dati

arithmetica universalis.

rzr

, quo angulus dba excedit duplum anguli dab : 8c angulus OEegerit duplus anguli dqm. Ad mq_ demitte perpendicula, A r,« , ca ’

do ; angulum dmq_ bifeca refla ms occuriente do in s ;

^ erunt triangula Docg, som fimilia; adeoque ocg om : : od. os ;

^ dividendo, ocg- om. om : : sd. os :: (per 3. VI. Elem.) dm. om.Quare (per 9. V. Elem.) ocg- om=dm. Didlis jam po-.r, od-/,vel bn, -b, Sc PR, Vel pn, - c, erit, ut in iuperiori Problemate,

° M ^ 7ZT5 et °Qi= adeoque ocg- om -

D °q + OMq-vM.q’ y hoc eft,

OBLEMA*

Geoml-

Pone jam

yy — bb

cc — icx 4 -a\v £.bhcc — ¥>bcxy 4 - ±xxyy -r-y, _

•xr + Et > P er

2bbyy-\-b*

y* — 2

■f- cc y b^

debitam redudlionem, orietur tandem/ 4 * ~ f^yy + 4 ^* yZlff

— 3-vl- + 2hcc + \bZ

- bb - p

divide omnia per/-£, Sc evadet/ 3 + byy + jjy + -o. Quare

— TfXX — ^ .v

Pundhim d eft ad curvam trium dimenlionum ; quae tamen eva-dtt Hyperbola, ubi angulus bpm ftatuitur nullus, live anguloruma d bafem unus, dba, duplus alterius, dab. Tunc enim, bn five bev anefcente, aequatio fiet//=3An;+ icx-~cc.

Ex hujus autem aequationis conftrudtione tale elicitur Theo-re rna. si centro c, Afymptotis cs, ct, angulum sct 120 gra-duum continentibus , deferibatur Hyperbola quavis dv, cujus Jemi-

axis fmt cv, ca : produc cv adB, ut fit vb = vc ; & ab a baciis utcunque rectis, ad, bd,concurrentibus ad Hyperbolum, eritangulus b a d dimidium anguliabd triens vero anguli ad e, quemredi a ad comprehendit cum bdprodudla. Hoc intelligendum eftde Hyperbola qua tranfit per punc-, t j N tum v. QuodJi ab iifdem punc-

b a redia, a d, b d, conveniant ad conjugatam Hy-

oian h quee tranft per a: tunc externorum angulorum trian-11 bafem ille ad b erit duplus alterius ad a .

— bxx

S 2

P R O B.