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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. XCTTI
= F B
in allera -. Ouod alibi, in tractacu de Conicis Sectionibus, dudum uel
Hoc quo melius explicem libet inde mutuari sequentem figuran.
aL.
In qua EIipfis, e quatuor Conjusata Byverbolx (sre Systema TEyperboli
cum,) idem habent Centrum; eoldem Conjugatos Axes tran(verlos; eoldem item
Verrices et Parametros ad eos axes spectanies. Sed INtExCCDTS DiaMCLTOS, 2d
eos vertices pertinentes, in altera Prorsum, in altera Retrortum aestimandas. Oujn-
Deu in Hyperbola, Diameter qux Incercepta diei Colet, ett diametri Frantverlae
concinuatio: Sed in Flipsi Circulore, Super Pransvertam replicatur. Onde ori-
cur Sionorum L = variatio. EL, in Elliple, Diametri Mechae (hoc est, con-
jusata Aiquales,) sune, si continuentur, Dingonales Rectansuli, quod (per Arium
vertices) Ellipli circumscribitur, ee Syltemati Fyperbolico inseribitur: Faedem,
Porro concinuaa, sunc harum Hyperbolarum AlyMPIOIX.
Fc quidem si (contra Fllip (eos naturam) Supponamus AD (diametrum in-
terceptam) lonsiorem quam est (crantrersa) A an (unde Rectangulum AD a, tiac
planum Negatirum, = f ADX = Da;) PrO DE quae supponitur ordinaca in
Ellipti; habebitur Dh, ordinata in oppotica Hyperbola. Guae quidem DI, cst
suxpolicirium Lacus (seu Lacus Lmasinarium vulso dictum) Ouadraci Negaciri:
n esE DE verum latus quacrati AHirmaciri. (Depote quarum Onacliata, sune
Rectansulis A Da proportionalia.) Suntque illa, medix proportionales, in Hy
perbola incer rectas altirmaciram et Negativam; sed, in F)ipsi incer duas AAI.
matiras.
sic quidem, si Flliptis sic Aiguilacera ee Rectangula; hoc est, s Ares conjueati
(qui lune Latus Rectum e Fransiersum; seu Parameter de Pransversa Diame.
TeF) sinc aequales; Hoc est, si Flliplis illa sit Circulus, (nam, ue Parallelosram.
mum rectangulum et aequilaterum, est Ouactratum; sic EIliplis rectaneula ee aequi-
latera, est Circulus:) Tum etiam correspondens Lyperbola erie rectangula d
aequilatera; e rectarum DE, Dh, quadrata (non cantum proporrionalia, dect )
aequalia rectangulis AD a. Ouod idem continset, S Caltem Aiquales sint conju-
Satae Diametri; quamvis non (uE conjusati AXes) ad anoulos rectos positX.
Oux omnia (ouamris, hie loci, Disreltio videatur,) Esui iamen elte poleruns
ad hacum Fixurarum naciran seruinum fecte inrellixenelat caculmque incer se
convenieuriam de discrepantiam.
Acque ita exo Clar. Neretoni mentem hac in re, his binis liceris indicalam; co-
natus Tum sideliter, et quam potuerim dilucide, explicare. Non quidem omnia
quae ibidem habencur exhibendo (es enim uiraque epistola bene lonsa) vec suis
verbis