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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
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Cap. XXXV. B UCLIDIS DECLARATIO.
ad secundum, majorem racionem, quam rercia ad quaream. Nam si A + B a +
(hoc CA Z + 1, = = + 2,) erie quoque = = =. Vet sc; Si A + F + B.
A F B
a = C
Ei erie divideneo a f L = (2 = ) 2. per pr. 17
30. Si composita prima cum secunda, ad secundam, majorem rationem habeat,
quam composita tertia cum quarta, ad quartam; habebit; per conversionem ratio
nis, prima cum secunda ad primam mmorem rationem quam teiria cum quarcan
ad cerciam. Nam si 4 f.
L
adeoque diridendo (uE prOB. PracCd.)
= =; erie inverte (per pr. 26.) f = =, _ componendo (uE proP. 28.)
A F B a + 6
37. Si sint tres quantitates A, B, C; aliaeque ipsis numero aequales an 6, 7,
sit que major ratio prima priorum ad secundam, quam primae postertorum ad se-
cundam; item secundae priorum ad tertiam (Sire aqualis, tive) major quam se-
cunda posteriorum ad terciam; erit quoque ex aequalitate major ratio primae prio-
rum ad terciam, quam primae posteriorum ad terriam. Nam II  = C, d
eric  
B
A
C(= DC= =)=
= -. Vel SiC; Si A + F.
C =) =. DeC PF. 22.
B = 5 e = = -; exic ex aequali
32. Si sint tres quantitates A, B, C; aliaeque ipsis numero aequales a, 6, y. dit-
que major ratio prima priorum ad secundam, quam secundae posteriorum ad ter-
tium; item secunda priorum ad cerriam (sive requaliS, Tirc) major quam primae
posteriorum ad secundam: eric quoque ex aequalitare major ratio prima prirum
ad terciam, quam prima posteriorum ad cerciam. Nam SI
eric  X
A F F.
c-
B
BC =E) =
=
=) =, et E = C, eric ex aequalius
PrOD. 23. 1
F F.
33. Si sit major ratio rocius ad cocam, quam abiatas ad ablatam; et t  rett
quae ad reliquam major ratio quam rotius ad tocam. Nam S =
permucando (Der PF. 27.)
Vel lic; Ouoniam
LB. a +6
B B
a +6
que = = = -, erit quoque L + B -
A F F. F B, A F B, F.
+ 6
Cdt
6 et per convertionem rationis, (per
6, adeo que
F6 ( a +6  a + C) =
a +
+6
I. + B
+6
B
a =6
A F B
b
F(= --. Per pr. 19.)
Hoc elt
=7
;Si
+6
adeo-
Vel SC;
+B
19r
FxIt