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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis (shelfmarks Leibn. Marg. 100:1/2, Stück 2; Leibn. Marg. 100:1/2)
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D, 
eest et
ce
Canri e la cies Focus) ale reto ausulo ABC, majores elle duobus
reCtis: TIMI AnEI MINOTES, (Der PTOP. X7.) Cadac ergo in lacus illud (BC
Dol
iplius productionem ex parre B. Prunt ergo aggregaca tam angulorum duorum
IA B ABD, quam (duorum angulorum) D AC ACD, aequalia dubbus le
etis, (per primam parrem hujus Lemmatis. ) Ideoque abjiciendo angulum com-
munem D A B, manebit angulus ABD aequalis duobus angulis BAC AC. V
Sune aurem duo ansuli ABD ABC, aequales duobus rectis (PEr PFOP. 13.
Ergo es ansulus ABC, cum duobus angulis B AC. ACB, aequabuntur duobus
rectis. Quod erat probandum.
3. Sine anguli (erianguli ABC) omnes acuci. DicO, AN-
sulos hujus criansuli aquales este duobus rectis.
Dmonstratio. Dermacur a Paa a perpendicularis AD in
latus BC (Per PFOP. T2.) Non cadet aurem illa in ucrumris
punctorum B C, (sic enim idem ansulus ellet et rectus e acu-
tus:) neque in iplam BC Polt ipsius productionem ex utraris
Parre; lic enim criansuli duo anguli majores essent duobus rectis,
nemve duo anguli ABD ADB, aut ACD ADC: Tum aucem minores duo-
DuS rectis, (per prop. T7.) Cadet ergo inter puncta B C. Sic autem duo an-
suti ABD BAD erunc recto aequales; item duo anguli ACD C AD aequa
les recto, (per primam partem hujus Lemmaris.) Ergo ansuli omnes crianguli
ABC aquantur duobus rectis. Quod erat probandum.
Etis Lemmatibus ira contirmatis: Dieo, lint duae rectae (in quas recta cadat) A B
C D; rectaque in has incidens P F, ipsalque secans in punctis P C. Sintque duo
anguli BE F OFTE minores duobus rectis; Fieri non porest quin vel corum
aler roctus erit ex reliquus acutns, vel ucerque aeucus, rel alier obtusus reliquu
que acucus: IPIae duae linex juxra cres hasce suppositiones ((eu calus) S prO-
ducancur in directum ad partes B D in intinicum, COnCUEreNE.
Demonstratio. L. Sic ansulus B F: C acucus e angulus DCP rectus. Suma
eur utriris in recta B E punctum G unde ducatur recta CFF perpendicularis
recta B F (ver PTOV. 12.) Oud vel coincider cum recta CD, vel cader ali
cubi inter puncta C. F, aut inter puncta P C, vel in puncto extra potito ex
DartC F.
Quarta aurem haec suxpolicia est impoltibilis. Secus enim sequeretur duos
angulos (II F. CF. EI (irianguli CHIF.) majores esse duotus rectis (Forer enim
GF. EL obculuS, pex PrOP. X3.) Quod ell impoltibile.
1
POOTUE ALUM CULHFU
fem; lineum CD, s proditeame in dicectum ex parce D, Acurrere rectae A B
juxta primam suppoticionem, manisestum cst.
Fuxca secundam vero supposicionem; impoltibile
elt uE recta CD occurrat rectae GFI. Si TecuS C.
nim, cadat in punctum s, eruneque duo anguli (eri-
anruli orimndi) nempe sCFI SHC aequales duo-
BuS reCtis; TunE aUTeM MInOreS, (DEF PTOP. L7.
Ouod est impossibile. Neque occurret (recta CD
rectae L C; (sequeretur enim necellario, duas rectas
comprehendere superticiem.) Necesle ett igitur ut
Occurrac rectae AB. (Ouippe cum C, D recta sC
criansulo inclusa, non potest in intinicum concinuari, quin alicubi criangulo
exeat.
sunia cerciam vero suppolicionem: Duplicerur (seu iverecur aux reperacur )
.