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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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DC LTONI
 LLP. L2.
Comparatione.
De Inculorum cum Arcubus quibus insistunt
cemtillam aucribuit ipse cextus Fuctiais, PrOp. 33. lib. 6. Saltem si propoliionis
hujus excrema clansula non (ic Zheonis, duc alterius cujusdam AHumenCI. Sed
e Archimedi, PrOP. L. de Dimensione Cirbuli, VOx Louds (Sector) accribuieur
consprehenso. Nec video cur Archimeats cextum Collicitare debcamus. VE nOn
it de voce licigandum, Si laxiore sentus de quoris Frilineo uturpetur, quod dua
bus Rectis concinetur ec Arcu circuli (aliutre currae) live Concaro lire Con-
vexo; dummodo Paris conster quid qulo ea voce incellectum velic.
Circuli consticucus elt, (sire intra Cire eera Circulum,) nunc dicendum erit. Nec
Vod Sectorum Aneuli sunt proporcionales Areubus quibus insistant; sive
sint anguli ad Centrum, sive Aneuli ad Circumserentiam: Ouodque
Aneulus ad Centrum, est Duplus Anculi ad Circumferentiam, eidem
Idem aurem de trujulmodi Ansulo, qut hec ad Cencrum nec ad Circumterentiam
est, quod leiam, qui rem hanc considerandam (uscepit. Ouam itaque speculatio.
2. Si Circuli Diametro D F, accommo.
detur, ad centrum C, angulus B AD: AF-
cus incercepcus BD, elt angulo proporcio.
nalis. (Per 26, 27. T.l. 3. C 33 FI. 6, FU
cliais.) HIOc CH, AECUS InTErCEPTuS BD
est ea pars cotius Circumterencix; quae ett
Angulus A, quatuOr RectorUM. EF prO-
Pierea Angulus A, dici solet cocidem Gra-
duum, quoc est ArCUS BD.
3. Si BA D A Crura continencia talem
aneulum, post decussationem in C Factam,
angulum Vercicalem R Formancia, continu-
entur ad oppolicam Circumterencia partem.
ATCUS INtETCEDEUS G F aequalis erit (per
52) ipIIBD, (Propter angulum verricalem B, ipti A aequalem.) Pe, consequen-
ter, Arcuum illorum Aggresacum BD Y C F ett veriulris Duplum. HOc etb,
BD F GF
D
4. Si ad F Diametri extremum, Formecur similis AnguluS A: AECUS intErCePCUIS
HD, eAt duplus ipsius BD. HOC cs, HD =BD FGF = 2BD. Ouontam
(per 20 EL. 3,) Angulus in Centro est duplus Anguli in Circumterencia, cidem
arcui insistencie
Vel sic: Duoniam (per constructionem) PHI, GCB, sunc Parallela, (utvOrC
aequales ansulos ad F D Faciences:) Adeoque HB = PC = BD: EHt, conseguen.
ier, HID = HIB F BD =- F G ] BD = -2BD. Per 63
5. Si ad aliud quodris ejusdem Diametri punctum K, intra circulum, Formetur
similis angulus A, ejusque Vercicalis F: DuOTUM incercEptOrum Areuum aBBTC.
Sacum F L. F ND elt duplum iptius BD. HIOCest FF ] ND = FC + BD -
2BD. Nam (ducta recta AM) duo incerni anguli F N L F M FD, aequan-
TUE ExtCEnO MIKD = A =FIF 1
(qui elt angulus in Circumterencia:) Adeo.
que ArcuS iptis oppotici PJ. = MD, simul aequancur areui huie oppolico
HD = 2BD. Per 64
Veltic: Duoniam FHL LM TunE Parallelae (urpore aequales angulos ad FD
Facientes;) EreO L L. = HM, e YL + MD = LM f WD = HID = 2BD. per 64
srcui insistentis: Jam olim ab Fuctide demonstracum est; eltque ab omnibus re-
cepcum. Ec quamris Sectoris nomen, Famoliori Gigniticatu, de eis qui ad Cencrum
lune, pocissimum uturpetur; tamen illis icem qui ad Circumterenciam FuINE, Vo-
Frilinco, extra circulum posico, duabus rectis ee Conrexo Areu quibus insiltune
nem libet sequentibus aliguot propolicionibus ulcerius prolequi.