324

Excerptum

QjJARTtJM.

EXCERPTA EX

15 . 1 nfuper, fi in arcus, b£, fagitta adindefiniti produdla, quaeratur punitumG, a quo a£tse reitae, gb, Gb, abfcindanttangentem ve quam proxime aequalemarcui ifti: efto circuli centrum c, dia-meter aK-^, '& fagitta AD=x : et erit

DB

(~\/dx-x z ) —d*x*— ^—— - 8cc. Et ae (=ab)==^

id* 8 d* xbd*

+ Jx. + Jl! + + 8cc ( aa ). Et ae - db : ad : : ae : ag. Q uare

6/a 40 d* >11

ag = id-jX- x dfj d - vel + &c (^)>, Finge ergo a g-^4-\^ etvicifiim erit dg (f d - jx) : db : : d a : a e - db. Quare ae - ^

+ -£! + -11^ +■ Lee. Adde db ; 8e prodit ae -d*x* + £s +

3^* 300 d*

Jfl + JJdt- + 8ec. Hoc aufer de valore ipfius ae fupra hab^ 0 ’

i\od £ 12OO d*

reflabit error + vel — 8cc. Quare in ag, cape AfH 00^

5 2 5 ^

$am partem da, et kg=hc, et aitae gbe, g be abfeindent tang^tem Ee quam proxime aequalem arcui b.a b ; errore tantum

ifte#

v . . - nsi^

(*“■) Per formulam fupra traditam § 1. arcus ex finu ; veribi Quod li huic-«quatioW r

2 xi *4

dematur, 'pars scilicet parti, hsec tertia veniet ae —db — ■

( bb ) Nempe ex hac analogia AE-DBtADr ae:ag, efficitur AGr

3*4

■} -- 7 +-?

35 di 28di

AD X AE

AE —DB.

Sed ad x ae =r * X ae rr xXd z x* + _

6</ T

Et AE —

S . 5 . 7

2X £ X*

DB .— ,4" ^7,

3 ^ s 2 8 . 4 '

Qua r e

r x 1 x*

xxd*x* + — f + , d + ~

AG -__ <

6 d* 6

+ 5.

x 2 5-r 3

40 d 1I 2d z

T +■

3 d 1 5 d*

2 , * , 3* .

+ » 3 + 5^ + 28-/ + ’

I 2*: 1

Unde divifione perafta veniet ag ” \d — -f- x - vel + ,

17 5^

( cc ) Nimirum fi capiatur ag — Id — \x — IH-, ablata ak r= relinquetur

% G

1 j 1 „ 1 _ I 2 A " 1 „ , I 2 .V

* !7S d m ’

, , r 3 ahxdh

— |.v x^x-= --

7 $d' I 75 d 7 d 7AK.

( <M ) Analyf. per Aquationes numero terminorum Infinitas. Cap. m. § 7.

('•) Immo errore hujus fere duplo, id quod ex sequenti computatione manifeftumfit. |A*