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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 298v, page id 00067993:0598
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is Aequatio ergo nunc landem ita stabit:
ax + equa cubus.
n
Rgra, cubus
Ergo. (gXa cubus - peq racubus -. pa 7
hgo BGXa cubus
4x
cubus
Ergo R4 Xa cubus = aX. Ergo Xa = a 2X. Ergo X a = a  X
Unde alium errorem observo:
Ergo Xa = a+ Er go X = a quod est absurdum.
X. 2X 3X.  4X Ctc hoc locu non est  X. sid est ipse sector  ax, ut ex figura apparet.
Ergo 7
per Ba Ba ea
etc = aX. Ergo X EX 3i Nimirum minima a. sempe est unitas
2 cui et applicantur arcus, Ergo cum dicitur 2X. SH. e mellige taL. SdX
Jam ergo axt Zx 3aX +aX saX
per La 2a 3a +a 5a.
dabit ax. 4a X gax 16aX 2a X
Ergo a X IX L3XH X4X LYX= axpax in ipsa multylicatione
a 2a 3a 4a
1
ax AaX 9aX iSax E5 ax. Atqui a. 4a 9 a 16 a etc = . ( a Ergo ax +aF gax = B ax
imio quia nunc in X. ducendum a. unitas ut β respondeatit etiam tria axa.
N3.
habelinus (ax, it est Pa ea x seu a a X = aX.
Nunc ergo tandem prodit aequatio verissima
Bax - aX
ax+ AX - aX = a X versr in aequatio infallibilis nota veritatis, ets.
diendiam tangentis
novi nihil p detegat.
dimidiam
Ut arius in distantiam a centro pcirculi ductus producit dplum sectorem, ita ductus in distantiam tangentio
un
a centro suo producit dupu segmentum. Esto arcus X. distantia tangentis sea radius a., distantia tangentes Z
erit sector ax segmentum XZ. Iam secto ratio sectoris ad segnientum: aX
7
34
a.
Erpo Theorema eligans, ut est distantia anturi anu a tompenle, ad radium foeu destantiam centri coculi a tompite) 
Hinc illud etium patet si antimeti duae senes arithmetiae proportionales in se inverse ducantur productum
esse numeri terminorum cubum dimidium temn demto eorundem tertia parte. seu (ubi aumeroru parte
At quid si aritmetice puportionales inverse ducantr ut harmonice proportionales:
6
vel
4
6
61 62 6-3 6- 4 6-5
16
66
pa- ax
ea
10
28
3X8 9
a
Jan a 4a 9g
ita est segmentum arcus ejusdem ad sectorem.
16+
E  ees
ab una parte, esse numerum termundium auitum m ipsum,
Hinc apparet summae hammonicae summem Plarem
mio unita non ascabenda, sed subintelligendi, t ascribitur
sextam
. 2
4
5
 - 1.
4 _ 16 1 1- 1
ductam in numerum terminorum, demta supra dicto numero terminorum ducto in planum.
duoni sumimar blari  tatio haec: summ. darmoni nam term.  num term.  plan. comi. summ. harm. = plan. com
plan com.
Num term.  plar. com.
320 16 240 100 124 120
ductum in planum, quod est num erator commanisus ub altera parte esse summam harmonicam
Summa Trianus = sum. simpl brach. sum. Dlarus
122
6o 40 30 24
107
2
19
120