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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 138, page id 175905688X:0160
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138
FL ORZMONDT DE BEAUNE
relinguetur = y  - = py y F = Pp. F r - 2
4y 2 ∞ 0. Ouare l E0-
cum mulciplicemus per 4yy, inveniemus y6 = 2 py 4 F p2
44 ∞0. Ouod demonstrare oportebat.
F 473.
Tam vero (I ponamus x + X = P x = - qX f r ∞0; Suppo-
nendo secunduI HaNCGCOMIELIAI ~ 2 = y X + = yy + = p.
∞O; etit X   = yy - = P∞ 2. ] yx. Vnde quadratum
Prioris partis xquale erir quadrato posterioris, hoc est, v+ L yy x2
F + y + -   p X  - f = pyy - = pp ∞ Y y X - - 9V -  24
4yy AC PeF
Conseguens, ∞+ - i yt. 1 p∞ :  = Byy-  = pp - qX- 24
+y200.
F qua SiFOllatur prima X + X L  p X 2 - q X - f  r ∞ O, remanebiE
p+ - =PYy + = PP - r. 99
ciplicetur per 4yy, InrenietuT p6 L 2 py + + p2
Ouod erat demonstrandum.
4+ 97 99∞0.
Non secus demonstrabuntur omnes reliqui casus secundum
utramlibecharum suppolicionum: nimirum, x = - y v. L = yy.
2P. 7, ~ 0, AUE, ve f y X  = yy. = p. =, ∞0, obterrando
tantum signa.  e, quemadmodum haec Geometria docet.
Cujus operationis ope in genere aequationes omnes, in quibus
radix incognita qor haber dimentiones, ad Formam, in hac Oeo-
metria propolicam, reduci posunE: nimirum,  L y. 2 p g4
 P
Vy.99∞0. ligna- e quxe praecipit, observando,
Sicut demonstrarimus. Ouohe, uc, Si dirisionis beneficio e qua-
tionem propolicam ad cam Formam reduCere POTTIIIUS, ita VE
post diritionem radix ejus y plures quam duas dimentiones non
admictat, ipsa per Geomerriam communem, juxta prxescripea
pasina 6 ec 7. hujus Ceometria inveniri postit. Oud inrenta,
mediantibus aequationibus x - y X -  L y2. = P. 2 ∞0, ec x L
yx. L =yy. =P. 2 000, Coblerrando signa -) e, ponenda
locis, ubi lunt omisa) invenietur quoque radix x; cujus locoin
altera requatione proradice uppolueramus y. AC rero LL aequatio
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