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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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C ap. L. XV.
In quinto casi
GBAD = (GHAKO =BAC =BRC =) DAE f BE.C -∞H.
DL K M = (∞SF Td =
Ergo EBAD = GL FM
In Sexto cali
OBAD = (BHAKO =RAC = BRC =) OAE + GK. C - BRC.
DL EN = (~SFF2 =
ErSO EBAD F GLEM
Ouod erat demonstrandum.
ettu Udode
AL.
Si autem jam supponatur, Planum hoc integrum circa AXem AC (continua.
cum) conrerti: tum punctum quodris in AFC sphaerica Superticie, e in F. AF
intinito plano cansente, similiter praestabit qualitum. Adeoque, qui anre fuit
locus ad Circumferentiam Circuli e Rectam Tansentem, jam tiet locus ad Super-
ficiem Spharicam e Planum Tansens.
Aliaque multa, ex eo tempore, tunt edita de Locis Geometricis; praelerrim in
ordine ad Aquationum Tolutiones Greometricas, carum que limires decerminandos:
Oux apud eos conspiciantur qui de Limitibus Squationum Scriplerunt.
Figo salrem duo subjungam, (alterum de Parabola, e de Hyperbola alterum,)
e ex urisque compoticum.
PR OBE E M A.
Data recta terminata FO, punctum S invenire (seu ralia quoslibet) unde in
daram (productam si opus) demissa perpendiculari S X (trianeulum faciente
Rd rectaneulum, rectarum FS, SR, summa vel differentiam aequet ipsam F0.
HOc cstu FO = FSLSR.
CONSTRVCFIO.
Esto F Focus parabolae, FO ejusdem ordinaca, A vertex: singula curra puncta
practant quaelicum. Nempe, s si S supra O, erit FO = PS + SR: si intra,
exIt FO =FS - SR.
DE M O NSPR A FIO
Ponatur enim. Parameter seu Lacus rectum I; erit
orso (ex natura Parabolae, ejusque FOci) AF =
HO = 3V. PONatIE FD (= = RS) ==a; EEDA (= PA
FFD = = I Fa) = e. FrIt erGO FR (=- D6) = V et
=V:  H = ab. Adeoque FS9 (= F R9 F SR9
=2 II = a I F aa: Ejusque radix FS = 3l = a. HIOC CAt,
FS = = I - a A sic S supra O; adeoque FS = SR
ZY = FO: velu AIS sIt intra O, FS = 31 L a
adeoque FS =SR = =l = FO. Priique Jocas ad
Parabolam.
Ouod si supponatur, cirea FO ut axem, convecti Planum: erie locus ad ju
persicrem solidi parabolici. Ouxe superticies, erit conrexa, quatenus ab ASO
(Tupra FO) describitur: Sed concara, quatenus ab OS (intra F O) deteribitur.
Idem comtinget facta convertione cirea axem AF: Nisi quod, cum, tota Cuper-
Ficies descripta, Futura sit Conrexa: FF PrO FO recta (in quam caclat perpendieu-
laris FR,) Substimendum sic FO planum, convertione rectae factam.
COROLL AR PV M.
Si contideretur FSR ue lemillis triansuli aequieruru verticet habentis :
Haec omnia criansula aequierura (sumpro S ubiris in superiori sesmento AO)
erunt
A L. _ F B R A.
AEC = ERC
AAF