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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis (shelfmarks Leibn. Marg. 100:1/2, Stück 2; Leibn. Marg. 100:1/2)
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Cap. XCV.
A L G F B R A.
direetionem, adeoque e dectiritatem, quae est rectae ibidem Cangents: Item (ex
prop. 6. cap. 20.) Motus compoliti directionem esse in Diagonio parallelopramm,
cujus latera et anguli exhibeant componentium celeritates et directiones.
Incellisatur jam (Fis. T.) A a Parabola, deleribi motu compoluo, ex aequabili se.
cundum A Z vel Va, e aequaliter accelerato secundum AV vet Le cujus itaque
particula iooXeorot (ver pY. 3. cap. X0. de Motu) Lunc series Priluanorum, quxe ad
seriem toridem ulcima aequalium, (hoc est, ad rectam ioexsoror cclericate  a ac
ouisira cranlisendam,) est ut L ad 2, (per Arith. Infin. pr. 64. vel pr. T. Cap. 5. de
Mot.) Adeoque, Tumpea VF = 2Y A, et complero FV au parallelosranimo:
juncta a f. est Pangens.
Idem similicer obtinehicur in Pacaboloidibus quibuscunque, oDC PrOP. 2, 5, 6, 2.
de NOt.
Aeque inde Facile (vel ex ildem principiis) oltendicur; si incellieatur Fix
AT. Lic consticuta, ut momenta (relpectu A H) ordinatarum YV, y co, Cint iplis
Ya yO, ordinatis proporcionalia; erunt Celeritates acquisitae in a, O, Peu V, D
polica A Y linea mocus aequabilis) rectis Lv, yc, proportionales: Et conse
quenter, uc A. Y Cillarum asgresatum) ad A F. Y (aggresatum tocidem maxi
mae aequalium,) sic V A (ageregacum celeritarum seu parricularum crescentium)
ad (asgresatum coridem maximae aequalium ) V F.
Spiratis AS a (fie. 6.) punctum a designatur
moti compolito ex recto per Aa, e circulari per
Va aequabilibus urrisque e iooxeorois. Erso, Cumpra
circuli tangente av == a V, ee completo Aav t
Parallelosrammo; juncta a F Spiralem cangCt.
Unde sacim emersit Archimedea quadratura
(sire Circuli Aire Sectoris cujulris) Proprer AF
Sin motmum alter, puta A a, Sic acceleratus ve
retardatus; pro a A, lumenda erit a B (in ea
ad illam racione quam illa poltulat acceleratio sei
retardatio,) eritque diagonium aB, Tansens qua
lita.
Ruadratricis A a B (FC. 3.) punctum a designa
tur mocu compolito ex recto per va, ee circulari
in Y a (aequabilibus et 100reoros.) Erso, Cumpea
cansente a V = aY, e complero parallelopram
mo VavF, juneta a F tanset Quadrarricem
Acque hinc alia quadratura, per Tangenten
quadratricis, propter vF = a V = a Y
IIla per quadracricis Basin, sic elicitur. Policis
CA= r AO = 9, XL - X OR- -a. KrIt (prOpter
Ouacratricis constructionem) AO. RQ:: A C.
aF = - r: : YZ. aZ = = X. EAtque a Z = a V
sumpro ubiris in A B puncto a praecerquam il
B, quo casu (eranelcente vtraque) exit a L. = a H.
adeoque X = r; hoc ct, YZ = X B = AC
Sed _v P. communis tansens
utrique CurVX ZB, AB.
Creloidis (Fic. 8.) punctum
a delcrihitur motu composito, ex
recto in a V, ee circulari in a B
(aequabitibus _ aeque velocibus.)
Erso, sumpra tansente av = a.
e completo l’avsi parallelo.
srammo, juncta a F Cycloidem
tanset. H.c quidem, propter ANS
aV (= aB1
2vaV, Occurret circuli aB crectae
diaMELTOI rertice.