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# Title: Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus (shelfmarks Leibn. Marg. 84:1, Stück 1; Leibn. Marg. 84:1)
# Folio 328, page id 826603459:0374
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ac
Elemensi quinti Fuclidis dectaratio.
22 Si sint quoteunq quancitates A, B, C, _C. aliaeque ipsis numero a
quales, a, B, 7, _C. quae binatim sumpia sint in eadem ratione, (pUCa
AB:: a. B, _ B. C:: β. y. _C.) es ex aequali in eadem ratione
erunt; Nempe A, C:: a. 7. Nam quia B
erie B X
AB
CC = BC-
F
deoque. A. C:: a. y. Ft similicer quorcunque fuerint verobi-
que quanticares. Habecur aurem hic exlemplum racionis com-
PolIEa; ut _ proP. Cequente.
23 Si sint ires quantitates A, B, C, _C. aliaeque ipsis numero aequa-
les a, B,73 quae binatim sumpiae sint in eadem ratione, sit antem perturba-
ea earum proportio; Cnempe A. B:: B. 7. e B. C: : a. B.)
e ex aequali in eadem ratione erunt. NempeA. C:: a. 7. Nam quia
B =
od
ce
XB
C B5 exic B, C
B
7B 7) adeoq A. C:: a. v
24 Si prima ad secundam, eandem habueritrarionem, quam tertia au
quartam; R. a:: B. B: quinta item ad secundam eandem habueritra-
tionem quam sexta ad quartam: C. a:: D. B. habebit etiam composi-
ia ex prima e quima ad secundam, eandem rationem quam terria cum
seaeta ad quariam. A + C. a :: B + D. B. NTam A
C
a B. Crit a
C
ae
1 +
c
adeoque A + C. a:: B F D. B. Vel GC, E opus, per lemmano
Arum; Si A. a:: B. B. _ C, -a:: D. B. CrIt (cum AB = aB.
cum CB = a D, ergo A6 F C6 = a B + a D, ideoque) A t
C. a:: B F D. C. FAque haec proxolicio, univertalis ad
PrOD. 2.
25 Si quauor maeniiudines proporrionales fuerint A F B. a +B
R. a (ticq; A F B omniu maxima, adeoq; _ a minima;) max
ima e minima reliquis duabus majores erunt. (A + B + a = at 6
R.) NNam per PrOP. 19. A + B. a+6(:: A. a):: B.6 adc0.
que, ex hyporties, B B. Ideoque A + a + BF A+ a F 6.
AIgue
CAP. 35