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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
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un
it
per
Pde
F
De recta lancente Cyeloidem primariam
Lemma.
YY SIE Circulus AOD, Diameter AD, tangens
VD, _ oY Tubcenta cuiris D0 ad rectos
angulos. Dico Fansentem eAe ArCu OPD
majorem. Ducatur Pangens oT. Ouoniam an
uli 20D, TD0 sunt aequales, ergo anguli
FOV, FVo sunc aequales. KrgO V FD aequa
lis est OT, TD Simul Tumpcis. Sed ip (∞ OF,
CL
Superant arcum OpD. PrSO VD major est AF-
cu OpD.
TI. Tildem potiris (I ducatur ux pe (vel oprE
tangenti VD parallela: dico legmentum externum
UP, etle arcu DO, (rel vn aTCU = c) majus: (C8
mencum vero internum De este arcu p0 (vel
XE aECU e c) minus. DuCatUE CubtenCa PO (Vel
D0) e pm (vel  ∞) subtentae ad rectos angulos. Angulus igitur opu ret
acurus elt, vel obcuus UE coFV.
Sic primo obtulus. Oroniam anguli VDa ea D sunt aequales, de vc parallela
ipsi VD, erso Fosceles est pCF, er∞O ve ec sunc etiam aequales, e quoniam cor e
eL obtulus ergo cou minor est op ee adhue minor ip(a u; sed cum aoV BIE tan-
gens, _ p. subtensa ad rectos angulos, erso demonstratum est cou majorem cAte
arcu con, ergo on major eAt areW CoN.
Sit secunco angulus u po aeucus, erro in triansulo omp, angulus omp est
aequalis recto minus angulo mop; et in criangulo Fpm, ansulus xBM, CIL X qua
lis recto minus angulo upo: sed anoulus npo est major angulo uco, rel an-
Sulo moD: ec ans. mox est minor angulo moD, ergo complementum anguli
upo scilicet rDm, est minus complemento ansuli imop, scilicet angulo omp;
erso in criansulo epm latuIS Em, est minus latere FP. Sed uI, rO aequales else
jam demontrancur, erso uP major elt ipta OM, e OM MajOx areU OP: erBO
uD. CAt MajOF areU OD.
Dico poltremo segmentum internum De esse minus arcu op. Duoniam enim
anguli Foe, re0 tunc aequales, ergo minor est angulus Poc angulo peD, erso
in criangulo poc lacus De minus est latere po; recta autem po minor olt areu
PO; ereo pe minor  accu p0. Simdiver demonsteacue de 1.
Problema.
Ad datum punctum c in Cycloide
Sta d Panoentem ducere.
Ducacur 10 bas parallela, e per
punctum o Genitoris ducatur subten (a
20u, cui parallela ducatur XLY, dico
rectam   tanoere in punCtO L. Nam
S non tangat, ergo SCCaL In I, erSO Ca-
dic intra curram aut rertus basem, aue
rexlus verticem.
Cadat primo Si Aeri PosTit vertus Ba
em de sc punctum aliquo d X inera cur-
SCITI S
ram: ee ducatur bali parallela XuP, _ producta secet curram in 8, et produca-
cur subrensa ad u. Ononiam erso alibi demonstratur e primis Cycloidis pro-
prietacibus esse quod Parallelae bali incer Cvetoidem e Cienitorem terminatae, snt
arcubus Genitoris ad verticem abscistis aequales: ergo 8p est aequalis arcui pODa,
et 10 areui op  ereo c0 plus accu oD aequalis ett ix SI B P. sed xu aequalis et
X XX Z
ipIX