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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 13
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Theor.
23) Suttrahenda arcribuntur signis
mutatis, + in -, et - in +, seu
f- (a - b) - f- a + b.
d
b
Nam f- (a - b) = (per 20)b
= (per 18) f - a + b 2. E D.
Aliter: Sit a - b = e, ajo erse - e - - a+b
seu f- c = f - a + b. Nam + e - e =
+ a - b - a + b (per 1) Ergo ab aqua-
libus tollendo aequalia, illinc + e, hinc
+ a = b restabunt (per 12) aqualia
=e et - a + b 8. Fi. D.
AP DL ICATIO CALCVLI ADRE5
ubi de Toto, parte; majore, minore;
positivo et privatino
si subtractio vel signum = evanescat,
(24) Explic. Elesi explicando notas for-
mula per res ipras, verbi gratia per
loneas rectas, sibi addem dac vel subtrahendas; ex evants cat tandem subtractio vel signum-
ita
tratendes semper destruendo  id quod est signo
= affertum sucib. gr. - b) per aignalis
molis signo + affertum, (nempe +b); tandem nihil aliud
remaneat in formula vel
dis gaequiva-
lente re, exgr. Linea afertum signo+ : Tunc tota formula repdicitur designare
minativa seu nihilo minore Hoc eet,
talem, ut ad ipram, andenda sit ipsius
moles, quo fiat nihil. Nempe quia veluti Exempli ausa si esset + C +b b
(per 11)  a d a ad das
a fit0.
d
Aolium. Onrpiriantur figura duae, ubi
in priore progreesus tit per lineam reitam
 et huic in derectum adjeitam rectam in hac formula, pro fta, suct
fie
a regressus per puncta dessignatus absiestsormota
extremo adjertu a in eadem certa
totali +a fit per pertam , ita in
1Fetmut
recta fia remanet e adeoque est fa-b- te. Hinc patet quando duae quantitates
=g. significant
Setolium
Alc. 19, doem raetam 3, i q maitore ls)
+(quae quantit
formula
et hae litere op s sianisica rent quantitates posi
tivas, +ta = b, et esset f+ a = e + b
hae literae omnes forent quantitates positiuae
resluta explicatae per res nullum in ultima
resolutione deprehenderetur continere signum
patet f+a -b significare + e. Nam 
rest
resolutione smmlcunt remaneret sigsnum f. H
ta = d, et esset d=f+at
tunc f+a= d significabit - g. Nam pros
in formula f+ a ad. substit uendo valorem
fiet f+a = f- a =g, id est - q
signis contraris affectae conjunguntur
semper alterutrum signorum penitus
posse tolli per explicationem unius quam
fitatis, quatenus continet alteram quan-
titatem (vid. 11) Patet etiam
formula f+a- d fiat nihil, addi debere
seu esse f+ a
d + g= C
quia sta-d=
jam -9+g =0. vel  resolutione resumta faa
2
f+a-
g. ( Ergo 5
d Stanse