—" cos(600 †. c) da— ain(600 †.") du— u' sin(300 †. ve) dw, † cos(300 P. b) duw= dvn, u' sin v' dνν— cos w du'— u“ cos e des²— sin v“ dun= G6I u' sin(300+ 2) dv— cos(300+) du— u cos(600+† v¹) do“— sin(600+ v“) dun= 6/* u' sin(600+ 2) dv— cos(600+) du+† u“ sin(300+”) do“— cos(300+† 2“) dun= 67 II Ex his aequationibus et duodecim antecedentibus levi opera derivantur valores †oso, Fftaft,

fu af,... XII XXII. uvenitur: Hu' cos v' do †‿ulzsin v' cos v' do'+ u' u“ sinv“ cos v de— B(O) u cosa do-+ & sin v' du † u' sin du ‿¶ u sin v“ sin"' du— B 0) sin v du+† gu' cos v' don Tu u gin cos v' do" u“e sin v“ cosv'— B00) u'“ cos v' du‿2 † Hsin v' du“ † u’ sin v' sin"" du" † u“ sin vie du“— B0O) sin v“' du“.

gu cos(300*)da †usin(300+*heos(300+v)Dde' †u'unsin(600+)cos(300+)B B(Ducos(300+")de*†

= 700.

Lsin00-)du X u sin 300+*)⸗du— u'sin(600+v)sin(300+)Ddu—B(Dein(300-")du éu' cos(600+ νJde‿‿u sin(300+')cos(600+e do usin(600+“) cos(600+ 0)—B(I)"cos(600—"Jde“*+ Ssin(600-vDdu“†usin(300- Dsin(600"JBdu u sin(600-+ n)edu— B1I)jn(600+")Bdu“.

Hu' cos(600—+Jdv usin(600—+†)cos(600-+*)Jde ‿u'u"eos(600+ v)cos(300+)deB(TV) u cos(600+ de‿

=I 4fu.

Ssin(600 Jdu+‿ u'sin(600-—+†)2du †unsin(600—+)cos(300+ b")du— BTX) sin(600+ v')du—= frr 4 Hu sĩn(300+)de‿—d-u' u in(600+ v) sin(300+“⁰)de— unsin(300⸗*n)cos(300+ v““)do"—BIV) u'sin(300+) do“ Scos(300)du ‿u'sin(600-†r)cos(300+b“) du“+u“ cos(300+“) du— B) cos(300+ v) du“. V — Hu'sin v de'— u¹2 sin o' cos u do ‿‿ u u sin v“' sin v' de+‿ BVI u' sin v' do“+‿ T S cos v' du' † u' eos v'e du— un sin'" cos v' du'— BVI) cOs v du—

VI J VI 1 7 ,A„,, 7 gr L n,,(vD,„, 47,,4=f d.. — Hucos v' dos‿—⸗fu' u cos v' cos v do‿‿use sin cos do+‿BDu? cos duε—

.— vI), — H sin du— u¹ cos vssin v du ‿‿ u sin»u duu”) in e07 don, V

Scos(300-vBdu ‿†‿ν cos(300-+):du— u'ein(600—+)cos(300+v)du— BrIII) cos(300*)du.—=I rm gu cos(600Jdoò‿—⸗u'u cos(300+)cos(600-+)d“unsin(600—+“)eos(600-+⁰)do+&BIII os(600+Jdo"— —sin(600-v Jdu— u'os(300-+")sin(600+)du“ u“in(600+b“)2 du—† BVIII) in(600- vn)duy.

e u/2cos(600-†')sin(600+')do'2‿uos(300+“'in(600—+)Jdo' † B0E) u'sin(600 d‿

u**ο(300+ v)Jsin(300+“)dn † u'u“si(600+‿ο)sin(300—+") do† BVIr) u'sin(300+ do

Sᷓcos(600 du ‿⁴ςωοs(600+ 2du—. u cos(300-+)cos(600+)du— B6) cos(600+‿)du= fr afr t gu'sin(300rDBdeu'u’ cos(600-)sin(300- v)d'— uuuscos(300-†*n)sin 300+n)dun— BDuin(300—† Jd 9. — Scos(300+οduν— u cos(600+ v0) cos(300+)du“‿ν eos(300+):du cos(300+)dun.. 2

— u¹ cos" dy u¹e sin cos deν— u¹ un¹ sin v' cos v de+ B6r!) u“ cos v de— — Hsinv du † u sin ve du“— u sin sin" du?+ BXII) sin vedu-+— An rn S u' cos ν⁴eννι—ʒ u¹ u¹, sinv cos v deune sin v cos v'ds—- BXII)„ cos v" 2+ 6— 5

S sin vdu— u sinv sinw dan †̃ u“'sin 02 du“— BII) in"duw. I

— gu cos300 R“)du Tu zin(30 †„)cos(300-†)Bde=u'usin(G00)cos(300,.*) B)Dnos(a00,†„)Jde

gin a0, Hudu Pa sin(300-v):u— u'sin(600)sin(300-†)du †. BrT.) in(00u)Bdu*= IrI Jfn. Gu cos(600+ b do‿—u u Sin(300 vjeos(600-.)Ddu †ursin(600+v)cos600-*)dv“ BTV)aos(600- uJdu— ain(600-)du— u'sin(300-+)sin(60+ b“ du †usin(600-+ v)edun—BTIV) in(600+v“')duu.

bu cos60 Tu)jdo-hu eain(600.Ps)eos(500)d Wras/us(00-4r)cosG00)N.BXDa os(500-.*)— 8 633 Gain G00-u)duru sin S0O0-)rdu—ulcos(300..)sin(600-)d"— BXn)sin 600 Ada). er= peri afn zu ain(300vDJde duu in(600-r)sin a00-Je—unads300p.“)ZSin 3009")Bdv’ BNA)e,in(aO0-*")der-h. 5 e0. 1. Sros(a0-b Jdu=u Sin(00- Gos300—)Jdu K’o(300-+):du BXVi)cas(300⸗)du“, 8½ †.