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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. L XXVIII. A L C F B R A.
FIae Demonstrationes sune, rem iplam quod spectar, eadem ipla cum Archimedeis
ibidem traditis, sed aliter exprelsa, ec in aliam formam redactae. Duipre cum illa.
prout apud irchimedem habentur, lacis perplexx rideantur, et quas Lectoris
mens parum exercitari haud facile capiar; eas in hane Synoplin redesi (quo me-
Iins deulo Tubjiciantur,) ad id rOSaLIS a D. Carolo Scarboroneh Equite (Medicinx
Doctore, e Screnistimi Regis Anslix Medico primario) Viro harum rerum peri-
tistimo: ea (que ad cum cransnisi Londinum in liceris Noremb. 22. 267T, dacis:
Tumulque Archimedis aliud perplexum Lemma, prop. 9. lecundi libri Tsorropico-
rum. Duod (quamris alio spectat) libet hic cum reliquis subjungere.
PROPOSFFIO.
Archimedis propolicio haec est: Si exponantur quatuor rectae in continua propor-
tione: quamque habet rationem earum minima, ad excessum quo maxima excedit
minimam, ealem habeat ascumpta recta ad tres quintas excessus quo maxima ex-
cedit tertiam: quamque habet rationem secrecarum manimae aupla, e secundae
quadruplae,  sextuplae tertiae, e tripla quariae; ad aecreeatum quintuplae maxi-
ma e decuplae secunda, e decupla tertia, e quintupla quartae; eam babeat
assumpta alia ad excessum quo proportionalium maxima excedit tertiam: Assumpiae
illae duae rectae sunt simul aequales duabus quintis maximae proportionatium.
Ouam ego propolitionem (sive de lineis, sive de aliis quibutris magnicudinibus
incer sc homogeneis,) Sic universaliter expono:
Sunto continue provortionales, aaaaac, ace, ee c.
Sicque, et. a = e:: Baa. a = a CC In 3.
E 2a + 4 aac. + 6 aec + 3 cec. 5ana + 20 auc + 10 ace + 5 cec:: eaa. aaa - aec.
Tum est, Ba a = 6aa = = a a a.
Hocele, (proprex analoBias,)
aaa - aee
aua = eec in 3 eec (= baa)
aua - aec, in 2 aau. + 4 auc + 6 aec + 3cC C (= caa)
== aa.
5aaa + 10aa0 = 10 aec.  5 eec
qua- aee
Hoc est (diritis omnibus per
3 eec 2aua + 4 aae = 6 aec = 3 eee
2 aaa
aaa = eee aua  2 aae + 2 aec  eec aaa = acc
Hoc est, (reductis omnibus ad communem denominatorem, coque sublato,)
Z eec in a - ae (= 3 a 3 - 3 ac3) in a3 = 2aae + 2 aec + e.
+2a + 4 aue + 6av + 30, in (a = e in a - ace =) a aec- a e. + act. 5
+ 3a  = 6a  + 6ae + 3a
22 + 440 + 6a ee = 3 c
3a103 - 6a e -6aue - 3ac
24 ee = 40e3 - 64 - 3 at e
= 22 C3 - 445 - 64 c = 3 a e
+ 2003 + 4 0e5 + 6aac2 + 3ac
a = 2a + 44 = 4u’ee . . . . - 400 = 40e = 2a e = B
P = 2a in a = e (= 24 - 20 e ) in a + 2aue + 2 ace + c = 7
2ad = 4aee = 4a ec = 24 8
-24C - 400 - 4a e = 20 
= 24 + 40c + 4a’ee . . . . . . - 400 - 4 4tc - 2a 8 -
Eorum