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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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Cap. XXI. A L G F B R A.
Geometrice autem conttruetur, sic. Fiac AB = B:
eique ad anoulos rectos Patuatur BC = = B. F.C du-
catur hyporenusa AC = Vu: B9 f = B9. Abscindatur
CD = BC. Frirque residuum AD = Vu: B9  a B9
Z P. Denique, MenTUTCtUIE AF = AD, PrO majore
Seomento.
Inrentio +2. C 2. Nempe, Comparatio basis obtusi an
culi, cum lateribus.
Esto triangulum BCD; cujus angutus incerior ad B, Sit obtuS. Hujus ba.
siS est DC; e latera BD, BC. Lsic (per 47 C +) BC9 = BA9 = C. AC
=DCq (=D A9 =) - BD9 = 2BD X BA = BA9: (Der 4 C 2, HaI DA est
BD F BA.) Ouare BCq F BD9 =DC9 = 2BD XBA.
(Nempe, extricis urinque aequalibus, ec cransposirione Facta.)
Ouod Theorema rerbis enunciatur, (IC: Qn amblyconis tri-
aneulis, quadratum subtendentis obtusum ansulum, excedit
summam quadratorum laterum, duplice rectaneulo sub uno
laterum circa obtusum ansulum, e seemento ipsius (continuati)
inter obtusum anculum e perpendiculum.
Inventio 13 C 2. Nempe, Comparatio basis acuti anguli, cum lateribus. Fsto
criansulum BC.D; cujus ansulus interior ad B Eic acurus. Flujus balis eAt C D:
_ latera BC, BD. TTICBC9BA 9 = C A g = DC 9 (- VF
F2BD x B A = B A 9 (nam D A =BD - = B A. ) Ouare BC 9 + BD9
=DCq F 2BD x B A. (Fodem modo procedet demonstratio, (I D PONALIIE
inser B et A; quippc jam D A = B A = B D, _ D A q, uE priu S.) In verbis, SC:
In trianculis obsiquaneulis (sire sine acutangula, sive obtulansula) quadratum
lateris subtendentis acurum aneulum, minus est quam summa quadratorum la-
eorum, duptice rectaneuto sub uno laterum circa acutum aneulum, e scemento
ipsius inter acurum illum aneulum e perpendiculum.
Fla dux propositiones tunt apud Fuclidem Theoremata, atque ut talia de
monstrantur. Elic autem proxonuntur ut Problemata: quo constet, quomocio ca
Pheoremata pocuiltent inveniri.
Inventio 14 C 2. Nempe, duadrati aequatis rectaneulo AB X BD. E. AO
AB F AD = 2BMI. Ouare BD sccatur aequalicer in M, et inaequaliter in A.
erit IBItUIE, Per 5 C 2, ABX AD = BMg = AM9. Jam SUPPONatIE AC9
ABX AD. Fiacque triangulum M AC, cujus hyporenusa C. MI-- BNI sC
misummae laterum. Cachetus erie AC latus quadraci quaesici, per 48 C F.
Complura habet ille exempla alia, (acute Patis expolita, in
varia materia,) quae apud illum quaerat Lector. Fgo unicum
adhuc axponam, quod est omnium ultimum; ubi, in unico
eroblemace, (Probl. 26.) brerem Cynoptin exhibet sectionum
meularium.
Numirum; De angulorum (inguie) sive peripheriarum bi
sectione, irilectione, quinquilectione, seprisectione, eec. Pauca
etiam, ad Analyrices praeltanriam, ulumque admirandum, ostendendum appo.
nat.
Distin.