128 N E W T O N I

Ca?utXIv. extremorum 8c mediorum valonbus m ie, cJ — - xX'*«

xvbb-cc+x v/— - xx, five c- x --- xx = xvbb-cc>

Et, partibus aequationis quadratis & rite difpolitis, x* - 2ex* +

ddcc

-(- ddaa xx — zddaacx -(- ddaacc— eebb

dd — ee O'

P R O B. XLI.

Invenire locum verticis trianguli, d, cujus bajis, ab, datur,anguli ad bafem, dab, dba, datam habent differentiam.

U BI angulus ad Verti'cem, live, quod perin'de eft, ubi lumina angulorumad bafem datur, docuit EU'< elides locum ver- m. 29. Eucii^ticis elfe circumferentiam cif'culi; propofuimus igitur in'ventionem loci ubi differeii'tia angulorum ad bafem da'tur, Sit angulus dba raaj° rangulo dab, litque abf e0'rum data differentia, re$ abf occurrente ad in f. Ili'fuper ad bf demittatur n ormalis de, ut Se ad ab normalis dc, occurrens bf in g. Di&&que ab ~ a, ac~x, Se cd -y, erit bc -a- x. Jam in triangnd 0bcg, cum dentur omnes anguli, dabitur ratio laterum, bc & q c ’fit ifta d ad a, 8c erit cg = — j - * . Aufer lianc de dc, live/, ^reflabit dg = tzdttdl. Prseterea, propter firoilia trianguladge, eft bg.bc:: dg.de. EK autem in triangulo bgc, a.di:cG^ c 'Adeoque aa. dd : : co^, bc^*, Sc componendo, aa+dd.dd:: bg^-B^’Et, extractisradicibus, V aa+dd. d (:: bg. bc) :: dg, de. Ergo PE **Adhsec, ctim angulus abf fit differentia angulof UIbad Se abd, adeoque anguli bad Se fbd sequentur, fimilia erv^

4 triangdP