## 74.PROP. VIII. PROBLEMA.

Sint duæ quantitates datæ A, B, & ratio quæli-
libet data C ad D: oportet invenire aliam
quantitatem, ut ratio ejus ad A ſit multipli-

Sit primò ratio C ad D commen-
ſurabilis, ſitque inter C & D com-
munis menſura E; & quoties E continetur in D toties ſit
ratio F ad A ſubmultiplicata rationis B ad A; & quoties E
continetur in C toties ſit ratio G ad A multiplicata rationis
F ad A: dico G eſſe quantitatem illam quæſitam. ratio G ad
A eſt multiplicata rationis F ad A in ratione C ad E, & ra-
tio F ad A eſt multiplicata rationis B ad A in ratione E ad D; & igitur ex æqualitate, ratio G ad A eſt multiplicata rationis

### 74.1.

EDC # AFBG

Quod ſi ratio C ad D ſit incommenſurabilis, geometricam
hujus problematis praxim eſſe impoſſibilem mihi perſuadeo; approximatione tamen fieri poteſt, aſſumendo rationem com-
menſurabilem ejus loco, quæ quàm proximè ad illam acce-
dat.

Sit ſeries convergens, cujus primi
termini convergentes ſint A, B, ſe-
cundi C, D, tertii E, F; ſintque
ſecundi termini ita facti à primis, ut
ratio B majoris ad A minorem ſit
multiplicata rationis C ad A in ra-
tione data mojoris inæqualitatis M ad N, & ut ratio B ad
A ſit multiplicata rationis D ad A in ratione data majoris
inæqualitatis M ad O: ſintque tertii termini eodem modo
facti ex ſecundis quo ſecundi facti ſunt ex primis; atque ita
continuetur ſeries.

### 74.1.

## G # H # A # B
# N # I # K # C # D
M ## R # S # E # F
# O # T # V # X # Y
### L ## Z

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