153

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arithmetica universalis.

bb

* n aquatione, aa^bx~cxx—yy, fcribatur, fiet aa + — —yy* Quareeft aa+~~ V z^, hoc eft, quadrato femiaxis minimi. Denique

. . ^ . . . r . 143^

111 valoribus i piarum, av, vq_, vz, jam inventis, lcnpto — 6 -~ pm«eunt ? 5 q = AV , = v «-> & “A; = vz '

143S J 14ZS V r 43

Problema-ta Geome-trica.

Analyfeos pars altera.

Supponatur jam baculum puncto a infiftens efte ar, Sc eritApianum meridionale, ac Rpzcgconus radiolus, cujus vertex eftSit infuper txz planum fecans Horizontem in vz, ut Sc me-ri dionale planum in tvx ; quae leCtio fit ad axem mundi coniveperpendicularis; Sc ipfum planum txz erit ad eundem axemPerpendiculare, Sc conum Pecabit in peripheria circuli tzx, quaeejus vertice pari ubique intervallo, rx, rz, rt, diftabit. Quam-°brem, fi ps ipfi tx parallela ducatur, fiet rs=rp, propter aequa-ns, RX, rt ; nec non sx-xc^, propter aequales, pv, vc^, Unde eftvel rz (= x) - — Denique ducatur rv ; Sc cum

Vz perpendiculariter infiftat plano rpq_, (leCtio utique exiftensPlanorum eidem perpendiculariter infiftentium) fiet triangulumRVz redtangulum ad v.

R

Dicftis jam ra = d, Av = e, vp, velvq_,=/, Sc vz=g; erit ap =f—e, Sc rp =VjJ- 2 cf+ ee + dd. Item A qj=/+<?, Sc r\/y/+ 2 ef+ ee + dd : adeoque rz(— )

_ VXf—2ef+ec + iId+ •///+ 2ef+ ce + cl d ^ (JlljUS

fttiadratum

1 " w 1 jj

3 - ^ -- - j - ~± -

( av 7 + vz<7 =r a q + /\vq + vz q—) dd+ ee+ gg. Jam, reducftione faCta,eft Vp~ > lge ffj re * + iddff + 2 ddee+d* = dd+ee -ff+ 2gg ; Sc, partibusSIRadratis ac in ordinem redadtis, ddff— ddgg+eegg -ffgg +g 4 ; five

Sc (valoribus

<hgf

sg

-dd+ee-ff+gg

iplorum ar, av

^6 ~ 1 q6« 4 ^ 1923«

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48«» 4-1287 ~

VOL. I.

_ . 08 aa 11 zaa^/ 3

Denique 6 , — r -,

, vQj Sc vz) pro d, e , /, ac g

2 aa 36x14x1433 o-

VH 3

reftitutis, oritur

143^

^7 -/ 7 -- 7

Sc inde, per reductionem,

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