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# Title: Leibniz-Handschriften zur Philosophie LH 4, 5, 10
# Folio 49r, page id 00069349:0097
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Propositio dd
clucenda in+ f- C
A70 (generaliter) esse 0 aequ. + bc
Demonstratio:
Ponatur d’aequ: t e + X. posito b aqu. X. et c exretente excessu
iporus d supra x seu suprab. erqoid.  idem erit quod
+ e F x = b,
-b in f - C
Ergotd- b in f- c idem erit quod te + X
jam te intf - c est ref - cc. et 1 - b
C
in +f- c si posito scit. hic X aequ. b) est aqut
 - cX
bf + bc. perprop. a. Ergo duo producta in unum colligendo,
Ergo colligendo + e + L - b in +f - C. Seurd- b in + f = C erit
ef - ce, +fx - c. x - b f + b c. At supratd - bih
intf.c, erat aequ. + d f - Cd - bf. C. Ergo hos duos valores
aequando et tollendo utrobique, - b f. fiet:
ef- ce + fX - Cx + bc aequ. df - cd. O.
quia d aegu. e+ X
Est autem te(+ SX aequtaf et = ce - c x aegu. = c diqua 000g
priori
ergotef- Ce + fx - cX aequ. el f - cd. Ergost un aequatione prio
tef - ce + fx -C X + bc aqu + a f- cd. e. tollantuur.
utrinque aequalia restabit  aequ. +
Quod erat demonstrandum.
b c
Benaldinus aliique qui calculi regulas demonstrare voluere, usi sunt propositionit Euclidis quod rec lib. 2.
Scholion,
Elementorum ad probundum quod  in  facit +. Unde Mariotus in sperimine Logico, negat eas propo–
sitiones, per caculum probari posse, fieri enim circulum. Sed quoniam hinc sequeretur vulgarissimas Arithmeticae
eri
operationes (ex quibus est ista operatio per + et -) pendee a propositionibus geometricis et linearum ducte quod
minimi rationi consentaneum est. hinc modum quaesivi demonstrandi hanc exprationem qogulam quod
in = facit + per purum calculum, quem vel in numeris vel in lineis interpretariicet. idque mihi (avale
rius quolque optasse videtur uando hujus algorith,ni demonstrationem desiderabat. Nam lincaresdemoustra
bionem ciold algebrista, ut Bombellum aliois extare nos poterat ignorare.