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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 250, page id 175905688X:0272
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D
250
F R ANCTSCF a SCHOOFF V
ctum in recta AB, per quod quae sica linea C. P crantire debet,
calculus occurrat nullo ancecedentium brerior, licet constructio
Eic valde breris. Oporiet enim tantum in recta C. 6 surnere C. D,
aequalem C B, quae perpendicularis est ad AB; ex deinde ex
puncto D rectam ducere DF, parallelam ipst AG, atque aequa-
lem CT: habebitur que hac ratione punctum F, per quod quaest
ta linea C P erit ducenda.) Ouoniam autem in hoc exemplo
calculus multo estbrerior, si in recta AO quaeratur punctum P,
per quod linea quaelica C P eransire debet, quam li guaratur in
recta AB, atque etiam construetio allata ex illo Facilius porest
octendi: vilum tuit breriorem hic subjunsere, atque constructio-
nem ex eo paretacere.
EAto ergoC A ∞ b, A. F. vel L. C ∞C, CM vel AB DX, N A
vel BC ∞Y, AP ∞ V, _P C ∞S; Critque TOTa PH D V. L ).
Cujus quadracu P V. F V y. + y y Ei subtrahatur a quadratole.
etx PC ∞5s, relinquetur quadratum recte CMI ∞ 55 = vr
2vy -yy. Undecum C M (IE D X, d quadrarum ejus D NX:
CLIEN X ∞SS - VV = 2 vy - 7y.
Fodem modo. Cin triangulo rectansuloB C. L. d quadrato ex
L. C ∞cc auteratur quadratum rectae BC Drr, relinquetur qua
dracum rectae BL ∞CC -py: ad eoque ipla BL ∞ V CC - yy:
qua ab AB ∞ x sublata, restabit A L ∞ X - V CC - yy.
Jam vero, cum, propter Cunilia criansula GM C e G AL,
CM SIc ad NI C, hoc eH, b f y ad x, sICUEC A ad AL, hoc cAt,
bad x = V cc = p y: eric rectansulum sub extremis xequale re
ctangulo sub mediis, nimirum
DX + Xy - Y bbcc F 2 b607
letis uerobique bx, ordinataque aquatione:
b
Xy ∞ Ybbc6. F = bCCγ LcC ) = by3 - pt. Deindeut eranescat
Tionum radicale, ducatur veraque pars in se quadrare, atque ad
tollendum xx lubsiruatur ejus lOco ss - vv = 2 vy = py, fet
que aequatio (syy = vvy y = - vy3 - pt ∞ bbcc + = bc67,.
=2b73 =y . Ub: si verinque auteratur y +, e tac transposr
Lio uE quanticates in y3 ducta unaim ObLiReAME XquationIS PAT
tet
Dr.