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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
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d
Arithmetica Insimtorum.
PROP. XXZ. Corollerium.
T Universalicer, Pieurae spirales (a spiralis princi-
pio exorsa, e eadem vel simili linea spirali termina-
ta) (unt ad inviceme in triplicata ratione rectarum con-
terminarum.
Cum enim ( per constructionem linex (piralis) eadem (cra.
tio rectarum MT, M T, eux cA angulOrIM PMT, PMT, In FIBUI
Tumpea anenl voce, colentu quo supra prOP. 5. ut & sectoris
voce, eo lentu quo lupra prop. 24.) lectorum PMT, PMT, ad
inricem racio (quae componitur ex ratione anculorum et du-
Plicaca racione radiorum,) eA rectarum MT, MP, ad invicem
racio criplieaca: Ec proprerca eadem erie etiam ad invicem ra-
eio feurarum spiralium MTM, MTM, qua illorum Scctorum
TUnCErienCCS. Per PF 24.
Sic v. 8. E recta MA Cunius circulationis) dicatur rY, de
circulus eo radio deleriprus dicacur Le; sxura spiralis eodem
cempore descripea crie Z c. Psicur in una circulacione cum le
mille hec recta concermina , =r = - Zr; circutus conterminus
Ex Z x C = ZC, qui ductus in 2 C numerum circulationum)
F Z X Z x Z x C = 32 C, cjul9; eriens ZC, eA higura spiralis
quae d circulacione integra e insuper lemisse describitur. PC
limilicer in quantacunq; circulatione.
PKOP. ZXZI. Corollarium.
Tvero ejusmodi fieura spirales, limeis spiralibus
dissimilibus, e rectis aegnalibus terminentur: (Pu-
ta si ALB inuna spirali, tanta sit quanta MC in a
lia:) erunt feura illae spirales homolosis suis rectis (pre
ta MA inuna e AIA in altera) reciproce proportiona-
les.
PrOp. 29.
NaM In PRIMIA CFIE SBUTA MABM Cduabus circularioniber
descripca) aequaliserienci ciculisui B bis Tumpei; Ec. in le-
cunda, fgUTA MABCM (cribus circulacionibus delcripca) X-
qualis
PFOD. 30, 3I.