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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)
# Folio 8, page id 824573315:0220
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arithmetica infinitorum.
PFOP. 1I.
SuInEeniM FCET MA, AB, BC. C. D, invicem aequales (PrOP-
ter aequabilem progreltum puncti mobilis in recta MA, eriam
concinuata, tancum in una circulacione aquabilicer progrect
entis quancum in alceras) adcog; ram radii MA, MB, NC,
MD, quam Peripheri (iltis raeliis descripea) A, B, C, D, TumE
2d in ricem HC 1,2, 3, 4. Si igicur Cumaneur peripheriae, prima
semel, secunda bis, cerciacer, quarra quarer, erune illa mulii
Dlas (DOca L A, 2B, 3C, 4D,) ut numeri quadcaci 1,4, 9, 16,
SIrC Tar, 2n2, 323, 424. PC proxeerea etiam horum mulciplo
rum Cemises, hoc eA (Per PrOP. 5.) spirales MA, MAB, MABC. 3
MABCI.
Vel alicer, E circuli primi peripheria PonatuE A--p, erie le
cundi B--2 P, cercii C =- 3 P, quarti D = 4 P, _ GC deinceps; &
1A -- IP, 2B = 2 a 2P = 4P, 3C--323p =9P, 4D= + X 4Y
16p; _C. EF (Der PCOP. 5) Curvae SpiraleS M A - = P
MAB == =B =
2B.
ZB MABC = ZC = ZP, MABCD = =D -
= P, etC. Ideog; ad inricem uE 1, 4, 9, 16, Qc. hoc est in dupII.
cata raciOnC reCtarUM MA, MB, MC, WD, _C. (qua lune a0
Inricem uc 1, 2, 3, 4, _C.) Ouoderac demonstrandum.
PROP. XI.
Corollo
iT universaliter; Ejusdem (vel similium) spiralis
seementa qualibet (a principio spiralis exorsa) sunt
ad invicem in duplicata ratione rectarum contermina
VuM.
Cum enim (per constructionem linex (pira lIS) eadem HEra-
siO reCtaTM M T, MY, qua c angulOrUM PMF, PMT,
Canguliroce colentu lumpea qui TapTa IMNIIEUE DEOP. 5.) T2a
EIOArCUNMPT, PT, Cquae ex duabu. illis rachonibus compon
NIEIE. ) AERE CUrVarUM MIT, NIF, (quae ictorum arcuum sUnE
Temistcs) eric duplicata raCIONIS rECtaTUM MT, MF, tOu UE
MTG. NT9.
Sicv. 8. si recta MR ( unius circulationis) dicatuF AY, et DC-
nipheria circuli primi (eo radio delcripca) 2P, erie spiralis
MA = = P. lsicur, in una circulatione cum Lemisse, Aet recta
COntErminE 3=r =Zr, de Peripheria concermini circuli Z P, qua
duct