*I0

N E W T O N 1

Caput xiv. fcripto 26F, emerget ee + cx - ds/aa +- xx. Iterumque quadratis.partibus, e^-riceex + cexx — ddaa+ddxx. Et, aequatione redudta,

XX

2cecx + c 4 — aadd r cec 4 - \/c'\Jd — aadS + aaddcc

-, feu x ——

dd — cc

dd — cc

Haud fecus problema refolvitur, ii linearum, ac 8e bc, fummavel quadratorum fumma aut differentia, vel proportio, vel rec-tangulum, vel angulus ab ipfis comprehenfus detur; vel etiam fivice redtae dc, circumferentia circuli, aut alia quaevis curva lineaadhibeatur, modo calculus, in hoc ultimo praefertim cafu, re-feratur ad lineam conjungentem pundta a & b.

P R O B. XXII.

Datis pojltione tribus reSiis , ad, ae, bf, quartam df ducere ,cujus partes i de, ef, prioribus intercepta ? datarum erunt lon-gitudinum .

A d bf demitte perpendicularem eg,ut 8e obliquam ec parallelamad, redlis tribus politione datis con-currentibus in a, b, 8t h, dic ab - a,

BH - b, AH - C, ED - d, EF - 6, 8^

he = x. Jam propter fimilia triangulaabh, ech, eft ah. ab::he. ec = 8 c

lx

ah. hb :: he. ch - Adde hb, Se fit cb =

bx + bc

Infuper, prop-

ter fimilia triangula fec, fdb, efc ed.cb::ef.fc - Deni-

•que(peri2 8c 13 .II. Elem.)eif +7FC (=cg)= ^ch^ -iCh;

hoc efl, -

-ee

zcbx -f 2 ebc

ebx + e ! 'c2dc

aaxx

cc

lix

c

hx . aadxx — ecdcc ebx ebc

—. Sive ———7 — + -7- + -7

2c ebx -+■ ebc d d

dc

ccx — dax — lbx . . .. rA cc — aa — ii ei - .

- i -- Hic, abbreviandi cama, pro- ~ h -fcnbe m ;

aadxx — eedee ebc

Sc erit + -j = m x ; ac terminis omnibus multiplicatis

proaad

aadxx — ecdcc ebex ebee

per x + c f het --+ — + = mxx + mcx. Iterum pro