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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 103, page id 797435492:0325
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V B CF.. ZI.
XXVIII. SiE CirCulAS AMB Cujus Radius C A, SC adhane per-
vendicularis recta D BP, Sic item curra A N P calis, ut duet d urcun- l1G. 15P
que recta P M N ad D P parallela (quae circulum secer in M, dictam
CurraM in NY) SIE recta P N aequalis Droui A M; Cir demum axe
AD, base D E deseripea Parabola AO P, heC extra eueram A N P
tora cadet.
C: 5133VE E eSLCASB, AIEACII M
Nam secet recta P HI parabolam in O; Se connectantur TuBCeNSa
AB, AM. estque D F. P N :: AEC A B, aEC. AMC AB. AN
:: D E. P O. quare P N + PO; unde liquet ProposEuM.
XZIX. Exhrinc (e C rulgo roris spatiorum ADB, AI F dimen.
3C A XDB 
sionibus) Facile colligirur haec regula: Z CA ]  CD ~ ArC. AB. 
POFFO SIPONatE arC. AB =- 30 grad. (IEquC2C A ==-LL3; juXtA
resulam istamm compucando, proveniet tota circumferentia major quam
355 minus fractione unitatis.
ZXX. Hinc eriam dato areu A B, nominarisque AB = p, C A = r; e
DB =C, ad inveniendum sinum rectum D B adhibebitur hXC Xqua-
io:
3FY pP
12rY
Orr -) pp Orr.  pp  = 0c. vel ponendok =
Bp = 4kC = ec. vel 2 h = V 4RR = Rp = c.
P
exic
C13. 13a
XXXI. Sic A M B Circulus, cujus Radius C A, d huic perpendi. F18. 253.
cularis recta D BF; SIE item CUIrVa AN P pars Cyoloidis ad Circulum
AMB perrinentis; demum ad axem AB, baCin D P Ntacuatur Para
bola AO F: HXCInEr2 Cycloidem tOta CadeF.
Erenim urcunque ducatur recta P M O N ad D F parallela, lineas
expoliras secans, ut cernis; connectanturque sabtensa AB, AM;
eAtque DE. PO:: AB. AM :: CAEV. AF. ANC DF. PN;
deoque P O -= P NI. unde constac Propositum.
XXXII. Extrinc, _ C noris seementorum circularis atque Cgeloida-
2C AXDB + CDXDB
lisidimensionibus, haec elicitur Regula
E AEC. AB.
  A1 - 2C D,.
Porro B Tueric are. AB = 30 grad. e POnaTuT 2 CA = F135 C
regula hac contectatus fore totam circumferentiam minorem quam
355. plusfractione.
Vides isitur uc c propolitis duabus regulis starim emersit Diametrs
ad Circumferentiam Proportio Metiana.
XXXIII. Duoniam exorbicanci se obviam dedie Crclois hoc adno
cabo Theorema, nelcio an uspiam ab illis, qui de Crcloide cam tuse
scriplerunc, animadversum: Completo Rectansulo ADFC, spatium
AFC