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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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A L G F B R A.
Ec similiter DF = BF L BD = fe Fd; (quod eodem plane modo intellixendum
et, ue de CF. jam dictum est.) Pieri aurem porest, ut calus alter de C Con
ringas alter de D: Duta, Si C lic dexerortum d B, e D Cinistrortum; (vel con-
Era.) Ouippe tuM CxiF C F = BF BC =fC -C: _EDF =BF + BD = fe 1
Oux omnia, pro situ punctorum B, C, D, ipso starim intmicu determinentur.
3. Ouantuim ad CM e DH: Id quidem incertum est (donec AnalySi id con-
ACC) an Futurum SIE CM =CF L FM, an CF -R M: (de Similiter de DN.)
Duoniam, licet ordo lirerarum A, F, MC, N inter sc; decerminatur ex ordinc
literarum A, F, G, FI; camen, an prorlum, an recrortum, sumendus (IL; non Con-
Etac, priusquam conster an A sic ulera vel citra punctum E; (urrumris enim
contingere porest, pro rariis rationibus assignaris, etiam eodem manente puncto F.)
Constat autem verum NI eE YI sinc ad caldem utraque, an ad ContrariaS PaTIES
Fis. 22. Licebit isitur, pro arbitrio, ponere (verbi Gratia) C M = C F f F M vel = CF
=EMI; (ee deinde DM, vel eodem, vel concrario signo, prouc Fuerint tum
CM, cum D N, vel utraque ad casdem, vel utraque ad contrarias partes iptuS F;
vel illa quidem ad contrarias, haec ad easdem; vel contra.) Nihil aucem hinc
obreniet incommodi: quippe id Solum Aec (A Concrario SIgnO quam ReVeTA SIF
supponatur,) quod, pro Ja, proveniet verobique -a. Semper utique hac
proveniet xquatio,
16=kd
In qua xquatione, A Fractionis Numerator de Denominator Fat vel uterque
altirmativus, vel uTErqUE neSATIVUS, exIE e quancicas atturmacira: tun tuerit eorum
altirmatirus alter, alier negatirus, erit e quantias neratira; et propterea litu lup-
poticioni contrario lumenda: Pura, SI F Supponatur in BF supra B A, contineet
rerera in ejus continuatione intra BA: d COntrA.
In Figuris 6,7,8, 9, 20, LF, +2 (exreris manentibus) F A varium sicum ob.
tinet. Nempe, P18. 6. cacit extra H; F18. 7, 8. inter L _ B; (illic post, tic
ante, incersectiones rectarum C G, DH;) L19. 9, inter B et C. Fi8. 10. inter C
e D. Fis. II. ultra D. Fig. 12. plures casus extibencur. Reliquis Figuris, alii
Tubinde calus exhibentur.
Intersectiones rectarum C G, DF, expositarum, antequam ad quaesiram quintam
perveniane, indicancur ex alio ordine punetorum A, F, C, FI, quam est puncto.
rum A, B, C, D. Ouod ipso Schemacum incuicu manilestum eAt.
Idem Problema alias constructum.
Fixpolitis, in eodem Plano (+ 2. LZ.) Gualuor Rectis; BA, de (huic in B, C, D
OCCUEEenteS) B P, C G, DHI; potitione dacis: Ouaeritur Ouinta, ut F AGH, qua
expolicas in P, A, C, H, ira secet uc Incersesmenta sine in ratione daca; pura,
AF, AC, AFI, in racione I, m, n
Constructio.
Cap. CV.
terlermentis; guorum ratid d bido lupponuntur dari. Unde ducancur fF355)BB
ipsi B a Parallelae, expolris AF, A Ci, AFI, occurrenres in f, e, B
Ouxe quidem puncta si tuerine in eadem recta; habetur qualitum. Ouippe
hujus recta sexmenca, erunt (propter parallelas) suis respectire alcirudinibus, hoc
est, iplarum parallelarum diltanciis, proporcionales; adeoque in ratione data.
In recta intinica (quae expoticam A B ucunque secet; puca in ay) sumancur,
af, ae. ah, in eadem ratione, et col one, cum ipts AF, AC, AtG in
E. 13. Si vero non tuerine ipta s, P, B, in una cademque recta, Talem erumc Bs, C
habebune incerlegmentis As, AC, AFI, provocconao. Quo calu
Sungantur f8, fh, secances iptam B A In y, 8; quae   CallCH la.
Acque in eadem secentur (respectire) BC, BD, I F, 4. Luta, uc F A, ad AC
DB, ipsis BF, CC, DI proporcionales: quipve tum hae, cum illa alticdines
tione (ab ipla AB) secta cru qua CCa LC l LC) I A.
Ocinde
sic F2 ad 28, e BF ad FC: et ut F A ad ALL, SC f d ad. d h, et Ba ad AD