EPISTOLIS. 3.15

Utente s /dx + vel - &c. multo minore fcilicet quam in Theo- c°*-

S 2 S a STRUCT.

ElUate Hugenii. Qu6d li fiat 7 ak : 3 ah : : dh : n ; et capiatur Mechanic *^ g -ch—/ z, erit error adhuc multo minor ( cc ).

16. Atque ita, fi Circuli fegmentum aliquod ba£ per Mechanicam^ e fignandum eflet: primo reducerem aream iftam in infinitam*.

^riem,puta hanc; b£a ~^d*x* — — -TL.— -^-r —-&:c( dd ). Oein

5I !5 r d i 3 (ni*

quaererem conftrudtiones Mechanicas, quibus hanc feriem proxi-affequerer : cujufmodi funt has. Age rectam ab, et erit feg-hientum ~&b\ = |ab + bd x|ad proxime ; exiftente. fcilicet erroretantum ■— Vdx + 8cc. in defeftu ( ee ) : vel proximius, erit feg-^entum illud (bifedto ad in f, & redta aLta bf) - - BF ^ AB x 4AD;e Xiftente errore folummodo v4&?.+ ( ff ) &c. qui femper minorer it quam totius fegmenti, etiamfi Tegmentum illud ad ufque* e uiicirculum augeatur.

17. Sic et in Ellipfi ba£, \vid.jig.pr secedent.] cujus vertex a, axis^teruter ak, 8c latus redtum ap ; cape pg = \ ap +

^ Hyperboli vero, cape pg - jAP + - 9 --- f 0 ^ lAP xad( ss ). Et*

a<Sta,.

~ AB ~ j di xi

J I. I ^'L- ** 2*

d ' x *' 2dl 8d\

§AB + BD Zz}d?Xt.. --j

2 «L

4 -ad —

x

Td

i x

^ A2 + bd X |ad = 2 .$ dixi

isr,

Area b£a — ^dix£ —( ff ) Errore rurfum duplo

5 d£

$di-

xi

IO d *

. AL

14 d*

> Differentia _ A — AVm— A

d £ d

^pe BF 1 — A B 2 —AF 2 —2DF X FA ZZ AB 2 — ZAF 2 = dx — f;

BF

ab -

V- dx — l x 1 — dixi-

4 d\x \ -'■

4BP +:AB = S ^|-i4

4 Ad

'h

9* i

2 7 x i

8 di

128^1

1024 ^

3 - r l

9 x i

2 7*1

2di

3 2 d-l-

2$bdi 4

9 A i

2 7 x i

32^4-

256 di

4 *

15

* x i

3 x i

9 X Z

5 'di "

ifidl

64 X 5 ^i-

Area ■