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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. C.t
A L G F B R A.
Deinde sumantur, ut as minus F y, ad AF; sic Bf ad BF, et C. 5 ad C. C, vel
DEI ad DFI. Juncta FG, rel FH, erir ipla F AG FI qualita. Ouippe, hoc
catum ipla sy puncta (quae alibi diverta cunc) coincident in eodem A puncto.
AF. AC. AHT (:: Z. m. 3) :: 2 F, 28, ah.
AF. AC: : aF. 28: : 7F. 78:: F B. FC.
AF. AH:: aF. ah:: dF. SH:: AB. AD.
OS =FY. AF::BF. BF:: C8. CC:: Db. DH
Scbolicim.
Ratio hujus operationis, haec est: Ouoniam, sumpro ubivis, in BF, puncto F:
sumi poterit (modo jam indicato) punctum sin CCm quo ducta recta fe, recta
AB Occurrens in y segmenta habebit y f, y 8, iptis AF, AG, proportionalia
Irem in DH Cumetur punctum h, quo ducta fh, rectae B A occurrens in 5
Segmenta Faciet Sf, sh, iplis AF, AHI, proportionalia. Id solum dec ad
Tolrendum Problema, uc ipta sy puneta coincidant: Ouod cum in unico puncto
contingat; illud sic porro inveltisabitur.
Nempe, vel sumpto alio quoris in BF puncto f, et huic respondentibus e, b:
unde nora eriam emergene v, s: Vel (quod eodem recidic) dirila recta BC IM F.
sicur diridenda erat f5 in y; e BD in a, sicur diridenda erat fh in d. (Ouod
tantundem est acque li intelligatur rectae BF punctum fin iplo B; quo catu
incelligenda erit sB, in CD.) Cum ixitur id quaratur, ut punctis AF vel s
coincidentibus, cranclear distancia illa ar seu Sy: C unique fuerie, Cumpro (in B F
puncto B, distantia AP; Cumpro vero puncto s, distancia Sy, minor quam AF.
(donec, puncto stranseresso punctum i. diltantia icerum continuo cxelcat,) can-
10 scilicet quanto punctum s’appropinquarerit puncto r; hoc est, quanto minor
est Sy quam AF, seu (quod potius dixerim) ry quam as: Sicque hOC DC.
crementum (quod mox probandum erit) proporcionale ipfi Bf rectae ; (Cou
quod idem elt, recta C5, vel Dh: quippe has invicem Proportionales elle, es
jam dictis Patis constat:) Frie, ut AS == Fy, ad AF; sic Bf ad BF. HIOC eAt:
si diltancia AF, proprer iplam Bf, minuatur quantuur clt A8 =Py; eranc(Cet
roca Ar (coincidencibus aF punctis) potito f in F; Cumpra scilicer BF ad Bf.
in ea ratione qua cA aP act AF =- sy, Tcu pocins LS = FY
(Dico aucem AS = P y Porius quam AF = Sy; ut perinde st Cire ica Cuma-
eur S, ut s crantiverir y, necne. Onanquam enim inde mutetur licus puncti. H:
nempe, si crantirerie exic P citra f; sin minus, ultra: Proportio camien Bf. a
BF utrobique manet, si dicamus aS = P y; non aurem A dICatuE AF - = 8 g.i s1SI
enim AS =F y minor sIC quam AP, erit f citra F; Si major, ulera; SI aqualiS,
coincident.)
Si vero comingae, COnra quam supponitur Py majorem eses qua a (adeo
que as -Fy quancitarem esse nesaciram, seu minorem quam nihil;) Indicio
hoc erir, non lumendum esse punctum F ad eas d B partes prouc erar suxposicum
(puca sursum rextus f;) Sed ad partes contrarias; Duca in fB deortum con.
einuata.
Ouod vero silceximus demonstrandum; nemipe, quod Occrementa AS L FY
sine ipsis BF rectis proportionalia; sc octenditur.
Sumantur in BF (F15. 14.) quodibet purcta s; de, in DH, coridem quXe F18. 14
illis correspondeant puncta h. Frunt (proprer sumiles sectiones rectaruum fh
adeoque adricdines proportionales) recta Dh iptis Bf proportionales. Sec Si
(propter similem ubique sectionem rectarum BD in a, de fh adeoque en in 8)
CrunE pbiane ex es ipsis BD, Bd proportionales. HTOC ot. DB F BC pE DM
op es pB L BC- AS (= SG) iptis BD, B a proportionales. FrgO. (di-
videndo) Be = D n e BC =AS, sire (mutatis signis) Dn = Be et Ad = Be
iildem BD, Ba proporcionales. Sunt aurem (ur modo demonttratum cst) nun
Dn cum BC 2deoque Dn - BC, ip(iS BF proportionales: FrBO e AS -- BC;
ideoque et as (quia B C) tune iptis Bf proporcionales.
M m m 3