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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 323, page id 175905688X:0345
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# Lines: 55 recognised, mean confidence 0.85
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Toblem
IIE Pop
ectiomm
Conieare
esivemm
Drebiend
tud
enei tui
em re
nOn po
maequili
dur
ean
e
COMMEATARIS EN LioKuM IIL.
323
Geometrix Mechodum requirere, ur, licerxe, quae in priori aequa
tione prounitare est accepta, quadratum reperiatur in ultimo
termino; in polteriori rero aequatione, ut literae, quae prounita-
te in termino ZZ est accepta, quadratum reperiatur in termino z
ac ejus cubus in termino ultiimo. Ftenim s habeatur aequatio
23 ∞ X bb2. c3, ac illius loco alia delidererur, cujus penuleimus
terminus habeata, ac ultimus aa: Fiat ut a ad b, sic b ad quartam,
qua roceturp: eritque ap D bb; Rursus, tiatut a 4 2d0c, (IcC2d
quartam, quae sicq; live etiam (quod eodem redit) ut a ad6, siCC
ad EOrtIAMI, guX VocetuFd; ac denuo uE a dd d, (ICC 2dg: eritque
Aag. ∞c3. UInde pro 23 ∞ F. bb Z. c3 scribi poteric Z ∞ F a PZ. a a9.
Tire, lumendo a prounitate: 23 ∞ +. PZ. 9.
Nec aliter HE Si habeatUrZ + ∞ X bbZZ. 63Z. d+ SubstittO
enim ap in locum bb, _t aag in locum c: (UIE anEC), Faciendum eAt,
Ut a 2d d, (ic d ad quartam, quae roceture, crirque ae a di ideo-
que aace xd. UIbirursus, (i Fiac, ut a 2d e, ita e ad cerriam, quX
roceturr, critar vee, ac proinde a3r ∞ d. Ica ut pro Requatione
propolitaZ +∞ X. bb2Z. C3Z. d+ reponi pOssIE Z + ∞ X a P Z Z.
a a 4Z. a3r, live, Cumendo a prO UnItaTC: = + ∞ 4. P Z Z.
q2. r. Ouod erat octendendum. Fadem est ratio aequationis
025. 97.
F quibus liquido constat, quanti si momenei in Geomerria
concipere unitatem, cum, praecer ejus urilitarem, primolibro
ostentam, non solum ejus beneticio aequationes 3 8 +, ut X 5
ee 6 dimensionum ita praeparentur, ut ha juxta unam e illae juxta
aliam regulam resolri queant; sed iplx etiam hoc pacto deligna-
txe ad numerosreterri, atque ad iplarum radices explicandas in-
Cerrire polsine, adeoque, quaenam inter Arichimeticam e CiCO-
metriam relatio ac conrenientia existat, cdoceant.
Deinde supponendo Parabolam F. AC jam descriptam esse.
es axem ejus esse ACDK L, latusque rectum a seu L.) Ubi li-
quet, quod, poltquam in aequatione resolvendâ quancitarem a leu
unitatem, uc proxime est explicarum, subrosarimus, camque
juxta regulam prolatere recto ParabolX F AC aum p LImUS, quo
Pacto Problemata omnia Solida unius ejuldemque Parabola opc
Tolri possint. Cum enim reduci semper queane ad xquationem
Erium aut quacuor dimensionum; superiorum formularum, de una.
eadem-
V