A ^ V, quaratur a ' ftve A C talis y m jun^a DC tartgAt Cnr- 
vam D^lj^n D. Ex r egula , nihil reficiendnm eft ah hac ^qHatione^ 
Qum in fingnlis ejm partihm referiatfir y vet v. -Ita quoque difpofita efi-y 
fit ah mo latere fint omnes illim partes in qulhm y S (^h altera y omnes 
in quihm v. SingnHs-itaqtie tami^m fr<zfigendi^ eft Exponens poteflattSy 
^4am in illis hahet y vel v ^ & in latere fimfi.ro tinftm y vtrtendnm in a, 
m fiat ba-2y airzvv. A jo nnnc , hanc zy£qHationem ofiendere 
modfim d^icend^ Tangent is ^ pm^umDy five ^tr:'"^^ = A C. 
Sic fi data finer it aqnatio q c[ + b y ~ y y 1=: v v \ eddem plane fieret 
cam priori t^qmtio pro Tangent e-^ahje^o ficiLq q^ut Regula pr<efcrihit^ 
Sic ex' 'z b y y - y 3 = y ^ 4 b y a - 3 y y a = 3 v ^ fitve a = 
Vbl^yy • bbyfxy,y>y3-==qvv,/^bb.a+2 zya+3 yya 
^iqvv & atrib-rrjVrrsy,- -Hat b>+ by Cy.^*==qq v vf z 
frs^y y a-4y.a,l=.2.qq,vvt3 Z ^ 
■ Verhm in fimiliht^ t^qtfatiomhm nulUm arhitror accidtre pojfe difficul' 
tat em, - 'Ali^qu^forfajf ?\ in illls occurrety qJ4arfimj>artes quadam conftant 
ex prodnElis y in v : ^Vt y jy y v - y ^ v v, ^c, -Sed h^d quoque 
levls efiy ut exempli^ p^teh'it/ Detfir enim y ^ == hy V - y v-vl Nihil 
ah illarepciendum erit yCHrn in fingnlis ejns partihiu'^reperiattir y vel v: 
Sedm ex RegHUpr<e[cripto difponatfir^ bis fiumindHm erit y y \ ^ & 
fi Attiendum tafn inJt&tere.dMrOy in qm [mt partes 'qt^tt hahent Vy qudm 
in fimj^tfy" ctijm partes %ahent y \ quandoquidem y v^ytam y qnkrh V 
sonH'kejJu .1 m&ndujmg it wr em ~r- 
£^ y '4^^ V y = b V V - y v*#". • V-*'*- i ■ 
-T umwf^tat^, m prius^lac ^qHdtioneHnJiliam 'i yy a -fV^Vil b v V 
«-zy v v^ AahitHr a'=r ^ 
Jtaenimintelligenddefi ,^^ ut^.n^.Tppc la •latere non crnfideretnr 
potefias ipfiius v, ideoque'tpfi Vy- Mxfion^s^^^ non deheat, fed 
tantiim ippHs yj ''Sitm co'nha ah alio -laiereiy^nyi wy cqnfiderarI.}!on de* 
bet potefias ipfius y\, fe'd'v^anlumy ' eiquejims £xponenfpr<eponii Sic fi 
feret y^tby^^rzqqv^-yyv faciendum e^fet y ^ + b y t v ^ y y 
= 2qqv^ — yyv^^ ^ haheretur aquatio pro Tangents 5 y ^ a 
4 b y 5 a + 2 V ^ y a= 6 q q v 3 ^ 3 ,y f v 3 ^ a = ^H^^^TJ) . 
At que his Exemplis ^arhitror y jne omnem, qu^ dari pojfet , Cafmm 
varietatem complex nm efe,^ C^ternm non erit fortajfe inmilcy fi $a qm 
generatim exj^ofui.^ ad lineam mliqu am lingular em apfiicem. Data fit 
igitur Curva BDy chjhs ea fit proprietas, ut fmpto, in illaquoltbet 
pmHa Dy fi jmgatMr B T>, & erigatMr adillammrmalls DEy occurs 
rcns re fid BE in Ey reel a D E fitfempsr admits datc^re^a.B^-E. Vt 
hah eat fir 
