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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 583, page id 851387705:0603
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poit
pode
d
in
 Mob ceta ala.
DOca; Dupli Dunidium, Friplum Friencis, Ouadrantis Ouadruplum; Selquial. F 18, 7, 8.
cerius Sublelquialcerum, ec. tancundem radent acque Ai quale.
Sequicur et 2 pujus BHPBF si racio A44 F, cum ejusdem reeiproca F. ad A.
CompOnatuT: prodibit raeio A P ad L. A, quae aequalitatis est
8cH0FYOM
F F AC quae praecedune Lemmaca, ex Racionum doclrina detumpra, huc cansenti-
LR mus, ob trequentem corum in sequentibus ulum.
Demonstrationes vero ita comparatxe lune (cum hie cum in sequencibus pallim,)
ut e Praxin Arichmetica quam Speciosam vocant, directe respiciant; et ad appo.
Tiras tiguras lineares (li cui id gratius videbitur) accommodeneur.
Exempli sracia. Ad propolicionem primam; perinde est line A e F. habeantur
pro Symbolis sire Speciebus Rrichmerieis; sire pro linearum adscriptarum, his no-
eis delignatarum, indiciis. Orroris enim modo procedit demonstratio, lire de LI.
neis, hire de iTeris.
Sic ad PsOP. 2. de 3 verinde luecedir demonllineio sire Tini an en Symibolu Rlich.
mecieae speciotia adeoque a quod ex harum, ipricem moscipsisatione oricus: five
desionet a Alcicudinem, e Balin, Paralleloorammi a. OuspDe Paralleloramma in
racione ex Balium et Alcuudinum racionibus compolita constip gorum est Adco.
que, ur Parallelogrammorum similium Laceribus, homologis reiaeseniet loseptis
tiones Componentes; ua Pacalseloerammis. iplisi COTuIVE Ai YIOeS CO.
DOlILX.
ArO
Sic ad. PCOB 4. Perinde cst, sire incellioamus quancitases AL, per eandem
mulciplicarasus eplaor A, n F. (mulciplicatione factas) in easem rariore extribere
cum ipsis A, B; sire Paralleloeramma r. A, r F, (Propen xgalss AIcirudines 2,)
esse ad inricem uc eorum Bales A, F.
Fesimitices ad Prop. 5. Sive dicamus quantitaces A ,  per au de r lipsit
SirC Paralleloramna
rA, rB, rC, (propter aequalem alcicudinem) Balibus proporcionasia; Sive eriam;
in similibus errangulis lacera A, B, C, etr Ar B, 5 Cn IB, eadem 188 nvicem esse
rarione: perinde elt.
tiem in Pcop. 6. Perinde cll tirc incelligamus A X F. = i A A: tive aequalia
dicamus Parallelosramma quorum Alcicudines suns uc A ad fis Beles vero his reci.
DFOCX, DemDC uE L. 2d A.
Id Tallem incerest; Duod demonstraciones, si lanquam Arhimeticx habeantur;
Gnivertaliores Tunc, _ de quocunque Ougncitatum senere pariter concludunt:
Si vero ad Lineas rel Paralselogranima speciarim respiciani; de sis solum directe
concludune, (idque ex ri Propolicionum varricularium de siis in blementis demon-
Stratarum: quales lune, Paralleloerammorum rationes componi ex rationibus
L
terum Flomoloeorum circa aequales ansulos; Paralleloeramma aequialta, esse ut
Bases: Paralleloeramma quorum Bases e Acirudines sunt reciproce proportiona.
les, esse Aiqualia, _c. ) de aliis vero, non nili accommodando ad alias quantira-
ces (putas Vires, Pondera, Velocirates, Dectiritaces, Bor ). caldem analogias guas
in Lineis vel Parallelosrammis, ézc. demonstratae tiieranE. 1G X
Fiso incerim, utur Demonstrationes hujusmodi, Drout Arichnetiea speoios
praxm directe respiciune, (adeoque unirersaliores existunt,) pociores exiltimem:
adeoque adseriptas tiguras, non nili unum aliquem ex multis catum, qui tub Uni
rerlati provolitione concinetur, (cui retiqui ramen, in aliis quanciracibus lunt
COnFOrmES,) exhibere: Si camen maline alii (quibus Demonstrationes Fineares
maxis atrideno) ue rationes omnes, in quibuleunque quanciraribus, ( guamquam
Lineis linc Hlererosencae) Lincis ureunque exhibeaneur; aque hinc ad ipsas de
quibus agicur quancitares transterantur, Ilis etiam lacistieri vellem. Idgue eo ma.
siS, ut quam incer se conjuncta sine ha binx demonstrandi mechodi, perspiciatur;
e quam tacili nesorio, demonstraciones Rationum Linsares, Lineis exuix, sim-
plicius simul et univertalius exhiberipollipl: 
au