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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 83v, page id 00068124:0166
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raenitus inn do halben product grfunde nesialis 195, andrison
summa 28 grgibus, sto bonum crerae die zochen selbst, nemulis
13 und 15 duois dac lenma 2 Lindus, uni as est dac problema
solvicet. Haben also altrio ein regol, daßt man aub grgrbenm sose
basi, und summ da bogdus seitus dat product dio salbus tiudus saitus
allereit pindus kian, ind gwear caenun obgrdachte 3t stuct in gangum
Und rational zasens gegibus, ob iit das product anis niuc ganga
 rationala hose, osun  surdo numero, raenum genis
die beydes gesuchten rin selbst brach n surdos habi soltn.
AB damit man in altus exempelus osac austos forthomum romma
ob mud man sondholris folgendat in acht nohmee. Meim dic eego gegebnnn
Regol lasort daßt man eini zohe non der andien abgirhi stll, und aber
dac babgrgogue werrdus vll ist grostro als datandvn, ist mus aran dat
signum- odeo minus wor dio different dir bengdus zosen sheribus. Und
verse differtaz mit dem signo= ist dab residuum. Weic nun mit
bersus numenis die dat signum - voo sis haben, in pro cedioens hanne
constructio problematis Geometris Geometria maxime naturalis, est
man unistu.
per Ellipsiu BFC, cujus axis major BC unus BC alter FE, BC est data basis t
at FC invenitur, si dimidium summae datae BA+ AC sonsumas, ut 14 lumas
et centris B et C radiis BF, CF 14 descrtbas arcus se secantes in F
et habebis punctum F. calculo habebis F si ex quadrato BF seu +4 ipsius 4
BA+ BC, detrnhas quadrulum B2 seu ipsius BC. Hoc ellipsis secabit
parallelam GH, ipsi BC parallelam, et intervallo datae AD dissitam
in punctis A et H itaque triangula ABC e. HBC satisfacient.
Hinc ale ad aliam poductionem Geometircam quaerendam exhiberi
videtur methodus aliqua, pro incognita querendo reltao EA, vel EH qua
es ambabus protlematis radicibus communis.
Retentis literis prioribus:
Nex da + dd aequ vV
+ bb + b Sxx - dd + XX = d d + dd) aequ vv
 XL
612
= b-
Ergo bb xx - bb dd aequ V + X V 2OVXX
a
et eodem modo 4 bb + b yy-dd + yy aequ vv
(4)
Ergo b sxx - dd  - b fyy da aequ yy - x X aequ. a y -(aX)
vv+y4bl
Ergo b a +yy -2ay - dd - b Syy-dd aequ ray - a a
e
ray -aa
t seu seu bsaa tyy -ray-dd aequ.
obrggt
aequray =aa +0v- 7y - bb
abb + b raa tyy - ray + dd F aat y fray + b syys - dd + +yy aequ. ()Bv.
(2ay(aa  vV F yy = 1b H 
 AH
H
9)
a
vHylHII
seu b syy-da aequ. vv - yy - = bb
Ergo bbyy - bbdd algo v- 2vVyy- : bb vv + y c bbyy + 1 14
os
eodem modo quadrando aequ. b.  et aa - ibb per compenda vocando-c. Fiit
pet aa - dd volando ee. fiet: 4
bb aa Y bb l1(2)
c
bbee +bbyy - 2abby ra. v 2vvyy+y - 2660D +2 Ccyy +gavvy- 4ay 4 gaayys dy +a
Aequationes  et i tollendo, habetur  9 et 12 jungent. tolletur ta ndemis, v
et habebitur v. t. sublata  habebitur aequatio in qua circus sola V
verum considerando. d altitudinem instar incognitae, tunc habebit
aequatio ultima secundum secundum V dabit aequationem dep licet
altam tamen extracibilem. quia ejus qua tuor radices seu valores ipsius
vel EH vel similiter infra BC sunt aequales. Unde ex aequi ultima extrahi
poterir radix quadrato quadratica, et ita deprimetur, licet alte assurger
videatur
aatay)