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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 38, page id 1066518432:0066
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38 DE VPETBUS EX MOTIBUS CORPORUM. LIB. I.
S CH O L F O N.
88. Ouanquam hoc lemma simplicitate sua nullius ulus prima
tronte rideatur, in eo tamen omnes quadraturarum methodi Fun-
dantur, quod prolixius quidem ostendi posset tam in antiquorum
mechodis quam recentiorum; sed breritatis gratia id eantum in ulu
Calculi integralis uno alteroque exemplo illustrabitur. Calculus in-
cegralis vel lummatorius cst invertus calculi differentialis, et con-
siltit in co, ut inveniatur quantitas A ex indecerminata quadam et
constantibus composita, ejus indolis, ut, si loco indeterminatae in
ea substituantur luccessire eadem indeterminata, sed clemento suo
simplici, ejusre 2p10, 3p10, 4pl0, 5plo ec. mulctata inde ex-
Tursant quantitates B, C, D, L ec. Quarum difterencix A =B,
B -C, C =D, D - F, eC. sint ejusdem forma cum elemento Peu
quantitate intinitesima summanda, ita ut prima differentia A = B,
exhibeat iplam quantitatem differentialem, cujus summa seu inte-
Srale quarItuT. VF Si curra quaedam sit quadranda, cujus axis dica-
tur X, ec ordinatx ad hunc axem y, ita ut arex elementum Futu-
rum sIc ydx. Area ipla invenietur, si haberi postit, quaedam quanti-
tas A ex indeterminata a ex quantitatibus datis leu constantibus
compolita, itaque comparata, uc, si in ea substituantur loco indeter-
minatx x, alix ∞ = dX, ∞ = 2d∞, X = 2d∞, ∞ = 4dX _ SIC dCInCCPS
in infinicum, inde proveniant magnitudines B, C, D, F, eC. Qua-
rum prima differentia A - B det ida, secunda B -C det secundum
elementum arexe ida in quo ordinata y jam relpondeatnon azi xe sed
axi x -da, suo scilicet elemento da imminuto, atque sic de reli-
quis respectire. Hlac enim ratione perspicuum cA, Omnes A =B,
B =C, C -D ecc. exhibere asgresacum omnium yda, gux in arca
continentur, seu hanc aream ipsam; jam si in serie quantitatum de-
crescentium A, B, C, D, F ec. minima dicatur MI, area quX-
SITa, juxta Lemma (5. 87.) perpetuo crit A =M, e SI ContingaE, UE
aliquando MI sit O, tunc area aequatur ipsi A. Minima vero quan-
titas M semper habebitur ex Maxima A, S scilicet loco indetermi-
natae a Substicuatur in ca x -nda, ubi n eR numerus elementorum,
in gux axis dirisus est, adeo ut ndi FIE =_, vel quod eodem re-
cidie, si loco x ibi substituatur o, quandoquidem a -ndx est 0;
quantitasque ex hac subsicutione resulrans erie minima M. Vnde
sI CCHEIAE DE Facta Subsitutione ipsius o leco indeterminate n in
quantitate A, haec eranelcat, tunc M erit =O, atque adeo area
Quae