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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. VTII. ANGULARLBUS.
Propotitionem sic Demonstro.
VM KL recta, sit rectae
aAB parallela quaeris (quip
pe parallelas omnes, cruribus
AX AZ interceptas, similiter
secabit A T recta,) eam sumo
quae per Z transit: adeoque, pro
KL, habeo XI, (punctis XB
coincidentibus:) quam in 8 ut-
canque secet a lrecta.
Tiem, pro M N (coincidenti.
Dus HZ) habeo Z n. Quae sit in
i similiter secta ac fuerat XL
.
ist E
In quacunque itaque ratione sit
Zn ad XL, in eadem erit Z.
ad Z8. Functis que Bi IZ, in
eadem erunt (propter communes
allitudines) triancula XBn
ZBI, ad XAI ZAG; item
XZn X XI, ad XZIXT8,
respective. Adeoque e XBR.
ZZn simul, hoc est Z BL, ad
X AI Z Z. L simul, BOC est Z A Z
Tiem ZBI X Ti simul, hoc est
ZBIZ, ad X A8 X T8 simul
hoc est X A T. Adeoque simili-
ter secatur triansulum X BZ. per
lineam (ex rectis compositam)
Bi Y, atque Z AZ. per AB L rectam. Sed e similiter sccatur idem Z BZ per
BY rectam, (propter communis Basis communem sectimem T.) Quod fieri non
potest nisi B L recia per i transeat, sitque Bi L una recta. Rectaisitur BI, sie di-
videns Zn ut rectam ZI diviserat R5, transit per 2.
Pariter de puncto D, sumpta OP in ea parallela quae per X transit (coinciden-
sibus OX:) Secetur X D inF, ut secta est XL in 8; at que juneantur DF FY.
Propter parallelas, tum C A XI, EUI CD XD; erunt, tum AZ. in I, tum
DZ in p, similiter sectae, atque CT. in Z.
Sunt ereotrianeulorum X A L Z A 8 ZZ I X Y8 altitudines, in eadem inter
seratione, ac alcitudines trianeulorum Z DD ZDE ZT. D Z LF: sed ex (propter
Bases XI X P similiter sectas in 8 e L) bases item habent in eadem inter se ra-
tione. Preo e triansula trianculis sunt inter se in eadem ratione. Adeoque Z A 8
XY8 simul, hoc est Z A T, in eadem ratione ad X AI ZZI simul, hoc est
XAZ; qua X DFX FF simul, BOC est XDEL, ad ZDD XZ P simul, hoc est
XDT. Pt propterea in eadem ratione secatur triansulum X AL. per  l rectam,
atque rriansulum XD Z. per lineam ( ex rectis compositam) DFT. Sed  Si
militer secatur idem XDT. per D T rectam. (Quod fieri non potest nisi DV
recta per F transeat, sitque DFL una recta.) Rectaieitur DF si dividens X P in
F, ut X I dividitur in 8, transit per X.
Ldemque de puncto P. eC. Similiter demonstrabitur.
D SCPE. 21. 1974.
soll. Nallis.