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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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L G F B
Verbi gratia: Rquationis hujuS a a = 2 a V 275 + 250 =0, ladices duxe tunt
75= V - 8
et A = Y 175 - V - 81,
PTOXIME PrOPOSItO.) Ouippe si ab 175 (quacato lemi coefticientis medii ter-
mini) auteratur absoluta quantitas 256, restabit =8+: Cujus itaque radix
quadratica V = 82, addita rel dempra Le. CC, exhibet aequationis
radicem a = V 275 = V = 8F. Fodem plarC MOO quo in Aquatione a a -
32a F 175 =0, A ab 256 (quadratO TCMI-CDCIACLLMLS 1O) autETaTIF, (ablolut2
in catu primo.
D. LXV
ui lunt ralores AB in casu
quantitas) 275, restabit f 82; cujus Laca 3, aca Vet dempta coetticiencis
32 dimidio, exhibet 26 F9; hoc cA = 25 aut. + 7, qui sunc ralores rectae AB
l L. MLbHII.
ffectiones Ceomerricae his accommodatae.
Scentum est, capice praecedeme, Ouic, in Cieometria, respondeat Radici
Exponendae jam sunc, tfectiones quaedam Cieometricae ae resolurio.
nem quacratiearum aequationum speclantes, qua radices habeane (quas VOCANL)
Genuina consticurio hujumodi aequationis. aa f. b a + a = 0, haec cst. CoeHi.
ciens B, Cst. Summa duarum quancitatum, quarum Rectan
sulum est a quancitas absoluta. Quod in magnicudini-
bus haud aptius explicabitur, quam ( Aat V
A a
diameter circuli, cui accommodetur V a (=- BS) ut I.
nus rectus, seu ordinatim applicata. F.P urique haec una
ex nocissimis Circuli affectionibus, quod sinus rectus, seu
ordinatim ad diametrum applicata, est media proporrio.
nalis inter diametri (quae dirimic) Termenta duo.
PoteCE autem BS (ejuldem lonsicudinis) indisserenter fumi ex veraris parte
rectae CT cenero insistentis. Hlabemus iraque, in Diametro, duo puncta BB
(duobus in Pemicircumferentia S S punctis respondentia) quorum utrumris dixi-
mic diamerrum in duo segmenta AB Ba; quae sunt quae sica radices dux. ACIr-
macira utraque, vel utraque Nesatira, prouc in Aquarione habetur =b a, vel
Ba
Prout autem creseit rectae B S longimdo, ita provius accedit (ex utravis parte)
B ad C; adeoque decrescit C B co tnus, seu lemi differentia radicum.
Ouoniam vero BS major esse non potest quam CY lemi-diameter: Guando
igitur V a major est quam =B, calus ille, sccundum hane constructionem, est im
Possibilis.
T. Tlujus icaque AEquationis, a a FB a F a = 0, Ceometrica F. Aectio (VE CuM
casus possibiles cum impossibiles una comprehendam; hoc est, quibus a auE non
TIE, auc Hl lasor quam = bb;) talis este poterie.
Super AC a = b, bisecta in C, erivatur perpendicularis C. P = V a; Sumplaque
PB = Z b, tiac (in ucramris parcem ipsius. C. P) criansutum PBC reclangulum.
Cujus itaque rectus angulus erir vel ad C vel ad B, PrOut PB aut PC major
est; adeoque BCi erut vel sinus vel Tangens (ad Radium PB) in PC cer-
minata.
tibus sic constructis; recta AB Ba sunc duo ralores a; uterque attir.
mativis H (in aequatione) HL, = Ba; uterque negatiruS, II sIE L Ba: lunE
que sur diei solent) Reales, s rectus angulus t ad C; Lmasinarii, 
Vrroque
quadrati nesatiri in AIgebra
imaeinarias, a quadraris lezaliris oriundas.