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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 158, page id 175905688X:0180
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258
FiK A N CZS CZ d SCHOOFEN
de, extracta radice, invenitur
a abb +2aacC = 2 bBCC = a + - b4 = c+ - . + cc d a
Fixtii-
bens quo pacto linea incoonitar ex cognitis a, b, 6, e ex ad arbi-
erium sumenda d, obcineri possit.
Caterum quoniam in Problemate, ad praecedentes Aquatio-
nes reducto, propter lineam d, qua hic modo major modo mi-
nor ad arbierium lumi porest, linex quoque x ee y inde majores ac
minores eradune, atque ob id Problema non determinatum exi-
sic, sed intinitas recipie solutiones: lubet _ alterum Problema,
quod omnino decerminatum est, atque in cujus solutione, ad y-
numquemque ex qualitis numeris inreltisandum, unam Aqua-
tionem cum aliâ compararimus, in medium afferre.
P R O B L E M A.
Arenire duos numeros, quorum summa mulcipli.
L cata per summam suorum quadratorum Faciar 7 E5:
ec differentia per difterentiam corundem quadratorum
F2ciat 99.
Supposito Problemate canquam jam Facto, pono promajori
numero qua lico x. L y, C Prominori x -y: critque lumma quae
litorum numerorum Dx, e corundem differentia ∞ 2 y.
Tam quia x L y e x - y in se ducti FaciunE X X + 2 x y L yy
_ X X = xy F py, quorum Cumma est : X X + py & ditterentia
xy: rectat UE =X X L 2y y multiplicata per 2 ∞, d 4 u y per 2 y.
vroducta 4x 3 f + X y y de B x y y linc dacis numeris 715 de 99
aqualia.
Ouocirca inventis duabus Aquationibus 4 X 3 L. + X yy ∞ 715
et Bx 7y ∞ 99, uc ex sis obtineatur uterque numerus incognitus
vecy comparounam Equationem cum alcera: mulciplicando pri-
mum utramque parrem prioris per 2, de FFB ∞ 3 F B X yy ∞ 1430,
ac deinde ex ea subrrahendo polteriorem B xyy ∞9), d reliri-
quitur Bx 3 ∞ 133T. In qua, siutrobique extrahatur radix Cubi-
Ca, habebitur 2 ∞ ∞ FF, 8 FCX ∞ 5=.
Postea ad inveniendum p diridatur Aiguatio polterior 8 ryy
∞ 99 per ja IAVeNEaM Z N ∞ II, de orietur Aquatio A y y ∞ 9.
InC
M
b
sibit
d
MeAt
subbt
Alte
HI G
PiDre
Aucci
Mlalum pIC
Ellal CBB
Hocct
Guiauti
led 1
quatulu
Subtale
denb 
Cacris.
Ubinor
Sic. cum
aical
Cdd; Gua I
Cdtaiun qu
IprodOnI
Biio aequip