T A B U L A
Mftivecn- p,. 3J& and 3jt) |r
Curvarum simpliciorum quai cijm E mipsi etHyperbola comparari possunt.
S it jam aGDvel PGD vel GD S Sectio Conica cujus Area ad Quadraturam Curva* propo fi ta? requiri tur, ii tq; ejus Centrum A,Axis KafVertex. a,b em laxis conjugatus AP, datum Abicifsa* principium A vel a vel cx, Abicifsa ABve] aBvel aA ) > — -x, Ordinata rcctangulaBD = v, et Area ABDPvelaBDGvel rBDG = j, exLilente <zG Ordinata ad punctum a.. Jungantur KD, AD, aL> ; ducatur tangens DT o ccurren; Abicifsa? AB mT, 8 f compleaturparallelogramum ABDO. Et liquando ad quadraturam Curva’ propolitai requiruntur Area* duarum Sectionum Conicarum,dicatur polterioris Abicifsa £,Ordinata t, et Area s'. Sit autem - 4 - differentia duarum quantitatum ubi incertum ell utrum pofterior de priori an pnor de pofteriori fubduci debeat .Et in Forma lexta fcribatur p pro Cff — 4ep .
C UR VA R UM Fo RMjE
I. C 2
II J 2
m <
rvV
U' 1
TTfz» -y
dz '
dz"''
UT*
dz **-* ...
dzi
c. +fz n y
e +/2 ” y
-y
vel si
sic
^=y
vel sic
YnmVCCJz* = y
S^-iVeU-JV—y
'V& -+JR y
vel sic
d
(•♦'vf-r/T» y
vel sic
= y
‘ Ve y
Sectionis Conict
_ a _
^ Atlcifsa Ordinata O
z' — x
C +/Z
V
C + V
./ d
= x
t
-£*
= r
-2» = X*
z* = x
i
z*
X
= X 2
i
di
= X
y* = X*
= X
= X
d
= V
d
C+J-x
d
e +jx
Jf-yx 3 -v
IJL v
X 2 = V
Vfx
4 - ex 2 = v
VP+ ex* - v
V Jx + ex* — v
V/x~+ &e* - V.
\^t + ex* = v
VT'
+ ex 2 = v
Vpc + <-vr J — v
vT
+ ex* = v
x + ex* = v
VJx 4- ex* = v
vffx 4 - ex 2 = v
CURVARUM /iRl^Ai
— .r = t =
aGDB
i
a! e . _ a-
- C •
a' ~2f de-v^edc = £.
W V
zxv±4s_ t= iAJ>Ga . Fiq.3.4.
!7 V'
2d .in . -tcs — zexv _ t-
w z
zd *!7 zde A' 2 + 2CXV-Ve\s_7nJ 2 -nf 2 + V
Pz x AL _ r = t = in aCDI, iv/ Ui APDB -4- TDBfi,.2i4
7 ?J 2 2 X 'T/ _
g ^x s-y VCJfUN- - c
— 2 d,
:f=|^APDB feu ^ aGDB
s -i xv - ^ b = y«GDK •**•'•*■
“^.r = t=rfx- aGDB z/eZ BDPR . . < •
ddfs — zdv 2oife
t ■
x r = Cf ln kAD aGI)A. %. 2 a.r
x r_ ^ v u _
^ X>r 2 XL ^
c = t /" in aGPA.^v
2 i
X S—xv — t
A in POD izclln AOT>Ga .Ty.zj. 4 .
*jx jxv -i-r = t = Aj- in ADGa * ■
AxJsFYxv=tr = I in aaDG^-j-A aPB .% .j.4.
A at B It
O
2
p
*d/
/
T A <Zz
B N
3 /a
K A T a *, B N
K A B il&i T
Ichnrt . Senex jculp