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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)
# Folio 579, page id 851708439:0603
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Cap. 1L.
AN G U L A R LBUS.
B, B, duo Crura. Manifestum elt, quod duorum An-
Sulorum d Diametro hac ad Balin Factorum (quo-
rum alter est alterius Reliduum ad duos Rectos,
AlEeF FaNEO ExCedit quanto alter Deticit d Recto.
Adeoque Ouadracum Cruris unius, puta Bq; tanto
Fxcectie, quanco Ouadratum alterius, puta B9, de
ficit a D9 L C9. FE Propterea, duo Limul, B9 ]
B9 = 2 D 9 + 2 C9.
T4. FVSO; Fisdem manentibus, Base e Diame-
tro Trraneuli, utcunque varie inclinatis: Idem ma-
net Recrecatum Duadratorum Crurum.
25. Idem incellisendum est, de Quadratis Fansentium Parabolae, FTyperbola
Fllipseos, (aliusre Currae Diamerrum et Ordinatas habentis,) ab Ordinatae cuju-
vis duobus Putremis, ad punctum Diametri (productae ( OpuS) in que occur-
runt Tancentes illae.
26. Idem limiliter accommodabitur Segmentis (talium Crurum leu Fangenti-
um) abscissis recta Basi parallela. Nimirum, Quadrata talium Seementorum
(Parallelis ulis IntCTCEPEOTuM) simul sumpta (eodem manente Fraperii AXC)
tantundem sunt: Ere crecta sinc illa Frapezia, live urcunque Inclinata. Nam ta-
lia Segmenca sune Poris suis Proporrionalia.
C A P. VI
Praecedentium Aplicatio ad partieulares Casus:
E. (IF Angulus A sic Rectus, seu praduum 90: C, F, coincidun; d 1 = 0.
DAdcoque = CD = 0. FL consequenter (per 57. Capiris praecedentis)
B9 = (C9 + D9+ = CD =) C9 + D9.
2. Si A = 220 grad. Fric V (angulus cruribus G, F, COnteNMIS) =60 gr.
Cut qui semper ct is quo disterune 2 A, a duobus rectis.) Et consequenter
EFu criansulum Aiquilacerum (nam e tales crune anguli ad batiu, quorum
uterris cst Reliduus ipsius A ad duos Rectos.) Rt PFOPTCrCA I = G. EF
B9 = C9 + D9 F CD.
3. Si A = 60 gr. Frit ilem V = 60 Br. FL p. = C. (NL prius.) Adeoque
B9 = C9 F D9- CD.
4. Si A = 135. Erit V = 90. Adeoque (per 5 F.) ug = C 9 = F9 hoc est
(prOPTCT ( = E,) _9 = 2CF9, et H = C V2. Adeoque B9 = C9 F D9FCDN2.
5. Si A = 45. Eric ilem V = 00. Adeoque (ut prius) H. = G. V 2. FG con.
sequenter, B9 = C.4 +D4 - CDV 2.
6. Si A = 150 (Tum V = +20. Adeoque (Per S2.) _9 = C9. f F9. F CF:
Zhoc ct (PrOPIET C = C,) _ 4 = 3C9; _ N = CV 3. EF
7. Si A = 30 (B9 = C9 + D9= CDV3.
8. Si A = 257Z (Tum V = 135. Et R =CV: 2 F V2: (Der 6 4.) ErBO
d. Si A = 2257B9 = C4 + DgLCDY: 2 +. 12.
20. Si A = 12235 Tum V = 45. EC P = G V: 2 = Y2: (Per 85.) ErGO
F2. Si A = 67 : B4 = C4. F D4LCDV: 2 =Y2.
Dddd2