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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)
# Folio 147, page id 851387705:0167
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ARTTHMEL
Cat. aIl.
-
L
Et 2SF = Z. X + Z F. Hoc est
(quia Z X = V q = A9, de Z = A F V;) 2SF
V9 - A9 Y V F. f AK. Adeoque Vg F FV
= A9 F 2SL = AF. ErgO (retolvendo aequatio.
nem) V: EF9 Y A9 AF + 2SF: = ZF =
Si aucem hiac methodo reperiatur V; Investinabicur P, proxolicionis prae-
cedencis, per pr. 48. (alia quidem torma, sed eodem ralore quo PrIUS. ) nEMpC
=EF F A F V: ZF 9. F A 9 = A H + 2SF:
60 Daris cermino maximo, communi excestu, de progrestionis TUMMa; V, C, S;
AatUT NUIETUS TErMIHOTUM. T. NTaM, PeF PrOP. 20. V = YF f P. = A. adeoque
2V = FF + Y = V + A = Z. E1BO, per DrOP. 45. 2S=YZ =EPV - F 4L
F T F. adeoque
+P Y = Y9. Er C retolvendo aequationem)
Y + : F FV: ; F 9. F V9 L VF - 2SF:
Nocandum aurem est, hujus aequationis (upoce ambisux) raclicem minorem
tunc conrenire, cum A major est quam Z L, (adeoque radicem universalem V: 3 F 9
_c. alticiendam ligno =;) majorem vero (adcoque f V: XC.) quoties A MINOF
elt quam ZL. Sin A = Z F; perinde erit uera elisatur; nam hoc calu rocum iIlud
quod noca radicalitacis acticitur, eraneleH.
67. Daris uildem; datur cerminus minimus A. Nam, per praecedenrem habetur
T. adeoque A Per PTOD. 20.
Vellic. Ouoniam (uc in PrOP. 65.) 2SF = V g = Ag f VF F. AB. TranL.
Donancur cermini (si sic V q F F V plus quam 2SF; quod cum concinsee, cum
A major elt quam F;) ad hianc TOrmam, A9 - A F. = V 9 + F. V - eSF: Cu-
jus aequationis radix clt sC f Y: F 9 + V g + E V = 25B: = A. Vet (A sC
V9 + E. V minus quam 28F: quod cum concinset, cum a minor eAt quam F;)
cransponantur ad hanc FOrmam, E A = A g = 2SF - V 9 F.V; cujuS a qua
tionis radix est ambigua, nempe : R + V: + F. 9 F V 9 F P, V - 2SC: = A. qua
rum raclicum major convenit quocies A major quam ZF; minor aucem quocies A
minor elt quam : F. Si aucem sic Vg F L. V = 2SF, maniteltum est (utroris
modo disponancur termini) A g _F A = 0, adeogue A = F.
Si aurem hac methodo repertacur a; inveltisabicur T, propoticionis praeceden.
HiS, Der PrOP. 48. Nempe Y =
V + EF. = V: sFg F Vq F FV = 25F. Ubi non
remere factum, quod cum Forma Superius cractica, sueric F, jam sit L. Nam quo
calir in illa Formâ cligenda erac radtix major, in hac minor eligenda cxic.
Acque hactenus Proprectionis Arihmerica cradicionem lacis videamur absol-
visse; cujus breviorem lynoptin capice sequence exhibebimus.
Nocandum autem est, propoliciones omnes hoc capice de Progrectione Arichme.
metica traditas, polte irem ad Progrectionem Geometricam (mutacis mucandis) non
ditticulter accommodari. Nempe substicuris tere illie Mulciplicatione ee Diri
tione pro hic imperatis additione de Subductione; item porestatum Constructione
Se Analysi, pro Musciplicatione de Diritione; et denique Rectangulorum agore.
Sato pro Duplo Cummae; (cum paucis inCuper aliis immutationibus:) Ouod ex
compararis hiscum prihioribus cocidem proposicionibus: Cap. XXXIII. (eodem
Oce lo) videre cA.
C A P. X
Proeressionis Arithmeticae brevior Synopsto.
IVM in praecedente Capire doctrinam Progrectionis Rrichmericae tulius prose-
scuci simus: libet hoc Capice selectas aliquoc propositiones, prosrestionet
continuam spectances, alio ordine summarim cractete, i utto guats Milurcu oculo
subsieiantur. Becencis iisdem quibus tupra Symibolis usi sumus.
LAC0.