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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
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P10)
N
c
Quod autem de Trianeulo jam dictum est, illud nempe fieurae ex infinitis Pa-
ralleloerammis constatae (sive inscriptae sive circumscriptae) aequale esse, jeu po.
tus eandem ficuram: intellicendum erit de quavis alia fieura plana; cum eadem
Tic In omnibus demonstrandi ratio. Nec quidem Planis solummodo, sed ex fieu
ris Solidis illud convenit: Si nempe. pre Paratelosrammis substituamus Prismata
(qua voce etiam Cxlindrulos comprehendi volo, auc etiam ejusmodi qualris figu-
ras uiter parassela plana similia sive rectisinoq sint sire cyprilinca sire multa,
aequabiliter Politas; ne lonsis verborum ambasibus utendum, HC.) Aique hoc
seriel loneo, ne quis genceps porgo emopllcationes et spectet ao  de
aliis tguis dicendu OCCUTFEE.
ec dD) R O D. rCL FF. allun clisslreu ci muen ruis
De Area Trianeuli.
Om Trianoulum constet ex infinitis sire lineis, sire Fat ACO-
sxammis, Arithimerice proxorcionalibus, a puncto MCHOatis et
ad basin CCMatIS, (ut patet ex jam dictS:) Frit Area Frianguli
aequalis Bali in Alcicudimis semillem ducta.
Flt enim nocissima apud Arichmetieos regula; Summam Arithmeticae proeressio
nis, sive omnium quotcunque terminorum aspreeatum, aequari aecresato extreme-
rum in semissem numeri terminorum ducto. Adeoque, S terminus minimus Tup.
Donaeur O, (PTOut hic Supponitur, cancundem enim raler punetum in paopit.
dine acque o Ciptra in numero;) idem erit excremorum aegregatum acque ipse
terminus maximus. Alcicudinem rerO FIBIITX, DEO nuMerO terminOrum in PrO-
greltione, substituo, hac de caula, Ouoniam cum nunierus terminorum suppOna
cur c, eric omnium consicudinum agerceatum = Bais, (quia Batis jam est ex.
CremOrUM RGBrEBatum.) Cum aurem cujullibet (linex vel parallelosrammi)
cralticies sive Alcicudo supponatur = Alcicudinis crianguli; in illam eota lon.
sicudinum summa ducenda est; adeoque = A in = B erie area. FRt aucem
∞Ax = B = Z AB. Adeo ut A (sigura alcitudo) non solum longicudinum
numerum, sed eundem in communem omnium altitudinem ductum, exhibeat
quae quidem communis alticudo ranco minor suxponenea est, quanto termini seu
Pongirudines Tunc plures.
Nocandum aucem est, Lhoc non solummodo in veris Frianeulis (rectilineis) va-
lere; sed e idem pariter evenire quamvis crura sint vel curvilinea, vel quomo-
docunque a recticudine distoria, modo rectae omnes basi paralbelae sint suis a verrice
distantiis proportionales, adeoque inter se Arithmetice proportionales. Ejulmodi
vero ticuram, cum sic Trianguli inttas, Lriansulum distorcurre, luvacum, aue
deformatum. licer appellare.
PROP.