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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
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DE SECTTODEBUS PFOP.XXXV
Inde sequitur; Ouadrata Ordinatim applicatarum Rectangulis Dia-
metro intercepta e agoregato diametrorum trancrerla et intCrCCPLX
comprehensis, esse proportionalia. Sunt enim ubique ut + ad l.
Adeoque, Prout lonsins à rertice remoretur punctum applicatio.
nis, ita semper auxeri Ordinatim applicatas. Nempe quia sic tam d
quam t F a (diameter intercepta, et aggregatum tranlrerlae ex inter-
CeptX) augentur, adeoque e eorum rectangula, et propterca quadrata
Ordinatim applicatarum his rectangulis proportionalia, adeoque et
ipsae Ordinatim applicatae.
Et propterea; FIrverbolam ex earum linearum numero csse, quae A.
suram non claudunt; Cum Ordinatim axplicarx (a verrice inchoan-
d0) Derpetuo crescant, adeoque et crescat crurum diraricatio, qua
idcirco nunquam lunt deinceps coitura.
Ideoque C Fyperbolae diametrum quamlibet non nis in unico Ver-
ticis puncto cidem Eyperbola occurrere; Duoniam nempe crelcen-
tibus continuo Ordinatim applicatis Arverbola curra d dliametro ma-
sis continuo resiliat, nunquam ideo deinceps coitura. Vertices enim
Oppositi, quanquam in eadtem diametro, non tamen lunt in eadem
yperbola, sed in OppOtis.
PROP. XXXVI.
De recta Fsyperbolam contingente.
Ecta HEyperbolam continsens diametro produetae inter verticem
 ex CentrII OCCUrreT. Punctum rero concurlus sic inguiremus.
SuDDONAtuE TaNGENS A F OCCUIETeNS, in F, diametro FI A producta, eique Or.
dinatim applicata a FI. Supponatur etiam ubiris cidem diametro Ordinatim ap.
Plicata DO, cansenti Occurrens in T. Sitque A VertEX, C centrum.
Dicancur autem (ob commodiorem calculum) Ha =b, HI A = d, Aa = 1.
(ideoque Ha = + F d, HIC = 35 F a,) FIF =f, HID = a, (ideoque DF =f + a
DA = a = a, Da = 1 = d = a.)
Tum (quia proxier Hyperbolam, quadrata Ordinacim. applicatarum sunt rectan.
gulis AHa proporcionalia, ut modo ostentum cst) erit HI AX H a. D AXD2::
10g. D0g. hoc est, 1 a. + a. 14. + d + a = 1a = 2da:: B. 2d + d + a = 1at 2 da p
2d = 2
FF (propter similia criangula) HF. Ha:: DF. DT. hoc cll, f. B: : f F a.
= B = D T. ejusque quactracum
he = DT9
Tum