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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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A L G F B R A.
Cum enim intermedii cermini, reperiantur omnes, cum intra cum supra inter.
sectam lineam; mulciplicando, se perimune, relictis tancum primo et ultimo
Fsinc sequitur Fuchidis arsumentatio es 1s0, (ex aequo Tive et aequat:) li SIE
iptorum A, B, C, D, Sc. quilibet ad consequencem Tuum, uc Tunt pLOTI
an B, y S, Sc. quilibet ad Cuum: eric ut illorum primus ad ultimum,  AOI.
Cap. XX.
HOc elt
Aquabie = x = x =, hoc est -
Ouippe cum Factores illi sint nis aequales, eriam factus Facto aquabitur.
Pariterque (ut loguuntur) in ordita pehhurbato: li erium A, B, C tocidemque
B7 3; TIE UE A ad B sic (nOn a ad B, Scd) B ad 7; e ut B ad C, sic a adB:
erit ctiamnum ut A al   d all 3. Hoc cAt,
exit = x -- = - x -; HoC est - -
Ouamris clum non comparentur eodem ordine, (cum sint B B lecundus _ ter-
rius terminus in priore comparatione, led BB primus et quartus in polteriore
se tamen mutuo destruune num BB in mulciplicatione priore, cum BB in poste.
riore. Neque aliud hoc est, quam E illic ponatur triplum duph, hic rero du
plum tripli; uctovrsue proc sexsuptum.
Idemque continget s plures adhue sine utrobique termini in ordine pertur
bato, dummodo ICCIMM omnes fiant tum antecedentes tum consequentes ra-
BC B0
tionum. PUtA, ABCiD et aB7d
BCD y5
AIque HX d proPOSItiOneS (qua LuI PrP. 22. 8 23. lib. 5. Fuclidis) de
arGUeNEatIONC ex aequo, lire l ordine directo tire in ordine perturbato, le
ciunc (rationis) compositionem per multiplicationem.
Fa vero quae sequitur (nimirum prop. 24. lib. 5.) eam composiionem respicit
quae elt per Aaditionem. Nimirum,
Si lit ut A ad a sc B ad B; atque ut C ad an sic D ad B: tum eric ut A. F C
2c an Hc B (D ac B. LloC etbus
dntta 
C
Similisque aa ACHEH paltin apu Luclidem aliolque.
inricem similes leu aequales; (lincque; verbi praria, nulc l 293,  BeVC;) ea qua
componendo oritus, diei (oler unius earum suplicata, criplieata, quadruplicata aliatre
mulciplicata pro numero similium ratIONUM SC COMPOHENEIUIM. SIC raLIOMIS
A ad B, (cujus F. xponenS est =,) duplicaca, criplicalan quadruplicata, dc. tunt
A
Si in ea per mulciplicationem compotulone rationum, rationes componendae sint