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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 27
# Folio 6v, page id 00068240:0012
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Dates Vli duobus lateribus etarea, invenire Dlum. serb
Dputgo tuta ABC BC, datur erem datut ergo et Yli atfitudo BCd) Ar sclae
quod
sit ex applicatione ipsius AB dimidie, ad aream datam
Constructio haec est, utique per facilis.
sit recta AB unum laterumdatorum. Centro B, rndio BC altero
Sigituatae inde dta AB
ad areum datum applicata. Areae datae aequale quadratum
D er quod transeat
AB
dabitur ac proinde et ejus quadrati latus
rectae n clige qua costituatur ipsi ad A ada angulos rectos
et per punctum D crauseat ipsi AB  parallelacin definita
quae circulum secabit in duobus ad summum punctis C vel
). junctisque AC, vel A(C) et BC vel B(C) ea
ABC vel AB(C) triangulum quaesitum.
quod si Recta DC crculum  non nisi in uno secet
erit
puncto, erit angulus Trianguli rectus. Si in nullo, problema erit
ABC
ampossibile, oportet ergo ut recta AD non sit major
quam  latus BC alioqui errim recta, et circulus se non
eadem sunt
ergonstratio constructionis manifesta est, nam primum latera AB, BC, sunt
secarent
cum datis E arequ quoque Triangulidt, seu ABC  et, ea est quae datarerat
nam nam eeris duplicus fscilet BA ditu quadinto ab E aequale est posueramus
ex constructione
constructione
duplum areae Trianguli ABC, aequatur rectangulo BAD, et rectangulum
rectangm tum
BAD aequatur quadrato ab E quia AB, E, AD continue proportictales ex constructione.
autem, et
datonguli ABC aequatur dato quadrato  ab E,, ac proinde area
ipsa triantuli ABC datae quantitati; semiquadrato scilicet ab E, aequalis facta erit,
E. F
C
dacimom laterum AB, BC.
Dati numeri Minimum invenire multiplicem; per quem alius datus numerus divisus
17b
v
d a unde vbd + yba p, ca, sive V,
relinquat unitatem
e
b
ca
vo
93b7
Ergo
bea
bd+ba
ese
dta
22C.
22 ca - a
7b.y
ca. Ergo ac be
bd +ba
22c22 + a- -. unde ca, Cid 2hy XC
1y
JiX) Ponne 22Cp 21 e + 1a, fiet: 21ea fa- a
3bV
adeoque 210a  id 7b V. et y21ea
17b
2
36y
C
Haec quaestio  p se se met ut ia dicam solvit, nami a dato numero dividendo aufera
tur unitas; residum numerus e dividatur per datum 7b, id enim fieri possen ecesse est
es
ut problema in integiis solvi queat. productius numer nea  yX dividatur
per maximum sirum divisorem q ipsomet tamen mero dato io producto mi
 phumero pro ipsomet numero dato proxime minorem Et quoticns ductus in dutum Jea
l
Satim autem agnosci potest
ductus in datum 7b. erit multiplex minimus quaesitus.
an problenti sit prossibile nam si numerus datus dividendus r C per alterum datum b
non potest vividi ut relinquatur unitas, nec per multiptiiem ejus dividipolent
b